From 8120f2bdf7163b61e4361b5f3e27901bf06b6193 Mon Sep 17 00:00:00 2001 From: Alexia Jolicoeur-Martineau Date: Tue, 7 Oct 2025 09:26:04 -0400 Subject: [PATCH] upload --- LICENSE | 21 + README.md | 147 + assets/TRM_fig.png | Bin 0 -> 354276 bytes assets/TRM_pseudocode.png | Bin 0 -> 266898 bytes config/arch/hrm.yaml | 24 + config/arch/transformers_baseline.yaml | 18 + config/arch/trm.yaml | 26 + config/arch/trm_hier6.yaml | 26 + config/arch/trm_singlez.yaml | 26 + config/cfg_pretrain.yaml | 42 + dataset/build_arc_dataset.py | 341 + dataset/build_maze_dataset.py | 140 + dataset/build_sudoku_dataset.py | 167 + dataset/common.py | 49 + evaluators/arc.py | 177 + .../combined/arc-agi_concept_challenges.json | 17863 ++++++++++++++++ .../combined/arc-agi_concept_solutions.json | 5384 +++++ .../arc-agi_evaluation2_challenges.json | 1 + .../arc-agi_evaluation2_solutions.json | 1 + .../arc-agi_evaluation_challenges.json | 1 + .../arc-agi_evaluation_solutions.json | 1 + .../arc-agi_training2_challenges.json | 1 + .../combined/arc-agi_training2_solutions.json | 1 + .../combined/arc-agi_training_challenges.json | 1 + .../combined/arc-agi_training_solutions.json | 1 + models/common.py | 32 + models/ema.py | 40 + models/layers.py | 169 + models/losses.py | 103 + models/recursive_reasoning/hrm.py | 294 + .../transformers_baseline.py | 342 + models/recursive_reasoning/trm.py | 297 + models/recursive_reasoning/trm_hier6.py | 323 + models/recursive_reasoning/trm_singlez.py | 294 + models/sparse_embedding.py | 132 + pretrain.py | 654 + puzzle_dataset.py | 250 + requirements.txt | 20 + utils/functions.py | 19 + 39 files changed, 27428 insertions(+) create mode 100644 LICENSE create mode 100644 README.md create mode 100644 assets/TRM_fig.png create mode 100644 assets/TRM_pseudocode.png create mode 100644 config/arch/hrm.yaml create mode 100644 config/arch/transformers_baseline.yaml create mode 100644 config/arch/trm.yaml create mode 100644 config/arch/trm_hier6.yaml create mode 100644 config/arch/trm_singlez.yaml create mode 100644 config/cfg_pretrain.yaml create mode 100644 dataset/build_arc_dataset.py create mode 100644 dataset/build_maze_dataset.py create mode 100644 dataset/build_sudoku_dataset.py create mode 100644 dataset/common.py create mode 100644 evaluators/arc.py create mode 100644 kaggle/combined/arc-agi_concept_challenges.json create mode 100644 kaggle/combined/arc-agi_concept_solutions.json create mode 100644 kaggle/combined/arc-agi_evaluation2_challenges.json create mode 100644 kaggle/combined/arc-agi_evaluation2_solutions.json create mode 100644 kaggle/combined/arc-agi_evaluation_challenges.json create mode 100644 kaggle/combined/arc-agi_evaluation_solutions.json create mode 100644 kaggle/combined/arc-agi_training2_challenges.json create mode 100644 kaggle/combined/arc-agi_training2_solutions.json create mode 100644 kaggle/combined/arc-agi_training_challenges.json create mode 100644 kaggle/combined/arc-agi_training_solutions.json create mode 100644 models/common.py create mode 100644 models/ema.py create mode 100644 models/layers.py create mode 100644 models/losses.py create mode 100644 models/recursive_reasoning/hrm.py create mode 100644 models/recursive_reasoning/transformers_baseline.py create mode 100644 models/recursive_reasoning/trm.py create mode 100644 models/recursive_reasoning/trm_hier6.py create mode 100644 models/recursive_reasoning/trm_singlez.py create mode 100644 models/sparse_embedding.py create mode 100644 pretrain.py create mode 100644 puzzle_dataset.py create mode 100644 requirements.txt create mode 100644 utils/functions.py diff --git a/LICENSE b/LICENSE new file mode 100644 index 0000000..654af60 --- /dev/null +++ b/LICENSE @@ -0,0 +1,21 @@ +MIT License + +Copyright (c) 2025. Samsung Electronics Co., Ltd. All Rights Reserved. + +Permission is hereby granted, free of charge, to any person obtaining a copy +of this software and associated documentation files (the "Software"), to deal +in the Software without restriction, including without limitation the rights +to use, copy, modify, merge, publish, distribute, sublicense, and/or sell +copies of the Software, and to permit persons to whom the Software is +furnished to do so, subject to the following conditions: + +The above copyright notice and this permission notice shall be included in all +copies or substantial portions of the Software. + +THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE +AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, +OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE +SOFTWARE. \ No newline at end of file diff --git a/README.md b/README.md new file mode 100644 index 0000000..11bc302 --- /dev/null +++ b/README.md @@ -0,0 +1,147 @@ +# Less is More: Recursive Reasoning with Tiny Networks + +This is the codebase for the paper: "Less is More: Recursive Reasoning with Tiny Networks" were we present a recursive reasoning approach that achieves amazing scores of 45% on ARC-AGI-1 and 8% on ARC-AGI-2 using a tiny 7M parameters neural network. + +[Paper](https://arxiv.org/abs/2510.04871) + +### How TRM works + +Tiny Recursion Model (TRM) recursively improves its predicted answer y with a tiny network. It starts with the embedded input question x and initial embedded answer y and latent z. For up to K improvements steps, it tries to improve its answer y. It does so by i) recursively updating n times its latent z given the question x, current answer y, and current latent z (recursive reasoning), and then ii) updating its answer y given the current answer y and current latent z. This recursive process allows the model to progressively improve its answer (potentially addressing any errors from its previous answer) in an extremely parameter-efficient manner while minimizing overfitting. + +

+TRM-Figure +

+ +### Requirements + +- Python 3.10 (or similar) +- Cuda 12.6.0 (or similar) + +```bash +pip install --upgrade pip wheel setuptools +pip install --pre --upgrade torch torchvision torchaudio --index-url https://download.pytorch.org/whl/nightly/cu126 # install torch based on your cuda version +pip install -r requirements.txt # install requirements +pip install --no-cache-dir --no-build-isolation adam-atan2 +wandb login YOUR-LOGIN # login if you want the logger to sync results to your Weights & Biases (https://wandb.ai/) +``` + +### Dataset Preparation + +```bash +# ARC-AGI-1 +python -m dataset.build_arc_dataset \ + --input-file-prefix kaggle/combined/arc-agi \ + --output-dir data/arc1concept-aug-1000 \ + --subsets training evaluation concept \ + --test-set-name evaluation + +# ARC-AGI-2 +python -m dataset.build_arc_dataset \ + --input-file-prefix kaggle/combined/arc-agi \ + --output-dir data/arc2concept-aug-1000 \ + --subsets training2 evaluation2 concept \ + --test-set-name evaluation2 + +## Note: You cannot train on both ARC-AGI-1 and ARC-AGI-2 and evaluate them both because ARC-AGI-2 training data contains some ARC-AGI-1 eval data + +# Sudoku-Extreme +python dataset/build_sudoku_dataset.py --output-dir data/sudoku-extreme-1k-aug-1000 --subsample-size 1000 --num-aug 1000 # 1000 examples, 1000 augments + +# Maze-Hard +python dataset/build_maze_dataset.py # 1000 examples, 8 augments +``` + +## Experiments + +### ARC-AGI (assuming 4 H-100 GPUs): + +```bash +run_name="pretrain_att_arc12concept_4" +torchrun --nproc-per-node 4 --rdzv_backend=c10d --rdzv_endpoint=localhost:0 --nnodes=1 pretrain.py \ +arch=trm \ +data_paths="[data/arc12concept-aug-1000]" \ +arch.L_layers=2 \ +arch.H_cycles=3 arch.L_cycles=4 \ ++run_name=${run_name} ema=True + +``` + +*Runtime:* ~3 days + +### Sudoku-Extreme (assuming 1 L40S GPU): + +```bash +run_name="pretrain_mlp_t_sudoku" +python pretrain.py \ +arch=trm \ +data_paths="[data/sudoku-extreme-1k-aug-1000]" \ +evaluators="[]" \ +epochs=50000 eval_interval=5000 \ +lr=1e-4 puzzle_emb_lr=1e-4 weight_decay=1.0 puzzle_emb_weight_decay=1.0 \ +arch.mlp_t=True arch.pos_encodings=none \ +arch.L_layers=2 \ +arch.H_cycles=3 arch.L_cycles=6 \ ++run_name=${run_name} ema=True + +run_name="pretrain_att_sudoku" +python pretrain.py \ +arch=trm \ +data_paths="[data/sudoku-extreme-1k-aug-1000]" \ +evaluators="[]" \ +epochs=50000 eval_interval=5000 \ +lr=1e-4 puzzle_emb_lr=1e-4 weight_decay=1.0 puzzle_emb_weight_decay=1.0 \ +arch.L_layers=2 \ +arch.H_cycles=3 arch.L_cycles=6 \ ++run_name=${run_name} ema=True +``` + +*Runtime:* < 36 hours + +### Maze-Hard (assuming 4 L40S GPUs): + +```bash +run_name="pretrain_att_maze30x30" +torchrun --nproc-per-node 4 --rdzv_backend=c10d --rdzv_endpoint=localhost:0 --nnodes=1 pretrain.py \ +arch=trm \ +data_paths="[data/maze-30x30-hard-1k]" \ +evaluators="[]" \ +epochs=50000 eval_interval=5000 \ +lr=1e-4 puzzle_emb_lr=1e-4 weight_decay=1.0 puzzle_emb_weight_decay=1.0 \ +arch.L_layers=2 \ +arch.H_cycles=3 arch.L_cycles=4 \ ++run_name=${run_name} ema=True +``` + +*Runtime:* < 24 hours + +## Reference + +If you find our work useful, please consider citing: + +```bibtex +@misc{jolicoeurmartineau2025tinyrecursionmodel, + title={Less is More: Recursive Reasoning with Tiny Networks}, + author={Alexia Jolicoeur-Martineau}, + year={2025}, + eprint={xxxxxxx}, + archivePrefix={arXiv}, + primaryClass={cs.AI}, + url={https://arxiv.org/abs/xxxxxxxxx}, +} +``` + +and the Hierarchical Reasoning Model (HRM): + +```bibtex +@misc{wang2025hierarchicalreasoningmodel, + title={Hierarchical Reasoning Model}, + author={Guan Wang and Jin Li and Yuhao Sun and Xing Chen and Changling Liu and Yue Wu and Meng Lu and Sen Song and Yasin Abbasi Yadkori}, + year={2025}, + eprint={2506.21734}, + archivePrefix={arXiv}, + primaryClass={cs.AI}, + url={https://arxiv.org/abs/2506.21734}, +} +``` + +This code is based on the Hierarchical Reasoning Model [code](https://github.com/sapientinc/HRM) and the Hierarchical Reasoning 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zX#~Cr1>Wr~*WUy2_{Oo)7s7^uYpT&q2IZQFa-M$lxlJHAai72I^|x(X*)Xq8aw|Bg zQ}Do(FAz+v9m;*)RL^xa6MyJ)5LdzvtMMNi88IqYkBT+`f89<@ zR4)&3!6lB*vK!}+m;N6}Z=ALH|9hG3Ho1K8{y^H`;NU}@YmffhcU=~KvxQ@&Er#3f zmoi5Azx`F`T18x*6J{HIe2B)buKu|9;roC41`q6SryUmne?J!IWIqfJeXQprx37de P89cQ|S`UkqEMNaGf@ 1 to handle multiple datasets + +ARCMaxGridSize = 30 +ARCAugmentRetriesFactor = 5 + +PuzzleIdSeparator = "|||" + + +@dataclass +class ARCPuzzle: + id: str + examples: List[Tuple[np.ndarray, np.ndarray]] + + +def arc_grid_to_np(grid: List[List[int]]): + arr = np.array(grid) + + # Shape check + assert arr.ndim == 2 + assert arr.shape[0] <= ARCMaxGridSize and arr.shape[1] <= ARCMaxGridSize + # Element check + assert np.all((arr >= 0) & (arr <= 9)) + return arr.astype(np.uint8) + + +def np_grid_to_seq_translational_augment(inp: np.ndarray, out: np.ndarray, do_translation: bool): + # PAD: 0, : 1, digits: 2 ... 11 + # Compute random top-left pad + if do_translation: + pad_r = np.random.randint(0, ARCMaxGridSize - max(inp.shape[0], out.shape[0]) + 1) + pad_c = np.random.randint(0, ARCMaxGridSize - max(inp.shape[1], out.shape[1]) + 1) + else: + pad_r = pad_c = 0 + + # Pad grid + result = [] + for grid in [inp, out]: + nrow, ncol = grid.shape + grid = np.pad(grid + 2, ((pad_r, ARCMaxGridSize - pad_r - nrow), (pad_c, ARCMaxGridSize - pad_c - ncol)), constant_values=0) + + # Add + eos_row, eos_col = pad_r + nrow, pad_c + ncol + if eos_row < ARCMaxGridSize: + grid[eos_row, pad_c:eos_col] = 1 + if eos_col < ARCMaxGridSize: + grid[pad_r:eos_row, eos_col] = 1 + + result.append(grid.flatten()) + + return result + + +def grid_hash(grid: np.ndarray): + assert grid.ndim == 2 + assert grid.dtype == np.uint8 + + buffer = [x.to_bytes(1, byteorder='big') for x in grid.shape] + buffer.append(grid.tobytes()) + + return hashlib.sha256(b"".join(buffer)).hexdigest() + + +def puzzle_hash(puzzle: dict): + # Hash the puzzle for checking equivalence + hashes = [] + for example_type, example in puzzle.items(): + for input, label in example.examples: + hashes.append(f"{grid_hash(input)}|{grid_hash(label)}") + + hashes.sort() + return hashlib.sha256("|".join(hashes).encode()).hexdigest() + + +def aug(name: str): + # Augment plan + trans_id = np.random.randint(0, 8) + mapping = np.concatenate([np.arange(0, 1, dtype=np.uint8), np.random.permutation(np.arange(1, 10, dtype=np.uint8))]) # Permute colors, Excluding "0" (black) + + name_with_aug_repr = f"{name}{PuzzleIdSeparator}t{trans_id}{PuzzleIdSeparator}{''.join(str(x) for x in mapping)}" + + def _map_grid(grid: np.ndarray): + return dihedral_transform(mapping[grid], trans_id) + + return name_with_aug_repr, _map_grid + + +def inverse_aug(name: str): + # Inverse the "aug" function + if PuzzleIdSeparator not in name: + return name, lambda x: x + + trans_id, perm = name.split(PuzzleIdSeparator)[-2:] + trans_id = int(trans_id[1:]) # Remove "t" letter + inv_perm = np.argsort(list(perm)).astype(np.uint8) + + def _map_grid(grid: np.ndarray): + return inv_perm[inverse_dihedral_transform(grid, trans_id)] + + return name.split(PuzzleIdSeparator)[0], _map_grid + + +def convert_single_arc_puzzle(results: dict, name: str, puzzle: dict, aug_count: int, dest_mapping: Dict[str, Tuple[str, str]]): + # Convert + dests = set(dest_mapping.values()) + converted = {dest: ARCPuzzle(name, []) for dest in dests} + for example_type, examples in puzzle.items(): + # Map to target split + dest = dest_mapping[example_type] + converted[dest].examples.extend([(arc_grid_to_np(example["input"]), arc_grid_to_np(example["output"])) for example in examples]) + + group = [converted] + + # Augment + if aug_count > 0: + hashes = {puzzle_hash(converted)} + + for _trial in range(ARCAugmentRetriesFactor * aug_count): + aug_name, _map_grid = aug(name) + + # Check duplicate + augmented = {dest: ARCPuzzle(aug_name, [(_map_grid(input), _map_grid(label)) for (input, label) in puzzle.examples]) for dest, puzzle in converted.items()} + h = puzzle_hash(augmented) + if h not in hashes: + hashes.add(h) + group.append(augmented) + + if len(group) >= aug_count + 1: + break + + if len(group) < aug_count + 1: + print (f"[Puzzle {name}] augmentation not full, only {len(group)}") + + # Append + for dest in dests: + # Convert the examples + dest_split, dest_set = dest + + results.setdefault(dest_split, {}) + results[dest_split].setdefault(dest_set, []) + results[dest_split][dest_set].append([converted[dest] for converted in group]) + + +def load_puzzles_arcagi(config: DataProcessConfig): + train_examples_dest = ("train", "all") + test_examples_map = { + config.test_set_name: [(1.0, ("test", "all"))], + config.test_set_name2: [(1.0, ("test", "all"))], + "_default": [(1.0, ("train", "all"))] + } + + test_puzzles = {} + results = {} + + total_puzzles = 0 + for subset_name in config.subsets: + # Load all puzzles in this subset + with open(f"{config.input_file_prefix}_{subset_name}_challenges.json", "r") as f: + puzzles = json.load(f) + + sols_filename = f"{config.input_file_prefix}_{subset_name}_solutions.json" + if os.path.isfile(sols_filename): + with open(sols_filename, "r") as f: + sols = json.load(f) + + for puzzle_id in puzzles.keys(): + for idx, sol_grid in enumerate(sols[puzzle_id]): + puzzles[puzzle_id]["test"][idx]["output"] = sol_grid + else: + # Fill with dummy + print (f"{subset_name} solutions not found, filling with dummy") + + for puzzle_id, puzzle in puzzles.items(): + for example in puzzle["test"]: + example.setdefault("output", [[0]]) + + # Shuffle puzzles + puzzles = list(puzzles.items()) + np.random.shuffle(puzzles) + + # Assign by fraction + for idx, (name, puzzle) in enumerate(puzzles): + fraction = idx / len(puzzles) + test_examples_dest = None + for f, dest in test_examples_map.get(subset_name, test_examples_map["_default"]): + if fraction < f: + test_examples_dest = dest + break + + assert test_examples_dest is not None + + if test_examples_dest[0] == "test": + test_puzzles[name] = puzzle + + convert_single_arc_puzzle(results, name, puzzle, config.num_aug, {"train": train_examples_dest, "test": test_examples_dest}) + total_puzzles += 1 + + print (f"Total puzzles: {total_puzzles}") + return results, test_puzzles + + +def convert_dataset(config: DataProcessConfig): + np.random.seed(config.seed) + + # Read dataset + data, test_puzzles = load_puzzles_arcagi(config) + + # Map global puzzle identifiers + num_identifiers = config.puzzle_identifiers_start # 0 is blank, start at 1 + identifier_map = {} + for split_name, split in data.items(): + for subset_name, subset in split.items(): + for group in subset: + for puzzle in group: + if puzzle.id not in identifier_map: + identifier_map[puzzle.id] = num_identifiers + num_identifiers += 1 + print (f"Total puzzle IDs (including ): {num_identifiers}") + + # Save + for split_name, split in data.items(): + os.makedirs(os.path.join(config.output_dir, split_name), exist_ok=True) + + # Translational augmentations + enable_translational_augment = split_name == "train" + + # Statistics + total_examples = 0 + total_puzzles = 0 + total_groups = 0 + + for subset_name, subset in split.items(): # "all" is the only subset + # Construct subset + results = {k: [] for k in ["inputs", "labels", "puzzle_identifiers", "puzzle_indices", "group_indices"]} + results["puzzle_indices"].append(0) + results["group_indices"].append(0) + + example_id = 0 + puzzle_id = 0 + + for group in subset: + for puzzle in group: + # Push puzzle + no_aug_id = np.random.randint(0, len(puzzle.examples)) + for _idx_ex, (inp, out) in enumerate(puzzle.examples): + inp, out = np_grid_to_seq_translational_augment(inp, out, do_translation=enable_translational_augment and _idx_ex != no_aug_id) + + results["inputs"].append(inp) + results["labels"].append(out) + example_id += 1 + + total_examples += 1 + + results["puzzle_indices"].append(example_id) + results["puzzle_identifiers"].append(identifier_map[puzzle.id]) + + puzzle_id += 1 + total_puzzles += 1 + + # Push group + results["group_indices"].append(puzzle_id) + total_groups += 1 + + for k, v in results.items(): + if k in {"inputs", "labels"}: + v = np.stack(v, 0) + else: + v = np.array(v, dtype=np.int32) + + np.save(os.path.join(config.output_dir, split_name, f"{subset_name}__{k}.npy"), v) + + # Metadata + metadata = PuzzleDatasetMetadata( + seq_len=ARCMaxGridSize * ARCMaxGridSize, + vocab_size=10 + 2, # PAD + EOS + "0" ... "9" + pad_id=0, + ignore_label_id=0, + blank_identifier_id=0, + num_puzzle_identifiers=num_identifiers, + total_groups=total_groups, + mean_puzzle_examples=total_examples / total_puzzles, + total_puzzles=total_puzzles, + sets=list(split.keys()) + ) + + # Save metadata as JSON. + with open(os.path.join(config.output_dir, split_name, "dataset.json"), "w") as f: + json.dump(metadata.model_dump(), f) + + # Save IDs mapping + with open(os.path.join(config.output_dir, "identifiers.json"), "w") as f: + ids_mapping = {v: k for k, v in identifier_map.items()} + json.dump([ids_mapping.get(i, "") for i in range(num_identifiers)], f) + + # Save Test Puzzles + with open(os.path.join(config.output_dir, "test_puzzles.json"), "w") as f: + json.dump(test_puzzles, f) + + +@cli.command(singleton=True) +def main(config: DataProcessConfig): + convert_dataset(config) + + +if __name__ == "__main__": + cli() + + + + + + + + + + + + diff --git a/dataset/build_maze_dataset.py b/dataset/build_maze_dataset.py new file mode 100644 index 0000000..7ebe267 --- /dev/null +++ b/dataset/build_maze_dataset.py @@ -0,0 +1,140 @@ +from typing import Optional +import math +import os +import csv +import json +import numpy as np + +from argdantic import ArgParser +from pydantic import BaseModel +from tqdm import tqdm +from huggingface_hub import hf_hub_download + +from common import PuzzleDatasetMetadata, dihedral_transform + + +CHARSET = "# SGo" + + +cli = ArgParser() + + +class DataProcessConfig(BaseModel): + source_repo: str = "sapientinc/maze-30x30-hard-1k" + output_dir: str = "data/maze-30x30-hard-1k" + + subsample_size: Optional[int] = None + aug: bool = False + + +def convert_subset(set_name: str, config: DataProcessConfig): + # Read CSV + all_chars = set() + grid_size = None + inputs = [] + labels = [] + + with open(hf_hub_download(config.source_repo, f"{set_name}.csv", repo_type="dataset"), newline="") as csvfile: # type: ignore + reader = csv.reader(csvfile) + next(reader) # Skip header + for source, q, a, rating in reader: + all_chars.update(q) + all_chars.update(a) + + if grid_size is None: + n = int(len(q) ** 0.5) + grid_size = (n, n) + + inputs.append(np.frombuffer(q.encode(), dtype=np.uint8).reshape(grid_size)) + labels.append(np.frombuffer(a.encode(), dtype=np.uint8).reshape(grid_size)) + + # If subsample_size is specified for the training set, + # randomly sample the desired number of examples. + if set_name == "train" and config.subsample_size is not None: + total_samples = len(inputs) + if config.subsample_size < total_samples: + indices = np.random.choice(total_samples, size=config.subsample_size, replace=False) + inputs = [inputs[i] for i in indices] + labels = [labels[i] for i in indices] + + # Generate dataset + results = {k: [] for k in ["inputs", "labels", "puzzle_identifiers", "puzzle_indices", "group_indices"]} + puzzle_id = 0 + example_id = 0 + + results["puzzle_indices"].append(0) + results["group_indices"].append(0) + + for inp, out in zip(tqdm(inputs), labels): + # Dihedral transformations for augmentation + for aug_idx in range(8 if (set_name == "train" and config.aug) else 1): + results["inputs"].append(dihedral_transform(inp, aug_idx)) + results["labels"].append(dihedral_transform(out, aug_idx)) + example_id += 1 + puzzle_id += 1 + + results["puzzle_indices"].append(example_id) + results["puzzle_identifiers"].append(0) + + # Push group + results["group_indices"].append(puzzle_id) + + # Char mappings + assert len(all_chars - set(CHARSET)) == 0 + + char2id = np.zeros(256, np.uint8) + char2id[np.array(list(map(ord, CHARSET)))] = np.arange(len(CHARSET)) + 1 + + # To Numpy + def _seq_to_numpy(seq): + arr = np.vstack([char2id[s.reshape(-1)] for s in seq]) + + return arr + + results = { + "inputs": _seq_to_numpy(results["inputs"]), + "labels": _seq_to_numpy(results["labels"]), + + "group_indices": np.array(results["group_indices"], dtype=np.int32), + "puzzle_indices": np.array(results["puzzle_indices"], dtype=np.int32), + "puzzle_identifiers": np.array(results["puzzle_identifiers"], dtype=np.int32), + } + + # Metadata + metadata = PuzzleDatasetMetadata( + seq_len=int(math.prod(grid_size)), # type: ignore + vocab_size=len(CHARSET) + 1, # PAD + Charset + pad_id=0, + ignore_label_id=0, + blank_identifier_id=0, + num_puzzle_identifiers=1, + total_groups=len(results["group_indices"]) - 1, + mean_puzzle_examples=1, + total_puzzles=len(results["group_indices"]) - 1, + sets=["all"] + ) + + # Save metadata as JSON. + save_dir = os.path.join(config.output_dir, set_name) + os.makedirs(save_dir, exist_ok=True) + + with open(os.path.join(save_dir, "dataset.json"), "w") as f: + json.dump(metadata.model_dump(), f) + + # Save data + for k, v in results.items(): + np.save(os.path.join(save_dir, f"all__{k}.npy"), v) + + # Save IDs mapping (for visualization only) + with open(os.path.join(config.output_dir, "identifiers.json"), "w") as f: + json.dump([""], f) + + +@cli.command(singleton=True) +def preprocess_data(config: DataProcessConfig): + convert_subset("train", config) + convert_subset("test", config) + + +if __name__ == "__main__": + cli() diff --git a/dataset/build_sudoku_dataset.py b/dataset/build_sudoku_dataset.py new file mode 100644 index 0000000..796b128 --- /dev/null +++ b/dataset/build_sudoku_dataset.py @@ -0,0 +1,167 @@ +from typing import Optional +import os +import csv +import json +import numpy as np + +from argdantic import ArgParser +from pydantic import BaseModel +from tqdm import tqdm +from huggingface_hub import hf_hub_download + +from common import PuzzleDatasetMetadata + + +cli = ArgParser() + + +class DataProcessConfig(BaseModel): + source_repo: str = "sapientinc/sudoku-extreme" + output_dir: str = "data/sudoku-extreme-full" + + subsample_size: Optional[int] = None + min_difficulty: Optional[int] = None + num_aug: int = 0 + + +def shuffle_sudoku(board: np.ndarray, solution: np.ndarray): + # Create a random digit mapping: a permutation of 1..9, with zero (blank) unchanged + digit_map = np.pad(np.random.permutation(np.arange(1, 10)), (1, 0)) + + # Randomly decide whether to transpose. + transpose_flag = np.random.rand() < 0.5 + + # Generate a valid row permutation: + # - Shuffle the 3 bands (each band = 3 rows) and for each band, shuffle its 3 rows. + bands = np.random.permutation(3) + row_perm = np.concatenate([b * 3 + np.random.permutation(3) for b in bands]) + + # Similarly for columns (stacks). + stacks = np.random.permutation(3) + col_perm = np.concatenate([s * 3 + np.random.permutation(3) for s in stacks]) + + # Build an 81->81 mapping. For each new cell at (i, j) + # (row index = i // 9, col index = i % 9), + # its value comes from old row = row_perm[i//9] and old col = col_perm[i%9]. + mapping = np.array([row_perm[i // 9] * 9 + col_perm[i % 9] for i in range(81)]) + + def apply_transformation(x: np.ndarray) -> np.ndarray: + # Apply transpose flag + if transpose_flag: + x = x.T + # Apply the position mapping. + new_board = x.flatten()[mapping].reshape(9, 9).copy() + # Apply digit mapping + return digit_map[new_board] + + return apply_transformation(board), apply_transformation(solution) + + +def convert_subset(set_name: str, config: DataProcessConfig): + # Read CSV + inputs = [] + labels = [] + + with open(hf_hub_download(config.source_repo, f"{set_name}.csv", repo_type="dataset"), newline="") as csvfile: + reader = csv.reader(csvfile) + next(reader) # Skip header + for source, q, a, rating in reader: + if (config.min_difficulty is None) or (int(rating) >= config.min_difficulty): + assert len(q) == 81 and len(a) == 81 + + inputs.append(np.frombuffer(q.replace('.', '0').encode(), dtype=np.uint8).reshape(9, 9) - ord('0')) + labels.append(np.frombuffer(a.encode(), dtype=np.uint8).reshape(9, 9) - ord('0')) + + # If subsample_size is specified for the training set, + # randomly sample the desired number of examples. + if set_name == "train" and config.subsample_size is not None: + total_samples = len(inputs) + if config.subsample_size < total_samples: + indices = np.random.choice(total_samples, size=config.subsample_size, replace=False) + inputs = [inputs[i] for i in indices] + labels = [labels[i] for i in indices] + + # Generate dataset + num_augments = config.num_aug if set_name == "train" else 0 + + results = {k: [] for k in ["inputs", "labels", "puzzle_identifiers", "puzzle_indices", "group_indices"]} + puzzle_id = 0 + example_id = 0 + + results["puzzle_indices"].append(0) + results["group_indices"].append(0) + + for orig_inp, orig_out in zip(tqdm(inputs), labels): + for aug_idx in range(1 + num_augments): + # First index is not augmented + if aug_idx == 0: + inp, out = orig_inp, orig_out + else: + inp, out = shuffle_sudoku(orig_inp, orig_out) + + # Push puzzle (only single example) + results["inputs"].append(inp) + results["labels"].append(out) + example_id += 1 + puzzle_id += 1 + + results["puzzle_indices"].append(example_id) + results["puzzle_identifiers"].append(0) + + # Push group + results["group_indices"].append(puzzle_id) + + # To Numpy + def _seq_to_numpy(seq): + arr = np.concatenate(seq).reshape(len(seq), -1) + + assert np.all((arr >= 0) & (arr <= 9)) + return arr + 1 + + results = { + "inputs": _seq_to_numpy(results["inputs"]), + "labels": _seq_to_numpy(results["labels"]), + + "group_indices": np.array(results["group_indices"], dtype=np.int32), + "puzzle_indices": np.array(results["puzzle_indices"], dtype=np.int32), + "puzzle_identifiers": np.array(results["puzzle_identifiers"], dtype=np.int32), + } + + # Metadata + metadata = PuzzleDatasetMetadata( + seq_len=81, + vocab_size=10 + 1, # PAD + "0" ... "9" + pad_id=0, + ignore_label_id=0, + blank_identifier_id=0, + num_puzzle_identifiers=1, + total_groups=len(results["group_indices"]) - 1, + mean_puzzle_examples=1, + total_puzzles=len(results["group_indices"]) - 1, + sets=["all"] + ) + + # Save metadata as JSON. + save_dir = os.path.join(config.output_dir, set_name) + os.makedirs(save_dir, exist_ok=True) + + with open(os.path.join(save_dir, "dataset.json"), "w") as f: + json.dump(metadata.model_dump(), f) + + # Save data + for k, v in results.items(): + np.save(os.path.join(save_dir, f"all__{k}.npy"), v) + + # Save IDs mapping (for visualization only) + with open(os.path.join(config.output_dir, "identifiers.json"), "w") as f: + json.dump([""], f) + + +@cli.command(singleton=True) +def preprocess_data(config: DataProcessConfig): + convert_subset("train", config) + convert_subset("test", config) + + +if __name__ == "__main__": + cli() diff --git a/dataset/common.py b/dataset/common.py new file mode 100644 index 0000000..5ff91bb --- /dev/null +++ b/dataset/common.py @@ -0,0 +1,49 @@ +from typing import List, Optional + +import pydantic +import numpy as np + + +# Global list mapping each dihedral transform id to its inverse. +# Index corresponds to the original tid, and the value is its inverse. +DIHEDRAL_INVERSE = [0, 3, 2, 1, 4, 5, 6, 7] + + +class PuzzleDatasetMetadata(pydantic.BaseModel): + pad_id: int + ignore_label_id: Optional[int] + blank_identifier_id: int + vocab_size: int + seq_len: int + num_puzzle_identifiers: int + total_groups: int + mean_puzzle_examples: float + total_puzzles: int + sets: List[str] + + +def dihedral_transform(arr: np.ndarray, tid: int) -> np.ndarray: + """8 dihedral symmetries by rotate, flip and mirror""" + + if tid == 0: + return arr # identity + elif tid == 1: + return np.rot90(arr, k=1) + elif tid == 2: + return np.rot90(arr, k=2) + elif tid == 3: + return np.rot90(arr, k=3) + elif tid == 4: + return np.fliplr(arr) # horizontal flip + elif tid == 5: + return np.flipud(arr) # vertical flip + elif tid == 6: + return arr.T # transpose (reflection along main diagonal) + elif tid == 7: + return np.fliplr(np.rot90(arr, k=1)) # anti-diagonal reflection + else: + return arr + + +def inverse_dihedral_transform(arr: np.ndarray, tid: int) -> np.ndarray: + return dihedral_transform(arr, DIHEDRAL_INVERSE[tid]) diff --git a/evaluators/arc.py b/evaluators/arc.py new file mode 100644 index 0000000..3003cbf --- /dev/null +++ b/evaluators/arc.py @@ -0,0 +1,177 @@ +from typing import Dict, Sequence, Optional +import os +import json + +import torch +import numpy as np +from numba import njit +import torch.distributed as dist + +from dataset.build_arc_dataset import inverse_aug, grid_hash, arc_grid_to_np +from dataset.common import PuzzleDatasetMetadata + +@njit +def _crop(grid: np.ndarray): + """Find maximum-sized rectangle without any EOS token inside. """ + grid = grid.reshape(30, 30) + + max_area = 0 + max_size = (0, 0) + nr, nc = grid.shape + + num_c = nc + for num_r in range(1, nr + 1): + # Scan for maximum c + for c in range(1, num_c + 1): + x = grid[num_r - 1, c - 1] + if (x < 2) | (x > 11): + num_c = c - 1 + break + + area = num_r * num_c + if area > max_area: + max_area = area + max_size = (num_r, num_c) + + return (grid[:max_size[0], :max_size[1]] - 2).astype(np.uint8) + + +class ARC: + required_outputs = {"inputs", "puzzle_identifiers", "q_halt_logits", "preds"} + + def __init__(self, data_path: str, + eval_metadata: PuzzleDatasetMetadata, + submission_K: int = 2, + pass_Ks: Sequence[int] = (1, 2, 5, 10, 100, 1000), + aggregated_voting: bool = True): + super().__init__() + self.pass_Ks = pass_Ks + self.submission_K = submission_K + self.aggregated_voting = aggregated_voting + self.blank_identifier_id = eval_metadata.blank_identifier_id + + # Load identifiers and test puzzles + with open(os.path.join(data_path, "identifiers.json"), "r") as f: + self.identifier_map = json.load(f) + with open(os.path.join(data_path, "test_puzzles.json"), "r") as f: + self.test_puzzles = json.load(f) + + # States + self._local_hmap = {} + self._local_preds = {} + + def begin_eval(self): + if not self.aggregated_voting: + # Clear previous predictions + self._local_hmap = {} + self._local_preds = {} + + def update_batch(self, batch: Dict[str, torch.Tensor], preds: Dict[str, torch.Tensor]): + # Collect required outputs to CPU + outputs = {} + q_values = None + + for collection in (batch, preds): + for k, v in collection.items(): + if k in self.required_outputs: + if k == "q_halt_logits": + q_values = v.to(torch.float64).sigmoid().cpu() + else: + outputs[k] = v.cpu() + + assert q_values is not None + + # Remove padding from outputs + mask = outputs["puzzle_identifiers"] != self.blank_identifier_id + outputs = {k: v[mask] for k, v in outputs.items()} + + # Get predictions + for identifier, input, pred, q in zip(outputs["puzzle_identifiers"].numpy(), outputs["inputs"].numpy(), outputs["preds"].numpy(), q_values.numpy()): + name = self.identifier_map[identifier] + orig_name, _inverse_fn = inverse_aug(name) + + input_hash = grid_hash(_inverse_fn(_crop(input))) + + pred = _inverse_fn(_crop(pred)) + assert np.all((pred >= 0) & (pred <= 9)), f"Puzzle {name}'s prediction out of 0-9 range." # Sanity check + + # Store into local state + pred_hash = grid_hash(pred) + + self._local_hmap[pred_hash] = pred + + self._local_preds.setdefault(orig_name, {}) + self._local_preds[orig_name].setdefault(input_hash, []) + self._local_preds[orig_name][input_hash].append((pred_hash, float(q))) + + def result(self, save_path: Optional[str], rank: int, world_size: int, group: Optional[torch.distributed.ProcessGroup] = None) -> Optional[Dict[str, float]]: + # Gather predictions to rank 0 for voting + global_hmap_preds = [None for _ in range(world_size)] if rank == 0 else None + dist.gather_object((self._local_hmap, self._local_preds), global_hmap_preds, dst=0, group=group) + + # Rank 0 logic + if rank != 0: + return + + submission = {} + correct = [0.0 for _ in range(len(self.pass_Ks))] + + for name, puzzle in self.test_puzzles.items(): + # Process test examples in this puzzle + submission[name] = [] + num_test_correct = [0 for _ in range(len(self.pass_Ks))] + for pair in puzzle["test"]: + input_hash = grid_hash(arc_grid_to_np(pair["input"])) + label_hash = grid_hash(arc_grid_to_np(pair["output"])) + + p_map = {} + for hmap, preds in global_hmap_preds: # type: ignore + for h, q in preds.get(name, {}).get(input_hash, {}): + p_map.setdefault(h, [0, 0]) + p_map[h][0] += 1 + p_map[h][1] += q + + if not len(p_map): + print (f"Puzzle {name} has no predictions.") + continue + + for h, stats in p_map.items(): + stats[1] /= stats[0] + + p_map = sorted(p_map.items(), key=lambda kv: kv[1], reverse=True) + + # vote for different Ks + for i, k in enumerate(self.pass_Ks): + ok = False + for h, stats in p_map[:k]: + ok |= h == label_hash + + num_test_correct[i] += ok + + # Query grids + pred_grids = [] + for h, stats in p_map[:self.submission_K]: + for hmap, preds in global_hmap_preds: # type: ignore + if h in hmap: + pred_grids.append(hmap[h]) + break + + # Pad to K + while len(pred_grids) < self.submission_K: + pred_grids.append(pred_grids[0]) + + submission[name].append({f"attempt_{i + 1}": grid.tolist() for i, grid in enumerate(pred_grids)}) + + # Total correctness + for i in range(len(self.pass_Ks)): + correct[i] += num_test_correct[i] / len(puzzle["test"]) + + # Save submission + if save_path is not None: + with open(os.path.join(save_path, "submission.json"), "w") as f: + json.dump(submission, f) + + # Final result + all_results = {f"ARC/pass@{k}": correct[i] / len(self.test_puzzles) for i, k in enumerate(self.pass_Ks)} + + return all_results \ No newline at end of file diff --git a/kaggle/combined/arc-agi_concept_challenges.json b/kaggle/combined/arc-agi_concept_challenges.json new file mode 100644 index 0000000..8ec9df7 --- /dev/null +++ b/kaggle/combined/arc-agi_concept_challenges.json @@ -0,0 +1,17863 @@ +{ + "ExtractObjects10": { + "train": [ + { + "input": [ + [1, 1, 1, 1, 1, 3, 3, 3, 2, 2, 1, 1, 1, 1, 1, 3, 3, 3, 2, 2], + [1, 1, 1, 1, 1, 3, 3, 3, 2, 2, 1, 1, 1, 1, 1, 3, 3, 3, 2, 2], + [1, 1, 1, 1, 1, 3, 3, 3, 3, 3, 1, 1, 1, 1, 1, 3, 3, 3, 3, 3], + [1, 1, 1, 1, 1, 3, 3, 3, 3, 3, 1, 1, 1, 1, 1, 3, 3, 3, 3, 3], + [3, 3, 3, 2, 2, 1, 1, 1, 1, 1, 3, 3, 3, 2, 2, 1, 1, 1, 1, 1], + [3, 3, 3, 2, 2, 1, 1, 1, 1, 1, 3, 3, 3, 2, 2, 1, 1, 1, 1, 1], + [3, 3, 3, 3, 3, 1, 1, 1, 1, 1, 3, 3, 3, 3, 3, 1, 1, 1, 1, 1], + [3, 3, 3, 3, 3, 1, 1, 1, 1, 1, 3, 3, 3, 3, 3, 1, 1, 1, 1, 1] + ], + "output": [ + [3, 3, 3, 2, 2], + [3, 3, 3, 2, 2], + [3, 3, 3, 3, 3], + [3, 3, 3, 3, 3] + ] + }, + { + "input": [ + [0, 0, 5, 5, 5, 5, 0, 0], + [0, 0, 5, 3, 3, 5, 0, 0], + [0, 0, 0, 0, 0, 0, 0, 0], + [0, 0, 0, 0, 0, 0, 0, 0], + [0, 0, 5, 5, 5, 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9, 7, 7, 2, 3, 7, 9, 4, 6, 7, 4, 2, 9, 2, 6, 6, 2, 9, 2, 4, 7, 6, 4, 9, 7, 3, 2, 7, 7], [3, 3, 4, 1, 3, 5, 6, 4, 2, 4, 7, 7, 1, 6, 7, 2, 2, 7, 6, 1, 7, 7, 4, 2, 4, 6, 5, 3, 1, 4], [3, 3, 1, 4, 6, 3, 4, 6, 2, 2, 7, 1, 6, 1, 2, 7, 7, 2, 1, 6, 1, 7, 2, 2, 6, 4, 3, 6, 4, 1], [6, 6, 3, 3, 6, 4, 4, 7, 1, 1, 2, 4, 7, 2, 1, 6, 6, 1, 2, 7, 4, 2, 1, 1, 7, 4, 4, 6, 3, 3], [6, 6, 3, 3, 4, 6, 7, 4, 1, 3, 2, 2, 2, 7, 6, 1, 1, 6, 7, 2, 2, 2, 3, 1, 4, 7, 6, 4, 3, 3], [3, 6, 6, 4, 6, 2, 9, 2, 9, 9, 9, 7, 2, 4, 1, 7, 7, 1, 4, 2, 7, 9, 9, 9, 2, 9, 2, 6, 4, 6], [5, 3, 4, 6, 7, 6, 2, 9, 9, 9, 7, 9, 2, 2, 7, 7, 7, 7, 2, 2, 9, 7, 9, 9, 9, 2, 6, 7, 6, 4], [6, 4, 4, 7, 9, 9, 6, 2, 9, 7, 9, 9, 3, 1, 2, 4, 4, 2, 1, 3, 9, 9, 7, 9, 2, 6, 9, 9, 7, 4], [4, 6, 7, 4, 9, 9, 7, 6, 7, 9, 9, 9, 1, 1, 2, 2, 2, 2, 1, 1, 9, 9, 9, 7, 6, 7, 9, 9, 4, 7], [4, 6, 7, 4, 9, 9, 7, 6, 7, 9, 9, 9, 1, 1, 2, 2, 2, 2, 1, 1, 9, 9, 9, 7, 6, 7, 9, 9, 4, 7], [6, 4, 4, 7, 9, 9, 6, 2, 9, 7, 9, 9, 3, 1, 2, 4, 4, 2, 1, 3, 9, 9, 7, 9, 2, 6, 9, 9, 7, 4], [5, 3, 4, 6, 7, 6, 2, 9, 9, 9, 7, 9, 2, 2, 7, 7, 7, 7, 2, 2, 9, 7, 9, 9, 9, 2, 6, 7, 6, 4], [3, 6, 6, 4, 6, 2, 9, 2, 9, 9, 9, 7, 2, 4, 1, 7, 7, 1, 4, 2, 7, 9, 9, 9, 2, 9, 2, 6, 4, 6], [6, 6, 3, 3, 4, 6, 7, 4, 1, 3, 2, 2, 2, 7, 6, 1, 1, 6, 7, 2, 2, 2, 3, 1, 4, 7, 6, 4, 3, 3], [6, 6, 3, 3, 6, 4, 4, 7, 1, 1, 2, 4, 7, 2, 1, 6, 6, 1, 2, 7, 4, 2, 1, 1, 7, 4, 4, 6, 3, 3], [3, 3, 1, 4, 6, 3, 4, 6, 2, 2, 7, 1, 6, 1, 2, 7, 7, 2, 1, 6, 1, 7, 2, 2, 6, 4, 3, 6, 4, 1], [3, 3, 4, 1, 3, 5, 6, 4, 2, 4, 7, 7, 1, 6, 7, 2, 2, 7, 6, 1, 7, 7, 4, 2, 4, 6, 5, 3, 1, 4], [3, 9, 7, 7, 2, 3, 7, 9, 4, 6, 7, 4, 2, 9, 2, 6, 6, 2, 9, 2, 4, 7, 6, 4, 9, 7, 3, 2, 7, 7], [9, 3, 7, 7, 3, 2, 9, 9, 6, 4, 4, 7, 9, 2, 6, 7, 7, 6, 2, 9, 7, 4, 4, 6, 9, 9, 2, 3, 7, 7], [7, 7, 3, 9, 7, 9, 3, 2, 5, 3, 4, 6, 2, 6, 9, 9, 9, 9, 6, 2, 6, 4, 3, 5, 2, 3, 9, 7, 9, 3], [7, 7, 9, 3, 9, 9, 5, 3, 3, 6, 6, 4, 6, 7, 9, 9, 9, 9, 7, 6, 4, 6, 6, 3, 3, 5, 9, 9, 3, 9], [2, 3, 7, 9, 5, 7, 4, 4, 1, 4, 3, 3, 4, 6, 7, 4, 4, 7, 6, 4, 3, 3, 4, 1, 4, 4, 7, 5, 9, 7], [3, 2, 9, 9, 7, 5, 4, 4, 4, 1, 3, 3, 6, 4, 4, 7, 7, 4, 4, 6, 3, 3, 1, 4, 4, 4, 5, 7, 9, 9]], "output": [[3, 1, 4, 4, 4], [3, 4, 1, 4, 4], [6, 6, 3, 3, 5], [4, 3, 5, 2, 3]]}, {"input": [[1, 9, 4, 4, 9, 9, 2, 7, 6, 6, 9, 9, 7, 6, 7, 2, 2, 7, 6, 7, 9, 9, 6, 6, 7, 2, 9, 9, 4, 4], [7, 1, 4, 4, 9, 9, 7, 2, 6, 6, 9, 9, 6, 7, 2, 7, 7, 2, 7, 6, 9, 9, 6, 6, 2, 7, 9, 9, 4, 4], [2, 7, 1, 9, 2, 7, 9, 9, 4, 4, 6, 6, 7, 2, 5, 1, 1, 5, 2, 7, 6, 6, 4, 4, 9, 9, 7, 2, 9, 1], [7, 2, 7, 1, 7, 2, 9, 9, 4, 4, 6, 6, 2, 7, 5, 5, 5, 5, 7, 2, 6, 6, 4, 4, 9, 9, 2, 7, 1, 7], [9, 6, 7, 2, 1, 9, 4, 4, 7, 6, 7, 2, 9, 2, 6, 4, 4, 6, 2, 9, 2, 7, 6, 7, 4, 4, 9, 1, 2, 7], [6, 9, 2, 7, 7, 1, 4, 4, 6, 7, 2, 7, 9, 9, 4, 6, 6, 4, 9, 9, 7, 2, 7, 6, 4, 4, 1, 7, 7, 2], [7, 2, 9, 6, 2, 7, 1, 9, 7, 2, 5, 5, 4, 5, 9, 2, 2, 9, 5, 4, 5, 5, 2, 7, 9, 1, 7, 2, 6, 9], [2, 7, 6, 9, 7, 2, 7, 1, 2, 7, 1, 5, 5, 4, 9, 9, 9, 9, 4, 5, 5, 1, 7, 2, 1, 7, 2, 7, 9, 6], [6, 6, 4, 4, 7, 6, 7, 2, 3, 7, 1, 4, 9, 7, 7, 6, 6, 7, 7, 9, 4, 1, 7, 3, 2, 7, 6, 7, 4, 4], [6, 6, 4, 4, 6, 7, 2, 7, 4, 3, 4, 4, 7, 9, 6, 7, 7, 6, 9, 7, 4, 4, 3, 4, 7, 2, 7, 6, 4, 4], [9, 9, 6, 6, 7, 2, 5, 1, 3, 7, 3, 7, 7, 6, 9, 7, 7, 9, 6, 7, 7, 3, 7, 3, 1, 5, 2, 7, 6, 6], [9, 9, 6, 6, 2, 7, 5, 5, 7, 7, 4, 3, 6, 7, 7, 9, 9, 7, 7, 6, 3, 4, 7, 7, 5, 5, 7, 2, 6, 6], [7, 6, 7, 2, 9, 9, 4, 5, 6, 6, 5, 9, 3, 7, 4, 4, 4, 4, 7, 3, 9, 5, 6, 6, 5, 4, 9, 9, 2, 7], [6, 7, 2, 7, 2, 9, 5, 4, 6, 6, 9, 5, 4, 3, 4, 1, 1, 4, 3, 4, 5, 9, 6, 6, 4, 5, 9, 2, 7, 2], [7, 2, 5, 5, 6, 4, 9, 9, 5, 9, 6, 6, 7, 7, 3, 7, 7, 3, 7, 7, 6, 6, 9, 5, 9, 9, 4, 6, 5, 5], [2, 7, 1, 5, 4, 6, 2, 9, 9, 5, 6, 6, 7, 3, 4, 3, 3, 4, 3, 7, 6, 6, 5, 9, 9, 2, 6, 4, 5, 1], [2, 7, 1, 5, 4, 6, 2, 9, 9, 5, 6, 6, 7, 3, 4, 3, 3, 4, 3, 7, 6, 6, 5, 9, 9, 2, 6, 4, 5, 1], [7, 2, 5, 5, 6, 4, 9, 9, 5, 9, 6, 6, 7, 7, 3, 7, 7, 3, 7, 7, 6, 6, 9, 5, 9, 9, 4, 6, 5, 5], [6, 7, 2, 7, 2, 9, 5, 4, 6, 6, 9, 5, 4, 3, 4, 1, 1, 4, 3, 4, 5, 9, 6, 6, 4, 5, 9, 2, 7, 2], [7, 6, 7, 2, 9, 9, 4, 5, 6, 6, 5, 9, 8, 8, 8, 8, 8, 8, 8, 3, 9, 5, 6, 6, 5, 4, 9, 9, 2, 7], [9, 9, 6, 6, 2, 7, 5, 5, 7, 7, 4, 3, 8, 8, 8, 8, 8, 8, 8, 6, 3, 4, 7, 7, 5, 5, 7, 2, 6, 6], [9, 9, 6, 6, 7, 2, 5, 1, 3, 7, 3, 7, 8, 8, 8, 8, 8, 8, 8, 7, 7, 3, 7, 3, 1, 5, 2, 7, 6, 6], [6, 6, 4, 4, 6, 7, 2, 7, 4, 3, 4, 4, 7, 9, 6, 7, 7, 6, 9, 7, 4, 4, 3, 4, 7, 2, 7, 6, 4, 4], [6, 6, 4, 4, 7, 6, 7, 2, 3, 7, 1, 4, 9, 7, 7, 6, 6, 7, 7, 9, 4, 1, 7, 3, 2, 7, 6, 7, 4, 4], [2, 7, 6, 9, 7, 2, 7, 1, 2, 7, 1, 5, 5, 4, 9, 9, 9, 9, 4, 5, 5, 1, 7, 2, 1, 7, 2, 7, 9, 6], [7, 2, 9, 6, 2, 7, 1, 9, 7, 2, 5, 5, 4, 5, 9, 2, 2, 9, 5, 4, 5, 5, 2, 7, 9, 1, 7, 2, 6, 9], [6, 9, 2, 7, 7, 1, 4, 4, 6, 7, 2, 7, 9, 9, 4, 6, 6, 4, 9, 9, 7, 2, 7, 6, 4, 4, 1, 7, 7, 2], [9, 6, 7, 2, 1, 9, 4, 4, 7, 6, 7, 2, 9, 2, 6, 4, 4, 6, 2, 9, 2, 7, 6, 7, 4, 4, 9, 1, 2, 7], [7, 2, 7, 1, 7, 2, 9, 9, 4, 4, 6, 6, 2, 7, 5, 5, 5, 5, 7, 2, 6, 6, 4, 4, 9, 9, 2, 7, 1, 7], [2, 7, 1, 9, 2, 7, 9, 9, 4, 4, 6, 6, 7, 2, 5, 1, 1, 5, 2, 7, 6, 6, 4, 4, 9, 9, 7, 2, 9, 1]], "output": [[3, 7, 4, 4, 4, 4, 7], [6, 7, 7, 9, 9, 7, 7], [7, 6, 9, 7, 7, 9, 6]]}, {"input": [[3, 1, 1, 9, 5, 6, 7, 1, 1, 4, 5, 7, 3, 9, 9, 1, 1, 9, 9, 3, 7, 5, 4, 1, 1, 7, 6, 5, 9, 1], [1, 3, 9, 5, 6, 5, 1, 7, 4, 1, 7, 5, 4, 3, 1, 3, 3, 1, 3, 4, 5, 7, 1, 4, 7, 1, 5, 6, 5, 9], [6, 9, 3, 1, 7, 1, 5, 6, 9, 9, 1, 4, 9, 1, 1, 4, 4, 1, 1, 9, 4, 1, 9, 9, 6, 5, 1, 7, 1, 3], [9, 1, 1, 3, 1, 7, 6, 5, 9, 9, 4, 1, 1, 3, 4, 1, 1, 4, 3, 1, 1, 4, 9, 9, 5, 6, 7, 1, 3, 1], [6, 6, 6, 7, 3, 1, 5, 9, 3, 4, 9, 1, 6, 7, 2, 5, 5, 2, 7, 6, 1, 9, 4, 3, 9, 5, 1, 3, 7, 6], [6, 6, 7, 6, 1, 3, 9, 1, 9, 3, 1, 3, 7, 6, 5, 2, 2, 5, 6, 7, 3, 1, 3, 9, 1, 9, 3, 1, 6, 7], [6, 7, 6, 6, 1, 9, 3, 1, 9, 1, 1, 4, 6, 9, 6, 7, 7, 6, 9, 6, 4, 1, 1, 9, 1, 3, 9, 1, 6, 6], [7, 6, 6, 6, 9, 6, 1, 3, 1, 3, 4, 1, 9, 6, 7, 6, 6, 7, 6, 9, 1, 4, 3, 1, 3, 1, 8, 8, 8, 8], [1, 4, 9, 9, 3, 9, 9, 1, 1, 1, 6, 1, 5, 2, 5, 5, 5, 5, 2, 5, 1, 6, 1, 1, 1, 9, 8, 8, 8, 8], [4, 1, 9, 9, 4, 3, 1, 3, 1, 1, 1, 6, 2, 5, 5, 5, 5, 5, 5, 2, 6, 1, 1, 1, 3, 1, 8, 8, 8, 8], [5, 7, 1, 4, 9, 1, 1, 4, 2, 2, 1, 1, 5, 5, 5, 2, 2, 5, 5, 5, 1, 1, 2, 2, 4, 1, 8, 8, 8, 8], [7, 5, 4, 1, 1, 3, 4, 1, 2, 1, 1, 1, 5, 5, 2, 5, 5, 2, 5, 5, 1, 1, 1, 2, 1, 4, 3, 1, 1, 4], [3, 4, 9, 1, 6, 7, 6, 9, 7, 6, 3, 3, 1, 1, 6, 1, 1, 6, 1, 1, 3, 3, 6, 7, 9, 6, 7, 6, 1, 9], [9, 3, 1, 3, 7, 6, 9, 6, 6, 7, 3, 3, 1, 1, 1, 6, 6, 1, 1, 1, 3, 3, 7, 6, 6, 9, 6, 7, 3, 1], [9, 1, 1, 4, 2, 5, 6, 7, 3, 3, 7, 6, 1, 2, 1, 1, 1, 1, 2, 1, 6, 7, 3, 3, 7, 6, 5, 2, 4, 1], [1, 3, 4, 1, 5, 2, 7, 6, 3, 3, 6, 7, 2, 2, 1, 1, 1, 1, 2, 2, 7, 6, 3, 3, 6, 7, 2, 5, 1, 4], [1, 3, 4, 1, 5, 2, 7, 6, 3, 3, 6, 7, 2, 2, 1, 1, 1, 1, 2, 2, 7, 6, 3, 3, 6, 7, 2, 5, 1, 4], [9, 1, 1, 4, 2, 5, 6, 7, 3, 3, 7, 6, 1, 2, 1, 1, 1, 1, 2, 1, 6, 7, 3, 3, 7, 6, 5, 2, 4, 1], [9, 3, 1, 3, 7, 6, 9, 6, 6, 7, 3, 3, 1, 1, 1, 6, 6, 1, 1, 1, 3, 3, 7, 6, 6, 9, 6, 7, 3, 1], [3, 4, 9, 1, 6, 7, 6, 9, 7, 6, 3, 3, 1, 1, 6, 1, 1, 6, 1, 1, 3, 3, 6, 7, 9, 6, 7, 6, 1, 9], [7, 5, 4, 1, 1, 3, 4, 1, 2, 1, 1, 1, 5, 5, 2, 5, 5, 2, 5, 5, 1, 1, 1, 2, 1, 4, 3, 1, 1, 4], [5, 7, 1, 4, 9, 1, 1, 4, 2, 2, 1, 1, 5, 5, 5, 2, 2, 5, 5, 5, 1, 1, 2, 2, 4, 1, 1, 9, 4, 1], [4, 1, 9, 9, 4, 3, 1, 3, 1, 1, 1, 6, 2, 5, 5, 5, 5, 5, 5, 2, 6, 1, 1, 1, 3, 1, 3, 4, 9, 9], [1, 4, 9, 9, 3, 9, 9, 1, 1, 1, 6, 1, 5, 2, 5, 5, 5, 5, 2, 5, 1, 6, 1, 1, 1, 9, 9, 3, 9, 9], [7, 6, 6, 6, 9, 6, 1, 3, 1, 3, 4, 1, 9, 6, 7, 6, 6, 7, 6, 9, 1, 4, 3, 1, 3, 1, 6, 9, 6, 6], [6, 7, 6, 6, 1, 9, 3, 1, 9, 1, 1, 4, 6, 9, 6, 7, 7, 6, 9, 6, 4, 1, 1, 9, 1, 3, 9, 1, 6, 6], [6, 6, 7, 6, 1, 3, 9, 1, 9, 3, 1, 3, 7, 6, 5, 2, 2, 5, 6, 7, 3, 1, 3, 9, 1, 9, 3, 1, 6, 7], [6, 6, 6, 7, 3, 1, 5, 9, 3, 4, 9, 1, 6, 7, 2, 5, 5, 2, 7, 6, 1, 9, 4, 3, 9, 5, 1, 3, 7, 6], [9, 1, 1, 3, 1, 7, 6, 5, 9, 9, 4, 1, 1, 3, 4, 1, 1, 4, 3, 1, 1, 4, 9, 9, 5, 6, 7, 1, 3, 1], [6, 9, 3, 1, 7, 1, 5, 6, 9, 9, 1, 4, 9, 1, 1, 4, 4, 1, 1, 9, 4, 1, 9, 9, 6, 5, 1, 7, 1, 3]], "output": [[6, 9, 6, 6], [9, 3, 9, 9], [3, 4, 9, 9], [1, 9, 4, 1]]}], "test": [{"input": [[4, 4, 1, 3, 5, 7, 7, 9, 6, 1, 6, 6, 4, 4, 7, 7, 7, 7, 4, 4, 6, 6, 1, 6, 9, 7, 7, 5, 3, 1], 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8, 8, 8, 8, 4, 4, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 4, 2, 8, 8, 8, 8, 6], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 3, 2, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 3, 2, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 3, 2, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 3, 2, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 4, 2, 8, 8, 8, 8, 8], [8, 8, 8, 5, 8, 8, 8, 8, 8, 8, 8, 8, 8, 1, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8]], "output": [[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 4, 4, 8, 8, 8, 8, 8, 8, 8, 8, 8], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 2, 4, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 2, 3, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 2, 3, 8, 8, 8, 8, 8, 8, 8, 8, 8], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 2, 3, 8, 8, 8, 8, 8, 8, 8, 8, 8], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 2, 4, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 4, 3, 3, 3, 3, 4, 4, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 2, 2, 2, 2, 2, 2, 4, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 1, 5, 8, 8, 6, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 1, 5, 8, 8, 6, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 1, 5, 8, 8, 6, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 1, 5, 8, 8, 6, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 1, 5, 8, 8, 6, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 1, 5, 8, 8, 6, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 1, 5, 8, 8, 6, 8, 8, 8, 8, 8, 4, 3, 3, 3, 3, 4, 4, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 1, 5, 8, 8, 6, 8, 8, 8, 8, 8, 2, 2, 2, 2, 2, 2, 4, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 1, 5, 8, 8, 6, 8, 8, 8, 8, 8, 8, 1, 5, 8, 8, 6, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 1, 5, 8, 8, 6, 8, 8, 8, 8, 8, 8, 1, 5, 8, 8, 6, 8, 8, 8, 8, 4, 4, 8, 8, 8, 8, 8], [8, 8, 1, 5, 8, 8, 6, 8, 8, 8, 8, 8, 8, 1, 5, 8, 8, 6, 8, 8, 8, 8, 4, 2, 6, 6, 6, 6, 6], [8, 8, 1, 5, 8, 8, 6, 8, 8, 8, 8, 8, 8, 1, 5, 8, 8, 6, 8, 8, 8, 8, 3, 2, 8, 8, 8, 8, 8], [8, 8, 1, 5, 8, 8, 6, 8, 8, 8, 8, 8, 8, 1, 5, 8, 8, 6, 8, 8, 8, 8, 3, 2, 8, 8, 8, 8, 8], [8, 8, 1, 5, 8, 8, 6, 8, 8, 8, 8, 8, 8, 1, 5, 8, 8, 6, 8, 8, 8, 8, 3, 2, 5, 5, 5, 5, 5], [8, 8, 1, 5, 8, 8, 6, 8, 8, 8, 8, 8, 8, 1, 5, 8, 8, 6, 8, 8, 8, 8, 3, 2, 1, 1, 1, 1, 1], [8, 8, 1, 5, 8, 8, 6, 8, 8, 8, 8, 8, 8, 1, 5, 8, 8, 6, 8, 8, 8, 8, 4, 2, 8, 8, 8, 8, 8], [8, 8, 1, 5, 8, 8, 6, 8, 8, 8, 8, 8, 8, 1, 5, 8, 8, 6, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8]]}, {"input": [[8, 8, 8, 8, 8, 1, 4, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 6, 8, 8, 8, 8, 8, 8, 8], [3, 8, 8, 8, 8, 1, 4, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 1, 2, 8, 8, 8, 8, 8, 8, 8, 1, 1, 1, 1, 1, 1, 1, 1, 1, 8, 8, 8, 8], [8, 8, 8, 8, 8, 1, 2, 8, 8, 8, 8, 8, 8, 8, 4, 2, 2, 2, 2, 2, 2, 4, 4, 8, 8, 8, 8], [8, 8, 8, 8, 8, 1, 2, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [9, 8, 8, 8, 8, 1, 2, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 1, 2, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 1, 2, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 1, 4, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 4, 1, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 4, 1, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 2, 1, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 2, 1, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 2, 1, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 2, 1, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 2, 1, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 2, 1, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 4, 1, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8]], "output": [[8, 8, 8, 8, 8, 1, 4, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 8, 6, 8, 3, 8, 8, 8, 8, 8], [3, 3, 3, 3, 3, 1, 4, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 8, 6, 8, 3, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 1, 2, 8, 8, 8, 8, 8, 8, 8, 1, 1, 1, 1, 1, 1, 1, 1, 1, 8, 8, 8, 8], [6, 6, 6, 6, 6, 1, 2, 8, 8, 8, 8, 8, 8, 8, 4, 2, 2, 2, 2, 2, 2, 4, 4, 8, 8, 8, 8], [8, 8, 8, 8, 8, 1, 2, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [9, 9, 9, 9, 9, 1, 2, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 1, 2, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 1, 2, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 1, 4, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 4, 1, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 4, 1, 3, 3, 3, 3, 3, 3, 3, 3, 3], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 2, 1, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 2, 1, 6, 6, 6, 6, 6, 6, 6, 6, 6], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 2, 1, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 2, 1, 9, 9, 9, 9, 9, 9, 9, 9, 9], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 2, 1, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 2, 1, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 4, 1, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8]]}], "test": [{"input": [[8, 8, 8, 8, 1, 1, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [9, 8, 8, 8, 4, 1, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 4, 2, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 3, 2, 2, 2, 2, 1, 1, 8, 8, 8, 8], [8, 8, 8, 8, 4, 2, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 3, 4, 4, 4, 4, 4, 1, 8, 8, 8, 8], [8, 8, 8, 8, 4, 2, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 4, 2, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 3, 3, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 3, 3, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 2, 4, 8, 8, 7], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 2, 4, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 2, 4, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 2, 4, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 1, 4, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 1, 1, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 1, 1, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 4, 1, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 4, 2, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 4, 2, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 4, 2, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 4, 2, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 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9, 8, 6, 5, 5, 5, 2, 9, 5, 9, 9, 5, 9, 2, 5, 5, 5, 6, 8, 9, 8, 8, 8, 4]]}, {"input": [[6, 7, 3, 7, 1, 7, 2, 2, 1, 7, 6, 5, 5, 7, 5, 7, 7, 5, 7, 5, 5, 6, 7, 1, 2, 2, 7, 1, 7, 3], [7, 6, 9, 9, 7, 7, 5, 5, 7, 6, 5, 1, 7, 7, 7, 7, 7, 7, 7, 7, 1, 5, 6, 7, 5, 5, 7, 7, 9, 9], [3, 9, 9, 7, 2, 5, 2, 7, 6, 5, 7, 6, 5, 7, 9, 9, 9, 9, 7, 5, 6, 7, 5, 6, 7, 2, 5, 2, 7, 9], [7, 9, 7, 9, 2, 5, 7, 7, 5, 1, 6, 6, 7, 7, 9, 4, 4, 9, 7, 7, 6, 6, 1, 5, 7, 7, 5, 2, 9, 7], [1, 7, 2, 2, 9, 9, 9, 6, 5, 7, 5, 7, 3, 3, 9, 9, 9, 9, 3, 3, 7, 5, 7, 5, 6, 9, 9, 9, 2, 2], [7, 0, 0, 0, 0, 0, 0, 5, 7, 7, 7, 7, 3, 6, 9, 6, 6, 9, 6, 3, 7, 7, 7, 7, 5, 9, 6, 9, 5, 5], [2, 0, 0, 0, 0, 0, 0, 9, 5, 7, 9, 9, 9, 9, 3, 6, 6, 3, 9, 9, 9, 9, 7, 5, 9, 9, 9, 9, 7, 2], [2, 0, 0, 0, 0, 0, 0, 7, 7, 7, 9, 4, 9, 6, 6, 3, 3, 6, 6, 9, 4, 9, 7, 7, 7, 9, 5, 6, 7, 7], [1, 0, 0, 0, 0, 0, 0, 7, 2, 6, 2, 5, 7, 7, 3, 7, 7, 3, 7, 7, 5, 2, 6, 2, 7, 5, 7, 5, 5, 6], [7, 0, 0, 0, 0, 0, 0, 7, 6, 6, 2, 4, 7, 3, 7, 7, 7, 7, 3, 7, 4, 2, 6, 6, 7, 7, 7, 7, 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3], [3, 3, 1, 1, 1, 3, 3, 3, 8, 8, 8, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 8, 2, 8, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 8, 8, 8, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3]], "output": [[8, 8, 8, 3, 3, 3, 3, 3, 3], [8, 2, 8, 3, 3, 3, 3, 3, 3], [8, 8, 8, 3, 3, 3, 3, 3, 3], [3, 3, 3, 8, 8, 8, 3, 3, 3], [3, 3, 3, 8, 2, 8, 3, 3, 3], [3, 3, 3, 8, 8, 8, 3, 3, 3], [3, 3, 3, 8, 8, 8, 3, 3, 3], [3, 3, 3, 8, 2, 8, 3, 3, 3], [3, 3, 3, 8, 8, 8, 3, 3, 3], [8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 2, 8, 8, 2, 8, 8, 2, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8]]}, {"input": [[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 6, 6, 6, 1, 1, 1, 1, 1, 1, 1, 1], [1, 6, 1, 6, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 6, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 8, 9, 9, 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8, 8, 8], [8, 8, 8, 8, 8, 1, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 2, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [3, 8, 8, 8, 8, 2, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 2, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 2, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 2, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 2, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 2, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 2, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 1, 8, 8, 8, 8]], "output": [[8, 8, 8, 8, 8, 2, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 2, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 2, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 2, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [3, 3, 3, 8, 8, 2, 8, 8, 8, 8, 8, 8, 3, 3, 3, 3, 3, 3, 3], [8, 8, 3, 8, 8, 2, 8, 8, 8, 8, 8, 8, 3, 8, 8, 8, 8, 8, 8], [8, 8, 3, 8, 8, 8, 8, 8, 8, 8, 8, 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8, 8, 6, 8, 6, 8, 8, 4, 4, 4, 8, 8, 2, 8, 2, 8, 8], [8, 8, 8, 8, 9, 8, 8, 6, 8, 6, 8, 8, 8, 4, 8, 8, 8, 2, 2, 2, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2]]}, {"input": [[8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 1, 1, 1, 8, 8, 1, 8, 1, 8, 8, 9, 8, 9, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 1, 8, 8, 8, 1, 1, 8, 8, 8, 9, 9, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 1, 1, 1, 8, 8, 1, 8, 1, 8, 8, 9, 9, 9, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 2, 8, 2, 8, 8, 0, 8, 8, 8, 8, 8, 8, 7, 8, 8, 9, 8, 9, 8, 8], [8, 8, 8, 2, 8, 8, 8, 0, 0, 0, 8, 8, 8, 8, 7, 8, 8, 9, 9, 8, 8, 8], [8, 8, 2, 8, 2, 8, 8, 0, 8, 0, 8, 8, 7, 7, 7, 8, 8, 9, 9, 9, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 7, 8, 8, 8, 8, 1, 1, 1, 8, 8, 8, 6, 6, 8, 8, 0, 0, 0, 8, 8], [8, 8, 7, 7, 7, 8, 8, 8, 1, 8, 8, 8, 8, 8, 6, 8, 8, 0, 0, 0, 8, 8], [8, 8, 7, 8, 8, 8, 8, 1, 1, 1, 8, 8, 8, 6, 6, 8, 8, 0, 0, 0, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 4, 8, 4, 8, 8, 2, 2, 8, 8, 8, 5, 5, 8, 8, 8, 1, 8, 1, 8, 8], [8, 8, 4, 8, 4, 8, 8, 2, 2, 2, 8, 8, 5, 8, 8, 8, 8, 1, 1, 8, 8, 8], [8, 8, 4, 4, 4, 8, 8, 8, 2, 8, 8, 8, 5, 5, 8, 8, 8, 1, 8, 1, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 9, 8, 8, 8, 8, 6, 6, 6, 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7, 4, 6, 4, 4, 9, 6], [4, 9, 6, 4, 6, 6, 1, 7, 6, 7, 6, 6, 6, 6, 7, 6, 7, 1, 6, 6, 4, 6, 9, 4], [1, 4, 5, 1, 4, 4, 7, 6, 7, 5, 7, 6, 6, 7, 5, 7, 6, 7, 4, 4, 1, 5, 4, 1], [4, 4, 6, 5, 6, 4, 5, 1, 6, 7, 6, 4, 4, 6, 7, 6, 1, 5, 4, 6, 5, 6, 4, 4], [5, 4, 4, 4, 9, 9, 1, 7, 1, 6, 7, 5, 5, 7, 6, 1, 7, 1, 9, 9, 4, 4, 4, 5], [9, 5, 4, 1, 4, 6, 7, 1, 5, 7, 1, 7, 7, 1, 7, 5, 1, 7, 6, 4, 1, 4, 5, 9]], "output": [[9, 5, 4, 1, 4, 6, 7, 1, 5, 7, 1, 7, 7, 1, 7, 5, 1, 7, 6, 4, 1, 4, 5, 9], [5, 4, 4, 4, 9, 9, 1, 7, 1, 6, 7, 5, 5, 7, 6, 1, 7, 1, 9, 9, 4, 4, 4, 5], [4, 4, 6, 5, 6, 4, 5, 1, 6, 7, 6, 4, 4, 6, 7, 6, 1, 5, 4, 6, 5, 6, 4, 4], [1, 4, 5, 1, 4, 4, 7, 6, 7, 5, 7, 6, 6, 7, 5, 7, 6, 7, 4, 4, 1, 5, 4, 1], [4, 9, 6, 4, 6, 6, 1, 7, 6, 7, 6, 6, 6, 6, 7, 6, 7, 1, 6, 6, 4, 6, 9, 4], [6, 9, 4, 4, 6, 4, 7, 5, 4, 6, 6, 1, 1, 6, 6, 4, 5, 7, 4, 6, 4, 4, 9, 6], [7, 1, 5, 7, 1, 7, 5, 8, 8, 5, 3, 6, 6, 3, 5, 8, 8, 5, 7, 1, 7, 5, 1, 7], [1, 7, 1, 6, 7, 5, 8, 6, 6, 3, 3, 8, 8, 3, 3, 6, 6, 8, 5, 7, 6, 1, 7, 1], [5, 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7, 6, 1, 5, 4, 6, 5, 6, 4, 4], [5, 4, 4, 4, 9, 9, 1, 7, 1, 6, 7, 5, 5, 7, 6, 1, 7, 1, 9, 9, 4, 4, 4, 5], [9, 5, 4, 1, 4, 6, 7, 1, 5, 7, 1, 7, 7, 1, 7, 5, 1, 7, 6, 4, 1, 4, 5, 9]]}, {"input": [[7, 9, 5, 5, 3, 5, 6, 9, 9, 9, 5, 6, 6, 5, 9, 9, 9, 6, 5, 3, 5, 5, 9, 7], [9, 7, 5, 1, 5, 3, 9, 3, 8, 6, 6, 2, 2, 2, 6, 8, 3, 9, 3, 5, 1, 5, 7, 9], [5, 5, 1, 3, 9, 3, 9, 8, 9, 5, 3, 2, 2, 2, 5, 9, 8, 9, 3, 9, 3, 1, 5, 5], [5, 1, 3, 7, 9, 9, 9, 6, 5, 9, 6, 2, 2, 2, 9, 5, 6, 9, 9, 9, 7, 3, 1, 5], [2, 2, 2, 2, 2, 9, 5, 6, 3, 6, 3, 2, 2, 2, 6, 3, 6, 5, 9, 3, 9, 9, 5, 3], [2, 2, 2, 2, 2, 3, 6, 6, 3, 9, 8, 2, 2, 2, 9, 3, 6, 6, 3, 9, 9, 3, 3, 5], [2, 2, 2, 2, 2, 6, 9, 7, 9, 9, 4, 2, 2, 2, 9, 9, 7, 9, 6, 5, 9, 9, 9, 6], [2, 2, 2, 2, 2, 6, 7, 9, 9, 1, 1, 4, 4, 1, 1, 9, 9, 7, 6, 6, 6, 8, 3, 9], [2, 2, 2, 2, 2, 3, 9, 9, 1, 7, 4, 3, 3, 4, 7, 1, 9, 9, 3, 3, 5, 9, 8, 9], [2, 2, 2, 2, 2, 9, 9, 1, 7, 1, 9, 7, 7, 9, 1, 7, 2, 2, 2, 2, 9, 5, 6, 9], [5, 6, 3, 6, 3, 8, 4, 1, 4, 9, 3, 9, 9, 3, 9, 4, 2, 2, 2, 2, 6, 3, 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7, 3, 7, 7, 7, 7, 3, 7, 4, 2, 6, 6, 7, 7, 7, 7, 1, 5], [1, 7, 6, 5, 5, 7, 5, 7, 2, 6, 2, 5, 7, 7, 3, 7, 7, 3, 7, 7, 5, 2, 6, 2, 7, 5, 7, 5, 5, 6], [2, 5, 7, 7, 6, 5, 9, 7, 7, 7, 9, 4, 9, 6, 6, 3, 3, 6, 6, 9, 4, 9, 7, 7, 7, 9, 5, 6, 7, 7], [2, 5, 2, 7, 9, 9, 9, 9, 5, 7, 9, 9, 9, 9, 3, 6, 6, 3, 9, 9, 9, 9, 7, 5, 9, 9, 9, 9, 7, 2], [7, 7, 5, 5, 9, 6, 9, 5, 7, 7, 7, 7, 3, 6, 9, 6, 6, 9, 6, 3, 7, 7, 7, 7, 5, 9, 6, 9, 5, 5], [1, 7, 2, 2, 9, 9, 9, 6, 5, 7, 5, 7, 3, 3, 9, 9, 9, 9, 3, 3, 7, 5, 7, 5, 6, 9, 9, 9, 2, 2], [7, 9, 7, 9, 2, 5, 7, 7, 5, 1, 6, 6, 7, 7, 9, 4, 4, 9, 7, 7, 6, 6, 1, 5, 7, 7, 5, 2, 9, 7], [3, 9, 9, 7, 2, 5, 2, 7, 6, 5, 7, 6, 5, 7, 9, 9, 9, 9, 7, 5, 6, 7, 5, 6, 7, 2, 5, 2, 7, 9]]}, {"input": [[9, 2, 9, 6, 2, 4, 1, 6, 8, 7, 7, 1, 5, 6, 7, 3, 3, 7, 6, 5, 1, 0, 0, 0, 0, 0, 0, 0, 0, 9], [2, 9, 6, 6, 4, 4, 1, 1, 7, 8, 5, 5, 6, 6, 7, 6, 6, 7, 6, 6, 5, 0, 0, 0, 0, 0, 0, 0, 0, 6], [9, 6, 6, 6, 1, 1, 4, 0, 0, 0, 0, 7, 7, 7, 3, 6, 6, 3, 7, 7, 7, 0, 0, 0, 0, 0, 0, 0, 0, 6], [6, 6, 6, 2, 6, 1, 6, 0, 0, 0, 0, 5, 3, 6, 6, 5, 5, 6, 6, 3, 5, 0, 0, 0, 0, 0, 0, 0, 0, 6], [2, 4, 1, 6, 2, 1, 2, 0, 0, 0, 0, 3, 1, 8, 6, 1, 1, 6, 8, 1, 3, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 2, 2, 0, 0, 0, 0, 6, 8, 8, 9, 8, 8, 9, 8, 8, 6, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 2, 2, 9, 9, 7, 7, 3, 6, 6, 9, 6, 9, 9, 6, 9, 6, 6, 3, 7, 7, 9, 9, 2, 2, 6, 4], [6, 1, 6, 2, 1, 2, 9, 2, 3, 6, 6, 5, 1, 8, 9, 8, 8, 9, 8, 1, 5, 6, 6, 3, 2, 9, 2, 1, 2, 6], [8, 7, 7, 1, 5, 6, 7, 3, 8, 5, 5, 8, 9, 6, 3, 3, 3, 3, 6, 9, 8, 5, 5, 8, 3, 7, 6, 5, 1, 7], [7, 8, 5, 5, 6, 6, 7, 6, 5, 8, 4, 3, 6, 9, 3, 6, 6, 3, 9, 6, 3, 4, 8, 5, 6, 7, 6, 6, 5, 5], [7, 5, 8, 7, 7, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 3, 3, 3, 5, 8, 4, 5, 6, 3, 7, 7, 7, 8], [1, 5, 7, 5, 3, 0, 0, 0, 0, 0, 0, 0, 3, 6, 3, 1, 1, 3, 6, 3, 4, 5, 3, 8, 5, 6, 6, 3, 5, 7], [5, 6, 7, 3, 1, 0, 0, 0, 0, 0, 0, 0, 8, 8, 6, 8, 8, 6, 8, 8, 3, 3, 6, 9, 1, 6, 8, 1, 3, 7], [6, 6, 7, 6, 8, 0, 0, 0, 0, 0, 0, 0, 8, 1, 7, 8, 8, 7, 1, 8, 6, 3, 9, 6, 8, 9, 8, 8, 6, 7], [7, 7, 3, 6, 6, 0, 0, 0, 0, 0, 0, 0, 6, 7, 7, 7, 7, 7, 7, 6, 3, 3, 3, 3, 9, 6, 9, 6, 6, 3], [3, 6, 6, 5, 1, 0, 0, 0, 0, 0, 0, 0, 8, 8, 7, 8, 8, 7, 8, 8, 1, 3, 6, 3, 8, 9, 8, 1, 5, 6], [3, 6, 6, 5, 1, 8, 9, 8, 3, 6, 3, 1, 8, 8, 7, 8, 8, 7, 8, 8, 1, 3, 6, 3, 8, 9, 8, 1, 5, 6], [7, 7, 3, 6, 6, 9, 6, 9, 3, 3, 3, 3, 6, 7, 7, 7, 7, 7, 7, 6, 3, 3, 3, 3, 9, 6, 9, 6, 6, 3], [6, 6, 7, 6, 8, 8, 9, 8, 6, 9, 3, 6, 8, 1, 7, 8, 8, 7, 1, 8, 6, 3, 9, 6, 8, 9, 8, 8, 6, 7], [5, 6, 7, 3, 1, 8, 6, 1, 9, 6, 3, 3, 8, 8, 6, 8, 8, 6, 8, 8, 3, 3, 6, 9, 1, 6, 8, 1, 3, 7], [1, 5, 7, 5, 3, 6, 6, 5, 8, 3, 5, 4, 3, 6, 3, 1, 1, 3, 6, 3, 4, 5, 3, 8, 5, 6, 6, 3, 5, 7], [7, 5, 8, 7, 7, 7, 3, 6, 5, 4, 8, 5, 3, 3, 3, 3, 3, 3, 3, 3, 5, 8, 4, 5, 6, 3, 7, 7, 7, 8], [7, 8, 5, 5, 6, 6, 7, 6, 5, 8, 4, 3, 6, 9, 3, 6, 6, 3, 9, 6, 3, 4, 8, 5, 6, 7, 6, 6, 5, 5], [8, 7, 7, 1, 5, 6, 7, 3, 8, 5, 5, 8, 9, 6, 3, 3, 3, 3, 6, 9, 8, 5, 5, 8, 3, 7, 6, 5, 1, 7], [6, 1, 6, 2, 1, 2, 9, 2, 3, 6, 6, 5, 1, 8, 9, 8, 8, 9, 8, 1, 5, 6, 6, 3, 2, 9, 2, 1, 2, 6], [1, 1, 4, 6, 2, 2, 9, 9, 7, 7, 3, 6, 6, 9, 6, 9, 9, 6, 9, 6, 6, 3, 7, 7, 9, 9, 2, 2, 6, 4], [4, 4, 1, 1, 1, 2, 2, 2, 6, 6, 7, 6, 8, 8, 9, 8, 8, 9, 8, 8, 6, 7, 6, 6, 2, 2, 2, 1, 1, 1], [2, 4, 1, 6, 2, 1, 2, 1, 5, 6, 7, 3, 1, 8, 6, 1, 1, 6, 8, 1, 3, 7, 6, 5, 1, 2, 1, 2, 6, 1], [6, 6, 6, 2, 6, 1, 6, 2, 1, 5, 7, 5, 3, 6, 6, 5, 5, 6, 6, 3, 5, 7, 5, 1, 2, 6, 1, 6, 2, 6], [9, 6, 6, 6, 1, 1, 4, 6, 7, 5, 8, 7, 7, 7, 3, 6, 6, 3, 7, 7, 7, 8, 5, 7, 6, 4, 1, 1, 6, 6]], "output": [[9, 2, 9, 6, 2, 4, 1, 6, 8, 7, 7, 1, 5, 6, 7, 3, 3, 7, 6, 5, 1, 7, 7, 8, 6, 1, 4, 2, 6, 9], [2, 9, 6, 6, 4, 4, 1, 1, 7, 8, 5, 5, 6, 6, 7, 6, 6, 7, 6, 6, 5, 5, 8, 7, 1, 1, 4, 4, 6, 6], [9, 6, 6, 6, 1, 1, 4, 6, 7, 5, 8, 7, 7, 7, 3, 6, 6, 3, 7, 7, 7, 8, 5, 7, 6, 4, 1, 1, 6, 6], [6, 6, 6, 2, 6, 1, 6, 2, 1, 5, 7, 5, 3, 6, 6, 5, 5, 6, 6, 3, 5, 7, 5, 1, 2, 6, 1, 6, 2, 6], [2, 4, 1, 6, 2, 1, 2, 1, 5, 6, 7, 3, 1, 8, 6, 1, 1, 6, 8, 1, 3, 7, 6, 5, 1, 2, 1, 2, 6, 1], [4, 4, 1, 1, 1, 2, 2, 2, 6, 6, 7, 6, 8, 8, 9, 8, 8, 9, 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4, 4, 5, 3], [8, 5, 5, 3, 4, 8, 8, 8, 3, 4, 4, 6, 8, 6, 8, 4, 4, 8, 6, 8, 6, 4, 4, 3, 8, 8, 8, 4, 3, 5], [8, 6, 4, 4, 1, 4, 7, 5, 6, 8, 7, 7, 6, 2, 1, 1, 1, 1, 2, 6, 7, 7, 8, 6, 5, 7, 4, 1, 4, 4], [8, 8, 4, 8, 4, 1, 5, 7, 8, 6, 7, 5, 4, 6, 1, 8, 8, 1, 6, 4, 5, 7, 6, 8, 7, 5, 1, 4, 8, 4]]}], "train": [{"input": [[6, 1, 2, 2, 4, 6, 2, 6, 8, 2, 8, 3, 3, 2, 3, 5, 5, 3, 2, 3, 3, 8, 2, 8, 6, 2, 6, 4, 2, 2], [6, 6, 2, 7, 6, 4, 6, 2, 2, 8, 3, 8, 3, 3, 5, 5, 5, 5, 3, 3, 8, 3, 8, 2, 2, 6, 4, 6, 7, 2], [1, 7, 6, 1, 2, 6, 4, 6, 8, 1, 8, 2, 3, 5, 5, 5, 5, 5, 5, 3, 2, 8, 1, 8, 6, 4, 6, 2, 1, 6], [7, 2, 6, 6, 6, 2, 6, 4, 1, 8, 2, 8, 5, 5, 5, 5, 5, 5, 5, 5, 8, 2, 8, 1, 4, 6, 2, 6, 6, 6], [7, 2, 8, 1, 6, 1, 7, 2, 3, 3, 3, 5, 7, 6, 4, 4, 4, 4, 6, 7, 5, 3, 3, 3, 2, 7, 1, 6, 1, 8], [2, 7, 1, 8, 6, 6, 2, 2, 2, 3, 5, 5, 6, 7, 4, 4, 4, 4, 7, 6, 5, 5, 3, 2, 2, 2, 6, 6, 8, 1], [8, 1, 7, 2, 2, 7, 6, 1, 3, 5, 5, 5, 6, 7, 7, 6, 6, 7, 7, 6, 5, 5, 5, 3, 1, 6, 7, 2, 2, 7], [1, 8, 2, 7, 7, 1, 6, 6, 5, 5, 5, 5, 7, 6, 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1], [8, 3, 8, 2, 3, 5, 5, 5, 7, 7, 6, 6, 4, 5, 7, 7, 7, 7, 5, 4, 6, 6, 7, 7, 5, 5, 5, 3, 2, 8], [3, 8, 2, 8, 5, 5, 5, 5, 7, 7, 8, 6, 5, 4, 7, 7, 7, 7, 4, 5, 6, 8, 7, 7, 5, 5, 5, 5, 8, 2], [3, 3, 3, 5, 7, 6, 6, 7, 8, 8, 8, 6, 6, 6, 5, 7, 7, 5, 6, 6, 6, 8, 8, 8, 7, 6, 6, 7, 5, 3], [2, 3, 5, 5, 6, 7, 7, 6, 8, 8, 6, 8, 8, 6, 7, 2, 2, 7, 6, 8, 8, 6, 8, 8, 6, 7, 7, 6, 5, 5], [3, 5, 5, 5, 4, 4, 7, 6, 8, 6, 8, 8, 7, 7, 6, 6, 6, 6, 7, 7, 8, 8, 6, 8, 6, 7, 4, 4, 5, 5], [5, 5, 5, 5, 4, 4, 6, 7, 6, 8, 8, 8, 7, 7, 8, 6, 6, 8, 7, 7, 8, 8, 8, 6, 7, 6, 4, 4, 5, 5], [5, 5, 5, 5, 4, 4, 6, 7, 6, 8, 8, 8, 7, 7, 8, 6, 6, 8, 7, 7, 8, 8, 8, 6, 7, 6, 4, 4, 5, 5], [3, 5, 5, 5, 4, 4, 7, 6, 8, 6, 8, 8, 7, 7, 6, 6, 6, 6, 7, 7, 8, 8, 6, 8, 6, 7, 4, 4, 5, 5], [2, 3, 5, 5, 6, 7, 7, 6, 8, 8, 6, 8, 8, 6, 7, 2, 2, 7, 6, 8, 8, 6, 8, 8, 6, 7, 7, 6, 5, 5], [3, 3, 3, 5, 7, 6, 6, 7, 8, 8, 8, 6, 6, 6, 5, 7, 7, 5, 6, 6, 6, 8, 8, 8, 7, 6, 6, 7, 5, 3], [3, 8, 2, 8, 5, 5, 5, 5, 7, 7, 8, 6, 5, 4, 7, 7, 7, 7, 4, 5, 6, 8, 7, 7, 5, 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4, 6, 6, 1, 7, 1, 1, 7, 4, 4, 7, 7, 8], [1, 4, 3, 2, 7, 4, 4, 7, 5, 5, 1, 1, 6, 4, 1, 1, 1, 1, 4, 6, 1, 1, 5, 5, 7, 4, 4, 7, 2, 3], [4, 1, 2, 3, 4, 7, 7, 4, 9, 9, 9, 9, 4, 6, 1, 1, 1, 1, 6, 4, 1, 1, 5, 5, 4, 7, 7, 4, 3, 2], [6, 9, 9, 9, 9, 9, 7, 8, 9, 9, 9, 9, 1, 6, 5, 8, 8, 5, 6, 1, 4, 6, 6, 6, 8, 7, 2, 3, 8, 8], [6, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 1, 1, 8, 5, 5, 8, 1, 1, 6, 4, 6, 4, 7, 8, 3, 2, 8, 8], [8, 8, 6, 9, 9, 9, 9, 9, 9, 9, 9, 9, 2, 2, 1, 6, 6, 1, 2, 2, 1, 1, 4, 6, 2, 3, 4, 1, 6, 6], [8, 8, 6, 9, 9, 9, 9, 9, 9, 9, 9, 9, 2, 2, 1, 1, 1, 1, 2, 2, 1, 1, 6, 4, 3, 2, 1, 4, 6, 6], [1, 1, 5, 9, 9, 9, 9, 9, 9, 6, 3, 3, 8, 8, 8, 2, 2, 8, 8, 8, 3, 3, 6, 4, 4, 6, 4, 6, 5, 5], [1, 1, 5, 9, 9, 9, 9, 9, 9, 4, 3, 3, 8, 8, 2, 8, 8, 2, 8, 8, 3, 3, 4, 7, 6, 4, 6, 6, 5, 5], [1, 7, 1, 1, 6, 4, 1, 1, 8, 6, 4, 6, 8, 2, 8, 8, 8, 8, 2, 8, 6, 4, 6, 8, 1, 1, 4, 6, 1, 1], [7, 1, 1, 1, 4, 6, 1, 1, 6, 8, 7, 4, 2, 8, 8, 8, 8, 8, 8, 2, 4, 7, 8, 6, 1, 1, 6, 4, 1, 1], [6, 6, 6, 4, 1, 1, 2, 2, 5, 4, 6, 6, 4, 6, 3, 3, 3, 3, 6, 4, 6, 6, 4, 5, 2, 2, 1, 1, 4, 6], [4, 6, 4, 6, 6, 1, 2, 2, 4, 5, 6, 6, 7, 4, 3, 3, 3, 3, 4, 7, 6, 6, 5, 4, 2, 2, 1, 6, 6, 4], [6, 4, 1, 1, 5, 8, 1, 1, 6, 6, 5, 4, 8, 6, 4, 6, 6, 4, 6, 8, 4, 5, 6, 6, 1, 1, 8, 5, 1, 1], [4, 6, 1, 1, 8, 5, 6, 1, 6, 6, 4, 5, 6, 8, 7, 4, 4, 7, 8, 6, 5, 4, 6, 6, 1, 6, 5, 8, 1, 1], [4, 6, 1, 1, 8, 5, 6, 1, 6, 6, 4, 5, 6, 8, 7, 4, 4, 7, 8, 6, 5, 4, 6, 6, 1, 6, 5, 8, 1, 1], [6, 4, 1, 1, 5, 8, 1, 1, 6, 6, 5, 4, 8, 6, 4, 6, 6, 4, 6, 8, 4, 5, 6, 6, 1, 1, 8, 5, 1, 1], [4, 6, 4, 6, 6, 1, 2, 2, 4, 5, 6, 6, 7, 4, 3, 3, 3, 3, 4, 7, 6, 6, 5, 4, 2, 2, 1, 6, 6, 4], [6, 6, 6, 4, 1, 1, 2, 2, 5, 4, 6, 6, 4, 6, 3, 3, 3, 3, 6, 4, 6, 6, 4, 5, 2, 2, 1, 1, 4, 6], [7, 1, 1, 1, 4, 6, 1, 1, 6, 8, 7, 4, 2, 8, 8, 8, 8, 8, 8, 2, 4, 7, 8, 6, 1, 1, 6, 4, 1, 1], [1, 7, 1, 1, 6, 4, 1, 1, 8, 6, 4, 6, 8, 2, 8, 8, 8, 8, 2, 8, 6, 4, 6, 8, 1, 1, 4, 6, 1, 1], [1, 1, 5, 5, 6, 6, 4, 6, 7, 4, 3, 3, 8, 8, 2, 8, 8, 2, 8, 8, 3, 3, 4, 7, 6, 4, 6, 6, 5, 5], [1, 1, 5, 5, 6, 4, 6, 4, 4, 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6, 6, 9], [2, 6, 9, 2, 9, 8, 6, 8, 9, 9], [2, 6, 6, 6, 2, 6, 6, 8, 9, 9], [6, 9, 2, 6, 6, 8, 8, 6, 9, 9], [2, 8, 3, 2, 6, 6, 2, 9, 8, 4], [8, 2, 8, 3, 2, 6, 9, 6, 4, 8], [3, 8, 8, 3, 9, 6, 6, 6, 9, 5], [2, 3, 3, 8, 6, 2, 2, 6, 9, 9]]}, {"input": [[3, 3, 2, 2, 8, 9, 9, 8, 8, 5, 5, 5, 1, 3, 3, 1, 1, 3, 3, 1, 5, 7, 7, 7, 7, 7, 9, 8, 2, 2], [1, 1, 2, 1, 9, 8, 8, 9, 5, 2, 5, 5, 3, 1, 1, 9, 9, 1, 1, 3, 5, 7, 7, 7, 7, 7, 8, 9, 1, 2], [2, 2, 1, 3, 9, 8, 8, 9, 8, 5, 2, 5, 3, 1, 9, 2, 2, 9, 1, 3, 5, 7, 7, 7, 7, 7, 8, 9, 3, 1], [2, 9, 1, 3, 8, 9, 9, 8, 5, 8, 5, 8, 1, 9, 1, 9, 9, 1, 9, 1, 8, 7, 7, 7, 7, 7, 9, 8, 3, 1], [8, 3, 8, 1, 3, 3, 1, 2, 1, 3, 3, 1, 9, 4, 9, 8, 8, 9, 4, 9, 1, 7, 7, 7, 7, 7, 3, 3, 1, 8], [3, 8, 3, 8, 1, 1, 2, 2, 3, 1, 1, 9, 2, 8, 8, 9, 9, 8, 8, 2, 9, 7, 7, 7, 7, 7, 1, 1, 8, 3], [8, 3, 8, 3, 9, 2, 1, 3, 3, 1, 9, 1, 9, 9, 8, 4, 4, 8, 9, 9, 1, 7, 7, 7, 7, 7, 2, 9, 3, 8], [1, 8, 3, 8, 2, 2, 1, 3, 1, 9, 2, 9, 9, 9, 2, 9, 9, 2, 9, 9, 9, 2, 9, 1, 3, 1, 2, 2, 8, 3], [8, 5, 8, 5, 1, 3, 3, 1, 3, 2, 6, 2, 9, 9, 6, 9, 9, 6, 9, 9, 2, 6, 2, 3, 1, 3, 3, 1, 5, 8], [5, 2, 5, 8, 3, 1, 1, 9, 1, 1, 2, 2, 9, 9, 4, 6, 6, 4, 9, 9, 2, 2, 1, 1, 9, 1, 1, 3, 8, 5], [5, 5, 2, 5, 3, 1, 9, 2, 6, 3, 1, 2, 6, 4, 9, 9, 9, 9, 4, 6, 2, 1, 3, 6, 2, 9, 1, 3, 5, 2], [5, 5, 5, 8, 1, 9, 1, 9, 3, 6, 1, 3, 9, 6, 9, 9, 9, 9, 6, 9, 3, 1, 6, 3, 9, 1, 9, 1, 8, 5], [1, 3, 3, 1, 9, 2, 9, 9, 8, 4, 3, 2, 3, 2, 2, 2, 2, 2, 2, 3, 2, 3, 4, 8, 9, 9, 2, 9, 1, 3], [3, 1, 1, 9, 4, 8, 9, 9, 4, 8, 2, 3, 1, 1, 2, 6, 6, 2, 1, 1, 3, 2, 8, 4, 9, 9, 8, 4, 9, 1], [3, 1, 9, 1, 9, 8, 8, 2, 3, 2, 8, 4, 6, 3, 1, 2, 2, 1, 3, 6, 4, 8, 2, 3, 2, 8, 8, 9, 1, 9], [1, 9, 2, 9, 8, 9, 4, 9, 2, 3, 4, 8, 3, 6, 1, 3, 3, 1, 6, 3, 8, 4, 3, 2, 9, 4, 9, 8, 9, 2], [1, 9, 2, 9, 8, 9, 4, 9, 2, 3, 4, 8, 3, 6, 1, 3, 3, 1, 6, 3, 8, 4, 3, 2, 9, 4, 9, 8, 9, 2], [3, 1, 9, 1, 9, 8, 8, 2, 3, 2, 8, 4, 6, 3, 1, 2, 2, 1, 3, 6, 4, 8, 2, 3, 2, 8, 8, 9, 1, 9], [3, 1, 1, 9, 4, 8, 9, 9, 4, 8, 2, 3, 1, 1, 2, 6, 6, 2, 1, 1, 3, 2, 8, 4, 9, 9, 8, 4, 9, 1], [1, 3, 3, 1, 9, 2, 9, 9, 8, 4, 3, 2, 3, 2, 2, 2, 2, 2, 2, 3, 2, 3, 4, 8, 9, 9, 2, 9, 1, 3], [5, 5, 5, 8, 1, 9, 1, 9, 3, 6, 1, 3, 9, 6, 9, 9, 9, 9, 6, 9, 3, 1, 6, 3, 9, 1, 9, 1, 8, 5], [5, 5, 2, 5, 3, 1, 9, 2, 6, 3, 1, 2, 6, 4, 9, 9, 9, 9, 4, 6, 2, 1, 3, 6, 2, 9, 1, 3, 5, 2], [5, 2, 5, 8, 3, 1, 1, 9, 1, 1, 2, 2, 9, 9, 4, 6, 6, 4, 9, 9, 2, 2, 1, 1, 9, 1, 1, 3, 8, 5], [8, 5, 8, 5, 1, 3, 3, 1, 3, 2, 6, 2, 9, 9, 6, 9, 9, 6, 9, 9, 2, 6, 2, 3, 1, 3, 3, 1, 5, 8], [1, 8, 3, 8, 2, 2, 1, 3, 1, 9, 2, 9, 9, 9, 2, 9, 9, 2, 9, 9, 9, 2, 9, 1, 3, 1, 2, 2, 8, 3], [8, 3, 8, 3, 9, 2, 1, 3, 3, 1, 9, 1, 9, 9, 8, 4, 4, 8, 9, 9, 1, 9, 1, 3, 3, 1, 2, 9, 3, 8], [3, 8, 3, 8, 1, 1, 2, 2, 3, 1, 1, 9, 2, 8, 8, 9, 9, 8, 8, 2, 9, 1, 1, 3, 2, 2, 1, 1, 8, 3], [8, 3, 8, 1, 3, 3, 1, 2, 1, 3, 3, 1, 9, 4, 9, 8, 8, 9, 4, 9, 1, 3, 3, 1, 2, 1, 3, 3, 1, 8], [2, 9, 1, 3, 8, 9, 9, 8, 5, 8, 5, 8, 1, 9, 1, 9, 9, 1, 9, 1, 8, 5, 8, 5, 8, 9, 9, 8, 3, 1], [2, 2, 1, 3, 9, 8, 8, 9, 8, 5, 2, 5, 3, 1, 9, 2, 2, 9, 1, 3, 5, 2, 5, 8, 9, 8, 8, 9, 3, 1]], "output": [[5, 5, 8, 8, 9], [5, 2, 5, 9, 8], [2, 5, 8, 9, 8], [5, 8, 5, 8, 9], [3, 3, 1, 2, 1], [1, 1, 3, 2, 2], [9, 1, 3, 3, 1]]}, {"input": [[3, 1, 8, 8, 6, 8, 8, 6, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 8, 8, 8, 6, 8, 8, 6, 8, 8], [2, 3, 8, 3, 8, 6, 1, 8, 8, 9, 9, 8, 2, 9, 8, 8, 8, 8, 9, 2, 8, 9, 9, 8, 8, 1, 6, 8, 3, 8], [1, 8, 3, 1, 8, 1, 6, 8, 4, 8, 9, 8, 9, 8, 9, 8, 8, 9, 8, 9, 8, 9, 8, 4, 8, 6, 1, 8, 1, 3], [8, 2, 2, 3, 6, 8, 8, 6, 8, 4, 8, 8, 9, 8, 9, 9, 9, 9, 8, 9, 8, 8, 4, 8, 6, 8, 8, 6, 3, 2], [3, 8, 8, 3, 3, 1, 3, 8, 9, 2, 9, 9, 9, 8, 9, 8, 8, 9, 8, 9, 9, 9, 2, 9, 8, 3, 1, 3, 3, 8], [8, 3, 1, 8, 2, 3, 8, 8, 9, 9, 8, 8, 8, 4, 8, 9, 9, 8, 4, 8, 8, 8, 9, 9, 8, 8, 3, 2, 8, 1], [8, 1, 3, 8, 2, 8, 3, 1, 9, 8, 9, 9, 9, 5, 4, 8, 8, 4, 5, 9, 9, 9, 8, 9, 1, 3, 8, 2, 8, 3], [3, 8, 8, 3, 8, 1, 2, 3, 9, 8, 8, 9, 5, 9, 8, 9, 9, 8, 9, 5, 9, 8, 8, 9, 3, 2, 1, 8, 3, 8], [8, 8, 4, 8, 9, 9, 9, 9, 2, 9, 8, 8, 5, 2, 5, 1, 1, 5, 2, 5, 8, 8, 9, 2, 9, 9, 9, 9, 8, 4], [8, 9, 8, 4, 2, 9, 8, 8, 8, 2, 8, 3, 2, 5, 4, 5, 5, 4, 5, 2, 3, 8, 2, 8, 8, 8, 9, 2, 4, 8], [8, 9, 9, 8, 9, 8, 9, 8, 8, 8, 2, 9, 5, 4, 5, 2, 2, 5, 4, 5, 9, 2, 8, 8, 8, 9, 8, 9, 8, 9], [9, 8, 8, 8, 9, 8, 9, 9, 8, 8, 8, 2, 1, 5, 2, 5, 5, 2, 5, 1, 2, 8, 8, 8, 9, 9, 8, 9, 8, 8], [9, 2, 9, 9, 9, 8, 9, 5, 8, 8, 6, 8, 2, 9, 3, 8, 8, 3, 9, 2, 8, 6, 8, 8, 5, 9, 8, 9, 9, 9], [9, 9, 8, 8, 8, 4, 5, 9, 8, 8, 4, 6, 8, 2, 8, 8, 8, 8, 2, 8, 6, 4, 8, 8, 9, 5, 4, 8, 8, 8], [9, 8, 9, 9, 9, 8, 4, 8, 6, 4, 8, 8, 8, 8, 2, 9, 9, 2, 8, 8, 8, 8, 4, 6, 8, 4, 8, 9, 9, 9], [9, 8, 8, 9, 8, 9, 8, 9, 8, 6, 8, 8, 8, 8, 8, 2, 2, 8, 8, 8, 8, 8, 6, 8, 9, 8, 9, 8, 9, 8], [9, 8, 8, 9, 8, 9, 8, 9, 8, 6, 8, 8, 8, 8, 8, 2, 2, 8, 8, 8, 8, 8, 6, 8, 9, 8, 9, 8, 9, 8], [9, 8, 9, 9, 9, 8, 4, 8, 6, 4, 8, 8, 8, 8, 2, 9, 9, 2, 8, 8, 8, 8, 4, 6, 8, 4, 8, 9, 9, 9], [9, 9, 8, 8, 8, 4, 5, 9, 8, 8, 4, 6, 8, 2, 8, 8, 8, 8, 2, 8, 6, 4, 8, 8, 9, 5, 4, 8, 8, 8], [9, 2, 9, 9, 9, 8, 9, 5, 8, 8, 6, 8, 2, 9, 3, 8, 8, 3, 9, 2, 8, 6, 8, 8, 5, 9, 8, 9, 9, 9], [9, 8, 8, 8, 9, 8, 9, 9, 8, 8, 8, 2, 1, 5, 2, 5, 5, 2, 5, 1, 2, 8, 8, 8, 9, 9, 8, 9, 8, 8], [8, 9, 9, 8, 9, 8, 9, 8, 8, 8, 2, 9, 5, 4, 5, 2, 2, 5, 4, 5, 9, 2, 8, 8, 8, 9, 8, 9, 8, 9], [8, 9, 8, 4, 2, 9, 8, 8, 8, 2, 8, 3, 2, 5, 4, 5, 5, 4, 5, 2, 3, 8, 2, 8, 8, 8, 9, 2, 4, 8], [8, 8, 4, 8, 9, 9, 9, 9, 2, 9, 8, 8, 5, 2, 5, 1, 1, 5, 2, 5, 8, 8, 9, 2, 9, 9, 9, 9, 8, 4], [3, 8, 8, 3, 8, 7, 7, 7, 7, 8, 8, 9, 5, 9, 8, 9, 9, 8, 9, 5, 9, 8, 8, 9, 3, 2, 1, 8, 3, 8], [8, 1, 3, 8, 2, 7, 7, 7, 7, 8, 9, 9, 9, 5, 4, 8, 8, 4, 5, 9, 9, 9, 8, 9, 1, 3, 8, 2, 8, 3], [8, 3, 1, 8, 2, 7, 7, 7, 7, 9, 8, 8, 8, 4, 8, 9, 9, 8, 4, 8, 8, 8, 9, 9, 8, 8, 3, 2, 8, 1], [3, 8, 8, 3, 3, 7, 7, 7, 7, 2, 9, 9, 9, 8, 9, 8, 8, 9, 8, 9, 9, 9, 2, 9, 8, 3, 1, 3, 3, 8], [8, 2, 2, 3, 6, 8, 8, 6, 8, 4, 8, 8, 9, 8, 9, 9, 9, 9, 8, 9, 8, 8, 4, 8, 6, 8, 8, 6, 3, 2], [1, 8, 3, 1, 8, 1, 6, 8, 4, 8, 9, 8, 9, 8, 9, 8, 8, 9, 8, 9, 8, 9, 8, 4, 8, 6, 1, 8, 1, 3]], "output": [[1, 2, 3, 9], [8, 3, 1, 9], [3, 8, 8, 9], [1, 3, 8, 9]]}, {"input": [[2, 9, 2, 9, 6, 4, 6, 2, 1, 2, 6, 6, 1, 1, 9, 4, 4, 9, 1, 1, 6, 6, 2, 1, 2, 6, 4, 6, 9, 2], [5, 5, 9, 5, 4, 6, 6, 6, 3, 6, 6, 6, 1, 1, 9, 9, 9, 9, 1, 1, 6, 6, 6, 3, 6, 6, 6, 4, 5, 9], [9, 9, 5, 9, 6, 6, 6, 4, 3, 2, 6, 2, 9, 9, 8, 4, 4, 8, 9, 9, 2, 6, 2, 3, 4, 6, 6, 6, 9, 5], [9, 9, 5, 2, 2, 6, 4, 6, 2, 3, 3, 1, 4, 9, 9, 8, 8, 9, 9, 4, 1, 3, 3, 2, 6, 4, 6, 2, 2, 5], [9, 8, 1, 8, 2, 9, 5, 9, 1, 1, 9, 4, 6, 6, 6, 6, 6, 6, 6, 6, 4, 9, 1, 1, 9, 5, 9, 2, 8, 1], [8, 9, 1, 1, 5, 5, 9, 2, 1, 1, 9, 9, 9, 9, 6, 6, 6, 6, 9, 9, 9, 9, 1, 1, 2, 9, 5, 5, 1, 1], [1, 1, 9, 8, 9, 9, 5, 9, 9, 9, 8, 9, 9, 1, 9, 6, 6, 9, 1, 9, 9, 8, 9, 9, 9, 5, 9, 9, 8, 9], [8, 1, 8, 9, 9, 9, 5, 2, 4, 9, 4, 8, 1, 9, 9, 6, 6, 9, 9, 1, 8, 4, 9, 4, 2, 5, 9, 9, 9, 8], [1, 3, 3, 2, 1, 1, 9, 4, 9, 9, 3, 4, 8, 8, 3, 8, 8, 3, 8, 8, 4, 3, 9, 9, 4, 9, 1, 1, 2, 3], [2, 6, 2, 3, 1, 1, 9, 9, 4, 4, 4, 8, 8, 8, 6, 3, 3, 6, 8, 8, 8, 4, 4, 4, 9, 9, 1, 1, 3, 2], [6, 6, 6, 3, 9, 9, 8, 4, 8, 9, 4, 9, 3, 6, 8, 8, 8, 8, 6, 3, 9, 4, 9, 8, 4, 8, 9, 9, 3, 6], [6, 6, 2, 1, 4, 9, 9, 8, 9, 3, 4, 9, 8, 3, 8, 8, 8, 8, 3, 8, 9, 4, 3, 9, 8, 9, 9, 4, 1, 2], [1, 1, 9, 4, 6, 9, 9, 1, 9, 9, 4, 1, 9, 9, 8, 4, 4, 8, 9, 9, 1, 4, 9, 9, 1, 9, 9, 6, 4, 9], [1, 1, 9, 9, 6, 9, 1, 9, 9, 9, 1, 4, 4, 4, 4, 3, 3, 4, 4, 4, 4, 1, 9, 9, 9, 1, 9, 6, 9, 9], [9, 9, 8, 9, 6, 6, 9, 9, 4, 1, 9, 9, 3, 9, 4, 9, 9, 4, 9, 3, 9, 9, 1, 4, 9, 9, 6, 6, 9, 8], [4, 9, 4, 8, 6, 6, 6, 6, 1, 4, 9, 9, 9, 8, 4, 9, 9, 4, 8, 9, 9, 9, 4, 1, 6, 6, 6, 6, 8, 4], [4, 9, 4, 8, 6, 6, 6, 6, 1, 4, 9, 9, 9, 8, 4, 9, 9, 4, 8, 9, 9, 9, 4, 1, 6, 6, 6, 6, 8, 4], [9, 9, 8, 9, 6, 6, 9, 9, 4, 1, 9, 9, 3, 9, 4, 9, 9, 4, 9, 3, 9, 9, 1, 4, 9, 9, 6, 6, 9, 8], [1, 1, 9, 9, 6, 9, 1, 9, 9, 9, 1, 4, 4, 4, 4, 3, 3, 4, 4, 4, 4, 1, 9, 9, 9, 1, 9, 6, 9, 9], [1, 1, 9, 4, 6, 9, 9, 1, 9, 9, 4, 1, 9, 9, 8, 4, 4, 8, 9, 9, 1, 4, 9, 9, 1, 9, 9, 6, 4, 9], [6, 6, 2, 1, 4, 9, 9, 8, 9, 3, 4, 9, 8, 3, 8, 8, 8, 8, 3, 8, 9, 7, 7, 7, 7, 7, 7, 7, 7, 2], [6, 6, 6, 3, 9, 9, 8, 4, 8, 9, 4, 9, 3, 6, 8, 8, 8, 8, 6, 3, 9, 7, 7, 7, 7, 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[0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 5, 5, 5, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]], "f8b3ba0a": [[[4], [1], [8]]], "f8c80d96": [[[4, 4, 4, 4, 4, 4, 5, 5, 4, 5], [5, 5, 5, 5, 5, 4, 5, 5, 4, 5], [5, 5, 5, 5, 5, 4, 5, 5, 4, 5], [4, 4, 4, 5, 5, 4, 5, 5, 4, 5], [5, 5, 4, 5, 5, 4, 5, 5, 4, 5], [5, 5, 4, 5, 5, 4, 5, 5, 4, 5], [4, 4, 4, 5, 5, 4, 5, 5, 4, 5], [5, 5, 5, 5, 5, 4, 5, 5, 4, 5], [5, 5, 5, 5, 5, 4, 5, 5, 4, 5], [4, 4, 4, 4, 4, 4, 5, 5, 4, 5]]], "f8ff0b80": [[[6], [1], [3]]], "f9012d9b": [[[1, 8, 8], [8, 8, 1], [8, 1, 8]]], "fafffa47": [[[0, 0, 0], [2, 0, 0], [0, 2, 0]]], "fcb5c309": [[[8, 8, 8, 8, 8, 8, 8, 8], [8, 0, 8, 0, 8, 0, 0, 8], [8, 0, 0, 0, 0, 0, 0, 8], [8, 0, 0, 0, 0, 0, 0, 8], [8, 0, 0, 0, 0, 0, 0, 8], [8, 0, 8, 0, 0, 0, 0, 8], [8, 0, 0, 0, 0, 8, 0, 8], [8, 8, 8, 8, 8, 8, 8, 8]]], "fcc82909": [[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 1, 0, 0, 0, 0, 2, 9, 0, 0], [2, 1, 0, 0, 0, 0, 1, 6, 0, 0], [3, 3, 0, 4, 7, 0, 3, 3, 0, 0], [3, 3, 0, 8, 4, 0, 3, 3, 0, 0], [0, 0, 0, 3, 3, 0, 3, 3, 0, 0], [0, 0, 0, 3, 3, 0, 3, 3, 0, 0], [0, 0, 0, 3, 3, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]], "feca6190": [[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 7], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 7, 8], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 7, 8, 9], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 7, 8, 9, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 7, 8, 9, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 7, 8, 9, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 7, 8, 9, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 7, 8, 9, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 7, 8, 9, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 7, 8, 9, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 6, 7, 8, 9, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 6, 7, 8, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 6, 7, 8, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 6, 7, 8, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 6, 7, 8, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 6, 7, 8, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 6, 7, 8, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 6, 7, 8, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]], "ff28f65a": [[[1, 0, 1], [0, 1, 0], [0, 0, 0]], [[1, 0, 1], [0, 1, 0], [1, 0, 0]], [[1, 0, 1], [0, 1, 0], [1, 0, 1]]], "ff805c23": [[[8, 8, 8, 8, 8], [0, 0, 8, 8, 0], [0, 8, 0, 0, 8], [8, 8, 8, 8, 8], [8, 0, 8, 8, 0]]]} \ No newline at end of file diff --git a/models/common.py b/models/common.py new file mode 100644 index 0000000..1a04505 --- /dev/null +++ b/models/common.py @@ -0,0 +1,32 @@ +import math + +import torch +from torch import nn + + +def trunc_normal_init_(tensor: torch.Tensor, std: float = 1.0, lower: float = -2.0, upper: float = 2.0): + # NOTE: PyTorch nn.init.trunc_normal_ is not mathematically correct, the std dev is not actually the std dev of initialized tensor + # This function is a PyTorch version of jax truncated normal init (default init method in flax) + # https://github.com/jax-ml/jax/blob/main/jax/_src/random.py#L807-L848 + # https://github.com/jax-ml/jax/blob/main/jax/_src/nn/initializers.py#L162-L199 + + with torch.no_grad(): + if std == 0: + tensor.zero_() + else: + sqrt2 = math.sqrt(2) + a = math.erf(lower / sqrt2) + b = math.erf(upper / sqrt2) + z = (b - a) / 2 + + c = (2 * math.pi) ** -0.5 + pdf_u = c * math.exp(-0.5 * lower ** 2) + pdf_l = c * math.exp(-0.5 * upper ** 2) + comp_std = std / math.sqrt(1 - (upper * pdf_u - lower * pdf_l) / z - ((pdf_u - pdf_l) / z) ** 2) + + tensor.uniform_(a, b) + tensor.erfinv_() + tensor.mul_(sqrt2 * comp_std) + tensor.clip_(lower * comp_std, upper * comp_std) + + return tensor diff --git a/models/ema.py b/models/ema.py new file mode 100644 index 0000000..2e52933 --- /dev/null +++ b/models/ema.py @@ -0,0 +1,40 @@ +import copy +import torch.nn as nn + +class EMAHelper(object): + def __init__(self, mu=0.999): + self.mu = mu + self.shadow = {} + + def register(self, module): + if isinstance(module, nn.DataParallel): + module = module.module + for name, param in module.named_parameters(): + if param.requires_grad: + self.shadow[name] = param.data.clone() + + def update(self, module): + if isinstance(module, nn.DataParallel): + module = module.module + for name, param in module.named_parameters(): + if param.requires_grad: + self.shadow[name].data = (1. - self.mu) * param.data + self.mu * self.shadow[name].data + + def ema(self, module): + if isinstance(module, nn.DataParallel): + module = module.module + for name, param in module.named_parameters(): + if param.requires_grad: + param.data.copy_(self.shadow[name].data) + + def ema_copy(self, module): + module_copy = copy.deepcopy(module) + self.ema(module_copy) + return module_copy + + def state_dict(self): + return self.shadow + + def load_state_dict(self, state_dict): + self.shadow = state_dict + diff --git a/models/layers.py b/models/layers.py new file mode 100644 index 0000000..5d5264b --- /dev/null +++ b/models/layers.py @@ -0,0 +1,169 @@ +from typing import Tuple +import einops +import torch +from torch import nn +import torch.nn.functional as F + +#try: +# from flash_attn_interface import flash_attn_func # type: ignore[import] +#except ImportError: +# # Fallback to FlashAttention 2 +# from flash_attn import flash_attn_func # type: ignore[import] +from torch.nn.functional import scaled_dot_product_attention + +from models.common import trunc_normal_init_ + + +CosSin = Tuple[torch.Tensor, torch.Tensor] + + +def _find_multiple(a, b): + return (-(a // -b)) * b + + +def rotate_half(x: torch.Tensor): + """Rotates half the hidden dims of the input.""" + x1 = x[..., : x.shape[-1] // 2] + x2 = x[..., x.shape[-1] // 2 :] + return torch.cat((-x2, x1), dim=-1) + + +def apply_rotary_pos_emb(q: torch.Tensor, k: torch.Tensor, cos: torch.Tensor, sin: torch.Tensor): + # q, k: [bs, seq_len, num_heads, head_dim] + # cos, sin: [seq_len, head_dim] + orig_dtype = q.dtype + q = q.to(cos.dtype) + k = k.to(cos.dtype) + + q_embed = (q * cos.unsqueeze(-2)) + (rotate_half(q) * sin.unsqueeze(-2)) + k_embed = (k * cos.unsqueeze(-2)) + (rotate_half(k) * sin.unsqueeze(-2)) + + return q_embed.to(orig_dtype), k_embed.to(orig_dtype) + + +class CastedLinear(nn.Module): + def __init__(self, + in_features: int, + out_features: int, + bias: bool): + super().__init__() + # Truncated LeCun normal init + self.weight = nn.Parameter( + trunc_normal_init_(torch.empty((out_features, in_features)), std=1.0 / (in_features ** 0.5)) + ) + self.bias = None + if bias: + # Zero init bias + self.bias = nn.Parameter(torch.zeros((out_features, ))) + + def forward(self, input: torch.Tensor) -> torch.Tensor: + return F.linear(input, self.weight.to(input.dtype), bias=self.bias.to(input.dtype) if self.bias is not None else None) + + +class CastedEmbedding(nn.Module): + def __init__(self, + num_embeddings: int, + embedding_dim: int, + init_std: float, + cast_to: torch.dtype): + super().__init__() + self.cast_to = cast_to + + # Truncated LeCun normal init + self.embedding_weight = nn.Parameter( + trunc_normal_init_(torch.empty((num_embeddings, embedding_dim)), std=init_std) + ) + + def forward(self, input: torch.Tensor) -> torch.Tensor: + return F.embedding(input, self.embedding_weight.to(self.cast_to)) + + +class RotaryEmbedding(nn.Module): + def __init__(self, dim, max_position_embeddings, base, device=None): + super().__init__() + + # RoPE + inv_freq = 1.0 / (base ** (torch.arange(0, dim, 2, dtype=torch.float32, device=device) / dim)) + t = torch.arange(max_position_embeddings, dtype=torch.float32, device=device) + freqs = torch.outer(t, inv_freq) + + # Different from paper, but it uses a different permutation in order to obtain the same calculation + emb = torch.cat((freqs, freqs), dim=-1) + self.cos_cached = nn.Buffer(emb.cos(), persistent=False) + self.sin_cached = nn.Buffer(emb.sin(), persistent=False) + + def forward(self): + return self.cos_cached, self.sin_cached + + +class Attention(nn.Module): + def __init__(self, hidden_size, head_dim, num_heads, num_key_value_heads, causal=False): + super().__init__() + + self.hidden_size = hidden_size + self.head_dim = head_dim + self.output_size = head_dim * num_heads + self.num_heads = num_heads + self.num_key_value_heads = num_key_value_heads + self.causal = causal + + self.qkv_proj = CastedLinear(self.hidden_size, (self.num_heads + 2 * self.num_key_value_heads) * self.head_dim, bias=False) + self.o_proj = CastedLinear(self.output_size, self.hidden_size, bias=False) + + def forward(self, cos_sin: CosSin, hidden_states: torch.Tensor) -> torch.Tensor: + batch_size, seq_len, _ = hidden_states.shape + + # hidden_states: [bs, seq_len, num_heads, head_dim] + qkv = self.qkv_proj(hidden_states) + + # Split head + qkv = qkv.view(batch_size, seq_len, self.num_heads + 2 * self.num_key_value_heads, self.head_dim) + query = qkv[:, :, :self.num_heads] + key = qkv[:, :, self.num_heads: self.num_heads + self.num_key_value_heads] + value = qkv[:, :, self.num_heads + self.num_key_value_heads:] + + # RoPE + if cos_sin is not None: + cos, sin = cos_sin + query, key = apply_rotary_pos_emb(query, key, cos, sin) + + # flash attn + query, key, value = map(lambda t: einops.rearrange(t, 'B S H D -> B H S D'), (query, key, value)) # needed for scaled_dot_product_attention but not flash_attn_func + attn_output = scaled_dot_product_attention(query=query, key=key, value=value, is_causal=self.causal) + attn_output = einops.rearrange(attn_output, 'B H S D -> B S H D') + attn_output = attn_output.view(batch_size, seq_len, self.output_size) # type: ignore + return self.o_proj(attn_output) + +class LinearSwish(nn.Module): + def __init__(self, hidden_size: int, reverse=False): + super().__init__() + + self.linear = CastedLinear(hidden_size, hidden_size, bias=False) + self.reverse = reverse + + def forward(self, x): + if self.reverse: + return F.silu(self.linear(x)) + else: + return self.linear(F.silu(x)) + + +class SwiGLU(nn.Module): + def __init__(self, hidden_size: int, expansion: float): + super().__init__() + inter = _find_multiple(round(expansion * hidden_size * 2 / 3), 256) + + self.gate_up_proj = CastedLinear(hidden_size, inter * 2, bias=False) + self.down_proj = CastedLinear(inter, hidden_size, bias=False) + + def forward(self, x): + gate, up = self.gate_up_proj(x).chunk(2, dim=-1) + return self.down_proj(F.silu(gate) * up) + +def rms_norm(hidden_states: torch.Tensor, variance_epsilon: float) -> torch.Tensor: + input_dtype = hidden_states.dtype + hidden_states = hidden_states.to(torch.float32) + + variance = hidden_states.square().mean(-1, keepdim=True) + hidden_states = hidden_states * torch.rsqrt(variance + variance_epsilon) + return hidden_states.to(input_dtype) diff --git a/models/losses.py b/models/losses.py new file mode 100644 index 0000000..2597cd6 --- /dev/null +++ b/models/losses.py @@ -0,0 +1,103 @@ +from typing import Any, Tuple, Dict, Sequence, Optional + +import torch +import torch.nn.functional as F +from torch import nn +import math + +IGNORE_LABEL_ID = -100 + + +def s(x, epsilon=1e-30): + return torch.where( + x<0, + 1/(1-x+ epsilon), + x + 1 + ) + + +def log_stablemax(x, dim=-1): + s_x = s(x) + return torch.log(s_x/torch.sum(s_x, dim=dim, keepdim=True)) + + +def stablemax_cross_entropy(logits, labels, ignore_index: int = -100, valid_mask=None): + logprobs = log_stablemax(logits.to(torch.float64), dim=-1) + + if valid_mask is None: + valid_mask = (labels != ignore_index) + transformed_labels = torch.where(valid_mask, labels, 0) + prediction_logprobs = torch.gather(logprobs, index=transformed_labels.to(torch.long).unsqueeze(-1), dim=-1).squeeze(-1) + + return -torch.where(valid_mask, prediction_logprobs, 0) + + +def softmax_cross_entropy(logits, labels, ignore_index: int = -100): + # Cast logits to f32 + # Flatten logits + return F.cross_entropy(logits.to(torch.float32).view(-1, logits.shape[-1]), labels.to(torch.long).view(-1), ignore_index=ignore_index, reduction="none").view(labels.shape) + + +class ACTLossHead(nn.Module): + def __init__(self, model: nn.Module, loss_type: str): + super().__init__() + self.model = model + self.loss_fn = globals()[loss_type] + + def initial_carry(self, *args, **kwargs): + return self.model.initial_carry(*args, **kwargs) # type: ignore + + def forward( + self, + return_keys: Sequence[str], + # Model args + **model_kwargs, + ) -> Tuple[Any, torch.Tensor, Dict[str, torch.Tensor], Optional[Dict[str, torch.Tensor]], torch.Tensor]: + # Model logits + # B x SeqLen x D + new_carry, outputs = self.model(**model_kwargs) + labels = new_carry.current_data["labels"] + + with torch.no_grad(): + # Preds + outputs["preds"] = torch.argmax(outputs["logits"], dim=-1) + + # Correctness + mask = (labels != IGNORE_LABEL_ID) + loss_counts = mask.sum(-1) + loss_divisor = loss_counts.clamp_min(1).unsqueeze(-1) # Avoid NaNs in division + + is_correct = mask & (torch.argmax(outputs["logits"], dim=-1) == labels) + seq_is_correct = is_correct.sum(-1) == loss_counts + + # Metrics (halted) + valid_metrics = new_carry.halted & (loss_counts > 0) + metrics = { + "count": valid_metrics.sum(), + + "accuracy": torch.where(valid_metrics, (is_correct.to(torch.float32) / loss_divisor).sum(-1), 0).sum(), + "exact_accuracy": (valid_metrics & seq_is_correct).sum(), + + "q_halt_accuracy": (valid_metrics & ((outputs["q_halt_logits"] >= 0) == seq_is_correct)).sum(), + "steps": torch.where(valid_metrics, new_carry.steps, 0).sum(), + } + + # Losses + + lm_loss = (self.loss_fn(outputs["logits"], labels, ignore_index=IGNORE_LABEL_ID, valid_mask=mask) / loss_divisor).sum() + q_halt_loss = F.binary_cross_entropy_with_logits(outputs["q_halt_logits"], seq_is_correct.to(outputs["q_halt_logits"].dtype), reduction="sum") + metrics.update({ + "lm_loss": lm_loss.detach(), + "q_halt_loss": q_halt_loss.detach(), + }) + # Q continue (bootstrapping target loss); Alexia: This fits Q-learning, but seems totally unecessary + q_continue_loss = 0 + if "target_q_continue" in outputs: + q_continue_loss = F.binary_cross_entropy_with_logits(outputs["q_continue_logits"], outputs["target_q_continue"], reduction="sum") + + metrics["q_continue_loss"] = q_continue_loss.detach() + # Filter outputs for return + detached_outputs = {k: outputs[k].detach() for k in return_keys if k in outputs} + + return new_carry, lm_loss + 0.5 * (q_halt_loss + q_continue_loss), metrics, detached_outputs, new_carry.halted.all() + diff --git a/models/recursive_reasoning/hrm.py b/models/recursive_reasoning/hrm.py new file mode 100644 index 0000000..9a1a503 --- /dev/null +++ b/models/recursive_reasoning/hrm.py @@ -0,0 +1,294 @@ +from typing import Tuple, List, Dict, Optional +from dataclasses import dataclass +import math +import torch +import torch.nn.functional as F +from torch import nn +from pydantic import BaseModel + +from models.common import trunc_normal_init_ +from models.layers import rms_norm, SwiGLU, Attention, RotaryEmbedding, CosSin, CastedEmbedding, CastedLinear +from models.sparse_embedding import CastedSparseEmbedding + +@dataclass +class HierarchicalReasoningModel_ACTV1InnerCarry: + z_H: torch.Tensor + z_L: torch.Tensor + + +@dataclass +class HierarchicalReasoningModel_ACTV1Carry: + inner_carry: HierarchicalReasoningModel_ACTV1InnerCarry + + steps: torch.Tensor + halted: torch.Tensor + + current_data: Dict[str, torch.Tensor] + + +class HierarchicalReasoningModel_ACTV1Config(BaseModel): + batch_size: int + seq_len: int + puzzle_emb_ndim: int = 0 + num_puzzle_identifiers: int + vocab_size: int + + H_cycles: int + L_cycles: int + + H_layers: int + L_layers: int + + # Transformer config + hidden_size: int + expansion: float + num_heads: int + pos_encodings: str + + rms_norm_eps: float = 1e-5 + rope_theta: float = 10000.0 + + # Halting Q-learning config + halt_max_steps: int + halt_exploration_prob: float + + forward_dtype: str = "bfloat16" + + # Alexia: added + mlp_t: bool=False # use mlp on L instead of transformer + +class HierarchicalReasoningModel_ACTV1Block(nn.Module): + def __init__(self, config: HierarchicalReasoningModel_ACTV1Config) -> None: + super().__init__() + + self.config = config + if self.config.mlp_t: + self.puzzle_emb_len = -(self.config.puzzle_emb_ndim // -self.config.hidden_size) + self.mlp_t = SwiGLU( + hidden_size=self.config.seq_len + self.puzzle_emb_len, # L + expansion=config.expansion, + ) + else: + self.self_attn = Attention( + hidden_size=config.hidden_size, + head_dim=config.hidden_size // config.num_heads, + num_heads=config.num_heads, + num_key_value_heads=config.num_heads, + causal=False + ) + self.mlp = SwiGLU( + hidden_size=config.hidden_size, + expansion=config.expansion, + ) + self.norm_eps = config.rms_norm_eps + + def forward(self, cos_sin: CosSin, hidden_states: torch.Tensor) -> torch.Tensor: + # B, L, D = hidden_states.shape + # Post Norm + if self.config.mlp_t: + hidden_states = hidden_states.transpose(1,2) + out = self.mlp_t(hidden_states) + hidden_states = rms_norm(hidden_states + out, variance_epsilon=self.norm_eps) + hidden_states = hidden_states.transpose(1,2) + else: + # Self Attention + hidden_states = rms_norm(hidden_states + self.self_attn(cos_sin=cos_sin, hidden_states=hidden_states), variance_epsilon=self.norm_eps) + # Fully Connected + out = self.mlp(hidden_states) + hidden_states = rms_norm(hidden_states + out, variance_epsilon=self.norm_eps) + return hidden_states + +class HierarchicalReasoningModel_ACTV1ReasoningModule(nn.Module): + def __init__(self, layers: List[HierarchicalReasoningModel_ACTV1Block]): + super().__init__() + + self.layers = torch.nn.ModuleList(layers) + + def forward(self, hidden_states: torch.Tensor, input_injection: torch.Tensor, **kwargs) -> torch.Tensor: + # Input injection (add) + hidden_states = hidden_states + input_injection + # Layers + for layer in self.layers: + hidden_states = layer(hidden_states=hidden_states, **kwargs) + + return hidden_states + + +class HierarchicalReasoningModel_ACTV1_Inner(nn.Module): + def __init__(self, config: HierarchicalReasoningModel_ACTV1Config) -> None: + super().__init__() + self.config = config + self.forward_dtype = getattr(torch, self.config.forward_dtype) + + # I/O + self.embed_scale = math.sqrt(self.config.hidden_size) + embed_init_std = 1.0 / self.embed_scale + + self.embed_tokens = CastedEmbedding(self.config.vocab_size, self.config.hidden_size, init_std=embed_init_std, cast_to=self.forward_dtype) + self.lm_head = CastedLinear(self.config.hidden_size, self.config.vocab_size, bias=False) + self.q_head = CastedLinear(self.config.hidden_size, 2, bias=True) + + self.puzzle_emb_len = -(self.config.puzzle_emb_ndim // -self.config.hidden_size) # ceil div + if self.config.puzzle_emb_ndim > 0: + # Zero init puzzle embeddings + self.puzzle_emb = CastedSparseEmbedding(self.config.num_puzzle_identifiers, self.config.puzzle_emb_ndim, + batch_size=self.config.batch_size, init_std=0, cast_to=self.forward_dtype) + + # LM Blocks + if self.config.pos_encodings == "rope": + self.rotary_emb = RotaryEmbedding(dim=self.config.hidden_size // self.config.num_heads, + max_position_embeddings=self.config.seq_len + self.puzzle_emb_len, + base=self.config.rope_theta) + elif self.config.pos_encodings == "learned": + self.embed_pos = CastedEmbedding(self.config.seq_len + self.puzzle_emb_len, self.config.hidden_size, init_std=embed_init_std, cast_to=self.forward_dtype) + else: + pass + + # Reasoning Layers + self.H_level = HierarchicalReasoningModel_ACTV1ReasoningModule(layers=[HierarchicalReasoningModel_ACTV1Block(self.config) for _i in range(self.config.H_layers)]) + self.L_level = HierarchicalReasoningModel_ACTV1ReasoningModule(layers=[HierarchicalReasoningModel_ACTV1Block(self.config) for _i in range(self.config.L_layers)]) + + # Initial states + self.H_init = nn.Buffer(trunc_normal_init_(torch.empty(self.config.hidden_size, dtype=self.forward_dtype), std=1), persistent=True) + self.L_init = nn.Buffer(trunc_normal_init_(torch.empty(self.config.hidden_size, dtype=self.forward_dtype), std=1), persistent=True) + + # Q head special init + # Init Q to (almost) zero for faster learning during bootstrapping + with torch.no_grad(): + self.q_head.weight.zero_() + self.q_head.bias.fill_(-5) # type: ignore + + def _input_embeddings(self, input: torch.Tensor, puzzle_identifiers: torch.Tensor): + # Token embedding + embedding = self.embed_tokens(input.to(torch.int32)) + + # Puzzle embeddings + if self.config.puzzle_emb_ndim > 0: + puzzle_embedding = self.puzzle_emb(puzzle_identifiers) + + pad_count = self.puzzle_emb_len * self.config.hidden_size - puzzle_embedding.shape[-1] + if pad_count > 0: + puzzle_embedding = F.pad(puzzle_embedding, (0, pad_count)) + + embedding = torch.cat((puzzle_embedding.view(-1, self.puzzle_emb_len, self.config.hidden_size), embedding), dim=-2) + + # Position embeddings + if self.config.pos_encodings == "learned": + # scale by 1/sqrt(2) to maintain forward variance + embedding = 0.707106781 * (embedding + self.embed_pos.embedding_weight.to(self.forward_dtype)) + + # Scale + return self.embed_scale * embedding + + def empty_carry(self, batch_size: int): + return HierarchicalReasoningModel_ACTV1InnerCarry( + z_H=torch.empty(batch_size, self.config.seq_len + self.puzzle_emb_len, self.config.hidden_size, dtype=self.forward_dtype), + z_L=torch.empty(batch_size, self.config.seq_len + self.puzzle_emb_len, self.config.hidden_size, dtype=self.forward_dtype), + ) + + def reset_carry(self, reset_flag: torch.Tensor, carry: HierarchicalReasoningModel_ACTV1InnerCarry): + return HierarchicalReasoningModel_ACTV1InnerCarry( + z_H=torch.where(reset_flag.view(-1, 1, 1), self.H_init, carry.z_H), + z_L=torch.where(reset_flag.view(-1, 1, 1), self.L_init, carry.z_L), + ) + + def forward(self, carry: HierarchicalReasoningModel_ACTV1InnerCarry, batch: Dict[str, torch.Tensor]) -> Tuple[HierarchicalReasoningModel_ACTV1InnerCarry, torch.Tensor, Tuple[torch.Tensor, torch.Tensor]]: + seq_info = dict( + cos_sin=self.rotary_emb() if hasattr(self, "rotary_emb") else None, + ) + + # Input encoding + input_embeddings = self._input_embeddings(batch["inputs"], batch["puzzle_identifiers"]) + + # Forward iterations + with torch.no_grad(): + z_H, z_L = carry.z_H, carry.z_L + for _H_step in range(self.config.H_cycles): + for _L_step in range(self.config.L_cycles): + if not ((_H_step == self.config.H_cycles - 1) and (_L_step == self.config.L_cycles - 1)): + z_L = self.L_level(z_L, z_H + input_embeddings, **seq_info) + if not (_H_step == self.config.H_cycles - 1): + z_H = self.H_level(z_H, z_L, **seq_info) + assert not z_H.requires_grad and not z_L.requires_grad + # 1-step grad + z_L = self.L_level(z_L, z_H + input_embeddings, **seq_info) + z_H = self.H_level(z_H, z_L, **seq_info) + + # LM Outputs + new_carry = HierarchicalReasoningModel_ACTV1InnerCarry(z_H=z_H.detach(), z_L=z_L.detach()) # New carry no grad + output = self.lm_head(z_H)[:, self.puzzle_emb_len:] + + # Q head + q_logits = self.q_head(z_H[:, 0]).to(torch.float32) + + return new_carry, output, (q_logits[..., 0], q_logits[..., 1]) + + +class HierarchicalReasoningModel_ACTV1(nn.Module): + """ACT wrapper.""" + + def __init__(self, config_dict: dict): + super().__init__() + self.config = HierarchicalReasoningModel_ACTV1Config(**config_dict) + self.inner = HierarchicalReasoningModel_ACTV1_Inner(self.config) + + @property + def puzzle_emb(self): + return self.inner.puzzle_emb + + def initial_carry(self, batch: Dict[str, torch.Tensor]): + batch_size = batch["inputs"].shape[0] + + return HierarchicalReasoningModel_ACTV1Carry( + inner_carry=self.inner.empty_carry(batch_size), # Empty is expected, it will be reseted in first pass as all sequences are halted. + + steps=torch.zeros((batch_size, ), dtype=torch.int32), + halted=torch.ones((batch_size, ), dtype=torch.bool), # Default to halted + + current_data={k: torch.empty_like(v) for k, v in batch.items()} + ) + + def forward(self, carry: HierarchicalReasoningModel_ACTV1Carry, batch: Dict[str, torch.Tensor]) -> Tuple[HierarchicalReasoningModel_ACTV1Carry, Dict[str, torch.Tensor]]: + # Update data, carry (removing halted sequences) + new_inner_carry = self.inner.reset_carry(carry.halted, carry.inner_carry) + + new_steps = torch.where(carry.halted, 0, carry.steps) + + new_current_data = {k: torch.where(carry.halted.view((-1, ) + (1, ) * (batch[k].ndim - 1)), batch[k], v) for k, v in carry.current_data.items()} + + # Forward inner model + new_inner_carry, logits, (q_halt_logits, q_continue_logits) = self.inner(new_inner_carry, new_current_data) + + outputs = { + "logits": logits, + "q_halt_logits": q_halt_logits, + "q_continue_logits": q_continue_logits + } + + with torch.no_grad(): + # Step + new_steps = new_steps + 1 + is_last_step = new_steps >= self.config.halt_max_steps + + halted = is_last_step + + # if training, and ACT is enabled + if self.training and (self.config.halt_max_steps > 1): + # Halt signal + # NOTE: During evaluation, always use max steps, this is to guarantee the same halting steps inside a batch for batching purposes + halted = halted | (q_halt_logits > q_continue_logits) + + # Exploration + min_halt_steps = (torch.rand_like(q_halt_logits) < self.config.halt_exploration_prob) * torch.randint_like(new_steps, low=2, high=self.config.halt_max_steps + 1) + + halted = halted & (new_steps >= min_halt_steps) + + # Compute target Q + # NOTE: No replay buffer and target networks for computing target Q-value. + # As batch_size is large, there're many parallel envs. + # Similar concept as PQN https://arxiv.org/abs/2407.04811 + next_q_halt_logits, next_q_continue_logits = self.inner(new_inner_carry, new_current_data)[-1] + + outputs["target_q_continue"] = torch.sigmoid(torch.where(is_last_step, next_q_halt_logits, torch.maximum(next_q_halt_logits, next_q_continue_logits))) + + return HierarchicalReasoningModel_ACTV1Carry(new_inner_carry, new_steps, halted, new_current_data), outputs diff --git a/models/recursive_reasoning/transformers_baseline.py b/models/recursive_reasoning/transformers_baseline.py new file mode 100644 index 0000000..7a08acc --- /dev/null +++ b/models/recursive_reasoning/transformers_baseline.py @@ -0,0 +1,342 @@ +""" +HRM ACT V2: Transformer Baseline for Architecture Ablation + +This is an architecture ablation of the Hierarchical Reasoning Model (HRM). +Key changes from V1: +1. REMOVED hierarchical split (no separate H and L levels) +2. REMOVED inner cycles (no H_cycles/L_cycles loops within reasoning) +3. KEPT ACT outer loop structure intact +4. KEPT all data preprocessing, embeddings, and evaluation infrastructure + +Architecture: Single-level transformer that processes the full 30x30 grid as a +900-token sequence, with the same positional encodings and sparse embeddings as V1. + +""" + +from typing import Tuple, List, Dict, Optional +from dataclasses import dataclass +import math + +import torch +import torch.nn.functional as F +from torch import nn +from pydantic import BaseModel + +from models.common import trunc_normal_init_ +from models.layers import rms_norm, SwiGLU, Attention, RotaryEmbedding, CosSin, CastedEmbedding, CastedLinear +from models.sparse_embedding import CastedSparseEmbedding + + +@dataclass +class Model_ACTV2InnerCarry: + z_H: torch.Tensor + + +@dataclass +class Model_ACTV2Carry: + inner_carry: Model_ACTV2InnerCarry + + steps: torch.Tensor + halted: torch.Tensor + + current_data: Dict[str, torch.Tensor] + + +class Model_ACTV2Config(BaseModel): + batch_size: int + seq_len: int + puzzle_emb_ndim: int = 0 + num_puzzle_identifiers: int + vocab_size: int + + H_cycles: int + + H_layers: int + + # Transformer config + hidden_size: int + expansion: float + num_heads: int + pos_encodings: str + + rms_norm_eps: float = 1e-5 + rope_theta: float = 10000.0 + + # Halting Q-learning config + halt_max_steps: int + halt_exploration_prob: float + act_enabled: bool = True # If False, always run halt_max_steps (no early stopping during training) + act_inference: bool = False # If True, use adaptive computation during inference + + forward_dtype: str = "bfloat16" + + +class Model_ACTV2Block(nn.Module): + def __init__(self, config: Model_ACTV2Config) -> None: + super().__init__() + + self.self_attn = Attention( + hidden_size=config.hidden_size, + head_dim=config.hidden_size // config.num_heads, + num_heads=config.num_heads, + num_key_value_heads=config.num_heads, + causal=False, + ) + self.mlp = SwiGLU( + hidden_size=config.hidden_size, + expansion=config.expansion, + ) + self.norm_eps = config.rms_norm_eps + + def forward(self, cos_sin: CosSin, hidden_states: torch.Tensor) -> torch.Tensor: + # Post Norm + # Self Attention + hidden_states = rms_norm( + hidden_states + self.self_attn(cos_sin=cos_sin, hidden_states=hidden_states), + variance_epsilon=self.norm_eps, + ) + # Fully Connected + hidden_states = rms_norm(hidden_states + self.mlp(hidden_states), variance_epsilon=self.norm_eps) + return hidden_states + + +class Model_ACTV2ReasoningModule(nn.Module): + def __init__(self, layers: List[Model_ACTV2Block]): + super().__init__() + + self.layers = torch.nn.ModuleList(layers) + + def forward(self, hidden_states: torch.Tensor, input_injection: torch.Tensor, **kwargs) -> torch.Tensor: + # Input injection (add) + hidden_states = hidden_states + input_injection + # Layers + for layer in self.layers: + hidden_states = layer(hidden_states=hidden_states, **kwargs) + + return hidden_states + + +class Model_ACTV2_Inner(nn.Module): + def __init__(self, config: Model_ACTV2Config) -> None: + super().__init__() + self.config = config + self.forward_dtype = getattr(torch, self.config.forward_dtype) + + # I/O + self.embed_scale = math.sqrt(self.config.hidden_size) + embed_init_std = 1.0 / self.embed_scale + + self.embed_tokens = CastedEmbedding( + self.config.vocab_size, + self.config.hidden_size, + init_std=embed_init_std, + cast_to=self.forward_dtype, + ) + self.lm_head = CastedLinear(self.config.hidden_size, self.config.vocab_size, bias=False) + self.q_head = CastedLinear(self.config.hidden_size, 2, bias=True) + + self.puzzle_emb_len = -(self.config.puzzle_emb_ndim // -self.config.hidden_size) # ceil div + if self.config.puzzle_emb_ndim > 0: + # Zero init puzzle embeddings + self.puzzle_emb = CastedSparseEmbedding( + self.config.num_puzzle_identifiers, + self.config.puzzle_emb_ndim, + batch_size=self.config.batch_size, + init_std=0, + cast_to=self.forward_dtype, + ) + + # LM Blocks + if self.config.pos_encodings == "rope": + self.rotary_emb = RotaryEmbedding( + dim=self.config.hidden_size // self.config.num_heads, + max_position_embeddings=self.config.seq_len + self.puzzle_emb_len, + base=self.config.rope_theta, + ) + elif self.config.pos_encodings == "learned": + self.embed_pos = CastedEmbedding( + self.config.seq_len + self.puzzle_emb_len, + self.config.hidden_size, + init_std=embed_init_std, + cast_to=self.forward_dtype, + ) + else: + raise NotImplementedError() + + # Reasoning Layers + self.H_level = Model_ACTV2ReasoningModule( + layers=[Model_ACTV2Block(self.config) for _i in range(self.config.H_layers)] + ) + + # Initial states + self.H_init = nn.Buffer( + trunc_normal_init_(torch.empty(self.config.hidden_size, dtype=self.forward_dtype), std=1), + persistent=True, + ) + + # Q head special init + # Init Q to (almost) zero for faster learning during bootstrapping + with torch.no_grad(): + self.q_head.weight.zero_() + self.q_head.bias.fill_(-5) # type: ignore + + def _input_embeddings(self, input: torch.Tensor, puzzle_identifiers: torch.Tensor): + # Token embedding + embedding = self.embed_tokens(input.to(torch.int32)) + + # Puzzle embeddings + if self.config.puzzle_emb_ndim > 0: + puzzle_embedding = self.puzzle_emb(puzzle_identifiers) + + pad_count = self.puzzle_emb_len * self.config.hidden_size - puzzle_embedding.shape[-1] + if pad_count > 0: + puzzle_embedding = F.pad(puzzle_embedding, (0, pad_count)) + + embedding = torch.cat( + (puzzle_embedding.view(-1, self.puzzle_emb_len, self.config.hidden_size), embedding), dim=-2 + ) + + # Position embeddings + if self.config.pos_encodings == "learned": + # scale by 1/sqrt(2) to maintain forward variance + embedding = 0.707106781 * (embedding + self.embed_pos.embedding_weight.to(self.forward_dtype)) + + # Scale + return self.embed_scale * embedding + + def empty_carry(self, batch_size: int): + return Model_ACTV2InnerCarry( + z_H=torch.empty( + batch_size, + self.config.seq_len + self.puzzle_emb_len, + self.config.hidden_size, + dtype=self.forward_dtype, + ), + ) + + def reset_carry(self, reset_flag: torch.Tensor, carry: Model_ACTV2InnerCarry): + return Model_ACTV2InnerCarry( + z_H=torch.where(reset_flag.view(-1, 1, 1), self.H_init, carry.z_H), + ) + + def forward( + self, carry: Model_ACTV2InnerCarry, batch: Dict[str, torch.Tensor] + ) -> Tuple[Model_ACTV2InnerCarry, torch.Tensor, Tuple[torch.Tensor, torch.Tensor]]: + seq_info = dict( + cos_sin=self.rotary_emb() if hasattr(self, "rotary_emb") else None, + ) + + # Input encoding + input_embeddings = self._input_embeddings(batch["inputs"], batch["puzzle_identifiers"]) + + # 1-step grad + z_H = self.H_level(carry.z_H, input_embeddings, **seq_info) + + # LM Outputs + new_carry = Model_ACTV2InnerCarry( + z_H=z_H.detach(), + ) # New carry no grad + output = self.lm_head(z_H)[:, self.puzzle_emb_len :] + + # Q head + q_logits = self.q_head(z_H[:, 0]).to(torch.float32) + + return new_carry, output, (q_logits[..., 0], q_logits[..., 1]) + + +class Model_ACTV2(nn.Module): + """ACT wrapper.""" + + def __init__(self, config_dict: dict): + super().__init__() + self.config = Model_ACTV2Config(**config_dict) + self.inner = Model_ACTV2_Inner(self.config) + + @property + def puzzle_emb(self): + return self.inner.puzzle_emb + + def initial_carry(self, batch: Dict[str, torch.Tensor]): + batch_size = batch["inputs"].shape[0] + + return Model_ACTV2Carry( + inner_carry=self.inner.empty_carry( + batch_size + ), # Empty is expected, it will be reseted in first pass as all sequences are halted. + steps=torch.zeros((batch_size,), dtype=torch.int32), + halted=torch.ones((batch_size,), dtype=torch.bool), # Default to halted + current_data={k: torch.empty_like(v) for k, v in batch.items()}, + ) + + def forward( + self, + carry: Model_ACTV2Carry, + batch: Dict[str, torch.Tensor], + compute_target_q: bool = False, + ) -> Tuple[Model_ACTV2Carry, Dict[str, torch.Tensor]]: + # Update data, carry (removing halted sequences) + new_inner_carry = self.inner.reset_carry(carry.halted, carry.inner_carry) + + new_steps = torch.where(carry.halted, 0, carry.steps) + + new_current_data = { + k: torch.where(carry.halted.view((-1,) + (1,) * (batch[k].ndim - 1)), batch[k], v) + for k, v in carry.current_data.items() + } + + # Forward inner model + new_inner_carry, logits, (q_halt_logits, q_continue_logits) = self.inner( + new_inner_carry, new_current_data + ) + + outputs = {"logits": logits, "q_halt_logits": q_halt_logits, "q_continue_logits": q_continue_logits} + + with torch.no_grad(): + # Step + new_steps = new_steps + 1 + is_last_step = new_steps >= self.config.halt_max_steps + + halted = is_last_step + + # Check if adaptive computation should be used + use_adaptive = (self.config.halt_max_steps > 1) and ( + (self.training and self.config.act_enabled) + or (not self.training and self.config.act_inference) + ) + + if use_adaptive: + # Halt signal based on Q-values (but always halt at max steps) + q_halt_signal = q_halt_logits > q_continue_logits + halted = halted | q_halt_signal + + # Store actual steps used for logging (only during inference) + if not self.training: + outputs["actual_steps"] = new_steps.float() + + # Exploration (only during training) + if self.training: + min_halt_steps = ( + torch.rand_like(q_halt_logits) < self.config.halt_exploration_prob + ) * torch.randint_like(new_steps, low=2, high=self.config.halt_max_steps + 1) + halted = halted & (new_steps >= min_halt_steps) + + # Compute target Q (only during training) + # NOTE: No replay buffer and target networks for computing target Q-value. + # As batch_size is large, there're many parallel envs. + # Similar concept as PQN https://arxiv.org/abs/2407.04811 + if self.training and compute_target_q: + next_q_halt_logits, next_q_continue_logits = self.inner( + new_inner_carry, new_current_data + )[-1] + + outputs["target_q_continue"] = torch.sigmoid( + torch.where( + is_last_step, + next_q_halt_logits, + torch.maximum(next_q_halt_logits, next_q_continue_logits), + ) + ) + + return Model_ACTV2Carry( + new_inner_carry, new_steps, halted, new_current_data + ), outputs diff --git a/models/recursive_reasoning/trm.py b/models/recursive_reasoning/trm.py new file mode 100644 index 0000000..5c3e39d --- /dev/null +++ b/models/recursive_reasoning/trm.py @@ -0,0 +1,297 @@ +from typing import Tuple, List, Dict, Optional +from dataclasses import dataclass +import math +import torch +import copy +import torch.nn.functional as F +from torch import nn +from pydantic import BaseModel +import random +from models.common import trunc_normal_init_ +from models.layers import rms_norm, LinearSwish, SwiGLU, Attention, RotaryEmbedding, CosSin, CastedEmbedding, CastedLinear +from models.sparse_embedding import CastedSparseEmbedding + +IGNORE_LABEL_ID = -100 + +@dataclass +class TinyRecursiveReasoningModel_ACTV1InnerCarry: + z_H: torch.Tensor + z_L: torch.Tensor + + +@dataclass +class TinyRecursiveReasoningModel_ACTV1Carry: + inner_carry: TinyRecursiveReasoningModel_ACTV1InnerCarry + + steps: torch.Tensor + halted: torch.Tensor + + current_data: Dict[str, torch.Tensor] + + +class TinyRecursiveReasoningModel_ACTV1Config(BaseModel): + batch_size: int + seq_len: int + puzzle_emb_ndim: int = 0 + num_puzzle_identifiers: int + vocab_size: int + + H_cycles: int + L_cycles: int + + H_layers: int # ignored + L_layers: int + + # Transformer config + hidden_size: int + expansion: float + num_heads: int + pos_encodings: str + + rms_norm_eps: float = 1e-5 + rope_theta: float = 10000.0 + + # Halting Q-learning config + halt_max_steps: int + halt_exploration_prob: float + + forward_dtype: str = "bfloat16" + + # Alexia: added + mlp_t: bool = False # use mlp on L instead of transformer + puzzle_emb_len: int = 16 # if non-zero, its specified to this value + no_ACT_continue: bool = True # No continue ACT loss, only use the sigmoid of the halt which makes much more sense + +class TinyRecursiveReasoningModel_ACTV1Block(nn.Module): + def __init__(self, config: TinyRecursiveReasoningModel_ACTV1Config) -> None: + super().__init__() + + self.config = config + if self.config.mlp_t: + self.puzzle_emb_len = -(self.config.puzzle_emb_ndim // -self.config.hidden_size) if self.config.puzzle_emb_len == 0 else self.config.puzzle_emb_len + self.mlp_t = SwiGLU( + hidden_size=self.config.seq_len + self.puzzle_emb_len, # L + expansion=config.expansion, + ) + else: + self.self_attn = Attention( + hidden_size=config.hidden_size, + head_dim=config.hidden_size // config.num_heads, + num_heads=config.num_heads, + num_key_value_heads=config.num_heads, + causal=False + ) + self.mlp = SwiGLU( + hidden_size=config.hidden_size, + expansion=config.expansion, + ) + self.norm_eps = config.rms_norm_eps + + def forward(self, cos_sin: CosSin, hidden_states: torch.Tensor) -> torch.Tensor: + # B, L, D = hidden_states.shape + # Post Norm + if self.config.mlp_t: + hidden_states = hidden_states.transpose(1,2) + out = self.mlp_t(hidden_states) + hidden_states = rms_norm(hidden_states + out, variance_epsilon=self.norm_eps) + hidden_states = hidden_states.transpose(1,2) + else: + # Self Attention + hidden_states = rms_norm(hidden_states + self.self_attn(cos_sin=cos_sin, hidden_states=hidden_states), variance_epsilon=self.norm_eps) + # Fully Connected + out = self.mlp(hidden_states) + hidden_states = rms_norm(hidden_states + out, variance_epsilon=self.norm_eps) + return hidden_states + +class TinyRecursiveReasoningModel_ACTV1ReasoningModule(nn.Module): + def __init__(self, layers: List[TinyRecursiveReasoningModel_ACTV1Block]): + super().__init__() + self.layers = torch.nn.ModuleList(layers) + + def forward(self, hidden_states: torch.Tensor, input_injection: torch.Tensor, **kwargs) -> torch.Tensor: + hidden_states = hidden_states + input_injection + for layer in self.layers: + hidden_states = layer(hidden_states=hidden_states, **kwargs) + return hidden_states + + +class TinyRecursiveReasoningModel_ACTV1_Inner(nn.Module): + def __init__(self, config: TinyRecursiveReasoningModel_ACTV1Config) -> None: + super().__init__() + self.config = config + self.forward_dtype = getattr(torch, self.config.forward_dtype) + + # I/O + + self.embed_scale = math.sqrt(self.config.hidden_size) + embed_init_std = 1.0 / self.embed_scale + + self.embed_tokens = CastedEmbedding(self.config.vocab_size, self.config.hidden_size, init_std=embed_init_std, cast_to=self.forward_dtype) + self.lm_head = CastedLinear(self.config.hidden_size, self.config.vocab_size, bias=False) + self.q_head = CastedLinear(self.config.hidden_size, 2, bias=True) + + self.puzzle_emb_len = -(self.config.puzzle_emb_ndim // -self.config.hidden_size) if self.config.puzzle_emb_len == 0 else self.config.puzzle_emb_len # ceil div + if self.config.puzzle_emb_ndim > 0: + # Zero init puzzle embeddings + self.puzzle_emb = CastedSparseEmbedding(self.config.num_puzzle_identifiers, self.config.puzzle_emb_ndim, + batch_size=self.config.batch_size, init_std=0, cast_to=self.forward_dtype) + + # LM Blocks + if self.config.pos_encodings == "rope": + self.rotary_emb = RotaryEmbedding(dim=self.config.hidden_size // self.config.num_heads, + max_position_embeddings=self.config.seq_len + self.puzzle_emb_len, + base=self.config.rope_theta) + elif self.config.pos_encodings == "learned": + self.embed_pos = CastedEmbedding(self.config.seq_len + self.puzzle_emb_len, self.config.hidden_size, init_std=embed_init_std, cast_to=self.forward_dtype) + else: + pass + + # Reasoning Layers + self.L_level = TinyRecursiveReasoningModel_ACTV1ReasoningModule(layers=[TinyRecursiveReasoningModel_ACTV1Block(self.config) for _i in range(self.config.L_layers)]) + + # Initial states + self.H_init = nn.Buffer(trunc_normal_init_(torch.empty(self.config.hidden_size, dtype=self.forward_dtype), std=1), persistent=True) + self.L_init = nn.Buffer(trunc_normal_init_(torch.empty(self.config.hidden_size, dtype=self.forward_dtype), std=1), persistent=True) + + # Q head special init + # Init Q to (almost) zero for faster learning during bootstrapping + with torch.no_grad(): + self.q_head.weight.zero_() + self.q_head.bias.fill_(-5) # type: ignore + + def _input_embeddings(self, input: torch.Tensor, puzzle_identifiers: torch.Tensor): + # Token embedding + embedding = self.embed_tokens(input.to(torch.int32)) + + # Puzzle embeddings + if self.config.puzzle_emb_ndim > 0: + puzzle_embedding = self.puzzle_emb(puzzle_identifiers) + + pad_count = self.puzzle_emb_len * self.config.hidden_size - puzzle_embedding.shape[-1] + if pad_count > 0: + puzzle_embedding = F.pad(puzzle_embedding, (0, pad_count)) + + embedding = torch.cat((puzzle_embedding.view(-1, self.puzzle_emb_len, self.config.hidden_size), embedding), dim=-2) + + # Position embeddings + if self.config.pos_encodings == "learned": + # scale by 1/sqrt(2) to maintain forward variance + embedding = 0.707106781 * (embedding + self.embed_pos.embedding_weight.to(self.forward_dtype)) + + # Scale + return self.embed_scale * embedding + + def empty_carry(self, batch_size: int): + return TinyRecursiveReasoningModel_ACTV1InnerCarry( + z_H=torch.empty(batch_size, self.config.seq_len + self.puzzle_emb_len, self.config.hidden_size, dtype=self.forward_dtype), + z_L=torch.empty(batch_size, self.config.seq_len + self.puzzle_emb_len, self.config.hidden_size, dtype=self.forward_dtype), + ) + + def reset_carry(self, reset_flag: torch.Tensor, carry: TinyRecursiveReasoningModel_ACTV1InnerCarry): + return TinyRecursiveReasoningModel_ACTV1InnerCarry( + z_H=torch.where(reset_flag.view(-1, 1, 1), self.H_init, carry.z_H), + z_L=torch.where(reset_flag.view(-1, 1, 1), self.L_init, carry.z_L), + ) + + def forward(self, carry: TinyRecursiveReasoningModel_ACTV1InnerCarry, batch: Dict[str, torch.Tensor]) -> Tuple[TinyRecursiveReasoningModel_ACTV1InnerCarry, torch.Tensor, Tuple[torch.Tensor, torch.Tensor]]: + seq_info = dict( + cos_sin=self.rotary_emb() if hasattr(self, "rotary_emb") else None, + ) + + # Input encoding + input_embeddings = self._input_embeddings(batch["inputs"], batch["puzzle_identifiers"]) + + # Forward iterations + it = 0 + z_H, z_L = carry.z_H, carry.z_L + # H_cycles-1 without grad + with torch.no_grad(): + for _H_step in range(self.config.H_cycles-1): + for _L_step in range(self.config.L_cycles): + z_L = self.L_level(z_L, z_H + input_embeddings, **seq_info) + z_H = self.L_level(z_H, z_L, **seq_info) + # 1 with grad + for _L_step in range(self.config.L_cycles): + z_L = self.L_level(z_L, z_H + input_embeddings, **seq_info) + z_H = self.L_level(z_H, z_L, **seq_info) + + # LM Outputs + new_carry = TinyRecursiveReasoningModel_ACTV1InnerCarry(z_H=z_H.detach(), z_L=z_L.detach()) # New carry no grad + output = self.lm_head(z_H)[:, self.puzzle_emb_len:] + q_logits = self.q_head(z_H[:, 0]).to(torch.float32) # Q-head; uses the first puzzle_emb position + return new_carry, output, (q_logits[..., 0], q_logits[..., 1]) + + +class TinyRecursiveReasoningModel_ACTV1(nn.Module): + """ACT wrapper.""" + + def __init__(self, config_dict: dict): + super().__init__() + self.config = TinyRecursiveReasoningModel_ACTV1Config(**config_dict) + self.inner = TinyRecursiveReasoningModel_ACTV1_Inner(self.config) + + @property + def puzzle_emb(self): + return self.inner.puzzle_emb + + def initial_carry(self, batch: Dict[str, torch.Tensor]): + batch_size = batch["inputs"].shape[0] + + return TinyRecursiveReasoningModel_ACTV1Carry( + inner_carry=self.inner.empty_carry(batch_size), # Empty is expected, it will be reseted in first pass as all sequences are halted. + + steps=torch.zeros((batch_size, ), dtype=torch.int32), + halted=torch.ones((batch_size, ), dtype=torch.bool), # Default to halted + + current_data={k: torch.empty_like(v) for k, v in batch.items()} + ) + + def forward(self, carry: TinyRecursiveReasoningModel_ACTV1Carry, batch: Dict[str, torch.Tensor]) -> Tuple[TinyRecursiveReasoningModel_ACTV1Carry, Dict[str, torch.Tensor]]: + + # Update data, carry (removing halted sequences) + new_inner_carry = self.inner.reset_carry(carry.halted, carry.inner_carry) + + new_steps = torch.where(carry.halted, 0, carry.steps) + + new_current_data = {k: torch.where(carry.halted.view((-1, ) + (1, ) * (batch[k].ndim - 1)), batch[k], v) for k, v in carry.current_data.items()} + + # Forward inner model + new_inner_carry, logits, (q_halt_logits, q_continue_logits) = self.inner(new_inner_carry, new_current_data) + + outputs = { + "logits": logits, + "q_halt_logits": q_halt_logits, + "q_continue_logits": q_continue_logits + } + + with torch.no_grad(): + # Step + new_steps = new_steps + 1 + is_last_step = new_steps >= self.config.halt_max_steps + + halted = is_last_step + + # if training, and ACT is enabled + if self.training and (self.config.halt_max_steps > 1): + + # Halt signal + # NOTE: During evaluation, always use max steps, this is to guarantee the same halting steps inside a batch for batching purposes + + if self.config.no_ACT_continue: + halted = halted | (q_halt_logits > 0) + else: + halted = halted | (q_halt_logits > q_continue_logits) + + # Exploration + min_halt_steps = (torch.rand_like(q_halt_logits) < self.config.halt_exploration_prob) * torch.randint_like(new_steps, low=2, high=self.config.halt_max_steps + 1) + halted = halted & (new_steps >= min_halt_steps) + + if not self.config.no_ACT_continue: + # Compute target Q + # NOTE: No replay buffer and target networks for computing target Q-value. + # As batch_size is large, there're many parallel envs. + # Similar concept as PQN https://arxiv.org/abs/2407.04811 + _, _, (next_q_halt_logits, next_q_continue_logits), _, _ = self.inner(new_inner_carry, new_current_data) + outputs["target_q_continue"] = torch.sigmoid(torch.where(is_last_step, next_q_halt_logits, torch.maximum(next_q_halt_logits, next_q_continue_logits))) + + return TinyRecursiveReasoningModel_ACTV1Carry(new_inner_carry, new_steps, halted, new_current_data), outputs diff --git a/models/recursive_reasoning/trm_hier6.py b/models/recursive_reasoning/trm_hier6.py new file mode 100644 index 0000000..c654474 --- /dev/null +++ b/models/recursive_reasoning/trm_hier6.py @@ -0,0 +1,323 @@ +from typing import Tuple, List, Dict, Optional +from dataclasses import dataclass +import math +import torch +import copy +import torch.nn.functional as F +from torch import nn +from pydantic import BaseModel +import random +from models.common import trunc_normal_init_ +from models.layers import rms_norm, LinearSwish, SwiGLU, Attention, RotaryEmbedding, CosSin, CastedEmbedding, CastedLinear +from models.sparse_embedding import CastedSparseEmbedding + +IGNORE_LABEL_ID = -100 + +@dataclass +class TinyRecursiveReasoningModel_ACTV1InnerCarry: + z_H: torch.Tensor + z_L1: torch.Tensor + z_L2: torch.Tensor + z_L3: torch.Tensor + z_L4: torch.Tensor + z_L5: torch.Tensor + z_L6: torch.Tensor + + + +@dataclass +class TinyRecursiveReasoningModel_ACTV1Carry: + inner_carry: TinyRecursiveReasoningModel_ACTV1InnerCarry + + steps: torch.Tensor + halted: torch.Tensor + + current_data: Dict[str, torch.Tensor] + + +class TinyRecursiveReasoningModel_ACTV1Config(BaseModel): + batch_size: int + seq_len: int + puzzle_emb_ndim: int = 0 + num_puzzle_identifiers: int + vocab_size: int + + H_cycles: int + L_cycles: int + + H_layers: int # ignored + L_layers: int + + # Transformer config + hidden_size: int + expansion: float + num_heads: int + pos_encodings: str + + rms_norm_eps: float = 1e-5 + rope_theta: float = 10000.0 + + # Halting Q-learning config + halt_max_steps: int + halt_exploration_prob: float + + forward_dtype: str = "bfloat16" + + # Alexia: added + mlp_t: bool = False # use mlp on L instead of transformer + puzzle_emb_len: int = 16 # if non-zero, its specified to this value + no_ACT_continue: bool = True # No continue ACT loss, only use the sigmoid of the halt which makes much more sense + +class TinyRecursiveReasoningModel_ACTV1Block(nn.Module): + def __init__(self, config: TinyRecursiveReasoningModel_ACTV1Config) -> None: + super().__init__() + + self.config = config + if self.config.mlp_t: + self.puzzle_emb_len = -(self.config.puzzle_emb_ndim // -self.config.hidden_size) if self.config.puzzle_emb_len == 0 else self.config.puzzle_emb_len + self.mlp_t = SwiGLU( + hidden_size=self.config.seq_len + self.puzzle_emb_len, # L + expansion=config.expansion, + ) + else: + self.self_attn = Attention( + hidden_size=config.hidden_size, + head_dim=config.hidden_size // config.num_heads, + num_heads=config.num_heads, + num_key_value_heads=config.num_heads, + causal=False + ) + self.mlp = SwiGLU( + hidden_size=config.hidden_size, + expansion=config.expansion, + ) + self.norm_eps = config.rms_norm_eps + + def forward(self, cos_sin: CosSin, hidden_states: torch.Tensor) -> torch.Tensor: + # B, L, D = hidden_states.shape + # Post Norm + if self.config.mlp_t: + hidden_states = hidden_states.transpose(1,2) + out = self.mlp_t(hidden_states) + hidden_states = rms_norm(hidden_states + out, variance_epsilon=self.norm_eps) + hidden_states = hidden_states.transpose(1,2) + else: + # Self Attention + hidden_states = rms_norm(hidden_states + self.self_attn(cos_sin=cos_sin, hidden_states=hidden_states), variance_epsilon=self.norm_eps) + # Fully Connected + out = self.mlp(hidden_states) + hidden_states = rms_norm(hidden_states + out, variance_epsilon=self.norm_eps) + return hidden_states + +class TinyRecursiveReasoningModel_ACTV1ReasoningModule(nn.Module): + def __init__(self, layers: List[TinyRecursiveReasoningModel_ACTV1Block]): + super().__init__() + self.layers = torch.nn.ModuleList(layers) + + def forward(self, hidden_states: torch.Tensor, input_injection: torch.Tensor, **kwargs) -> torch.Tensor: + hidden_states = hidden_states + input_injection + for layer in self.layers: + hidden_states = layer(hidden_states=hidden_states, **kwargs) + return hidden_states + + +class TinyRecursiveReasoningModel_ACTV1_Inner(nn.Module): + def __init__(self, config: TinyRecursiveReasoningModel_ACTV1Config) -> None: + super().__init__() + self.config = config + self.forward_dtype = getattr(torch, self.config.forward_dtype) + + # I/O + + self.embed_scale = math.sqrt(self.config.hidden_size) + embed_init_std = 1.0 / self.embed_scale + + self.embed_tokens = CastedEmbedding(self.config.vocab_size, self.config.hidden_size, init_std=embed_init_std, cast_to=self.forward_dtype) + self.lm_head = CastedLinear(self.config.hidden_size, self.config.vocab_size, bias=False) + self.q_head = CastedLinear(self.config.hidden_size, 2, bias=True) + + self.puzzle_emb_len = -(self.config.puzzle_emb_ndim // -self.config.hidden_size) if self.config.puzzle_emb_len == 0 else self.config.puzzle_emb_len # ceil div + if self.config.puzzle_emb_ndim > 0: + # Zero init puzzle embeddings + self.puzzle_emb = CastedSparseEmbedding(self.config.num_puzzle_identifiers, self.config.puzzle_emb_ndim, + batch_size=self.config.batch_size, init_std=0, cast_to=self.forward_dtype) + + # LM Blocks + if self.config.pos_encodings == "rope": + self.rotary_emb = RotaryEmbedding(dim=self.config.hidden_size // self.config.num_heads, + max_position_embeddings=self.config.seq_len + self.puzzle_emb_len, + base=self.config.rope_theta) + elif self.config.pos_encodings == "learned": + self.embed_pos = CastedEmbedding(self.config.seq_len + self.puzzle_emb_len, self.config.hidden_size, init_std=embed_init_std, cast_to=self.forward_dtype) + else: + pass + + # Reasoning Layers + self.L_level = TinyRecursiveReasoningModel_ACTV1ReasoningModule(layers=[TinyRecursiveReasoningModel_ACTV1Block(self.config) for _i in range(self.config.L_layers)]) + + # Initial states + self.H_init = nn.Buffer(trunc_normal_init_(torch.empty(self.config.hidden_size, dtype=self.forward_dtype), std=1), persistent=True) + self.L1_init = nn.Buffer(trunc_normal_init_(torch.empty(self.config.hidden_size, dtype=self.forward_dtype), std=1), persistent=True) + self.L2_init = nn.Buffer(trunc_normal_init_(torch.empty(self.config.hidden_size, dtype=self.forward_dtype), std=1), persistent=True) + self.L3_init = nn.Buffer(trunc_normal_init_(torch.empty(self.config.hidden_size, dtype=self.forward_dtype), std=1), persistent=True) + self.L4_init = nn.Buffer(trunc_normal_init_(torch.empty(self.config.hidden_size, dtype=self.forward_dtype), std=1), persistent=True) + self.L5_init = nn.Buffer(trunc_normal_init_(torch.empty(self.config.hidden_size, dtype=self.forward_dtype), std=1), persistent=True) + self.L6_init = nn.Buffer(trunc_normal_init_(torch.empty(self.config.hidden_size, dtype=self.forward_dtype), std=1), persistent=True) + + # Q head special init + # Init Q to (almost) zero for faster learning during bootstrapping + with torch.no_grad(): + self.q_head.weight.zero_() + self.q_head.bias.fill_(-5) # type: ignore + + def _input_embeddings(self, input: torch.Tensor, puzzle_identifiers: torch.Tensor): + # Token embedding + embedding = self.embed_tokens(input.to(torch.int32)) + + # Puzzle embeddings + if self.config.puzzle_emb_ndim > 0: + puzzle_embedding = self.puzzle_emb(puzzle_identifiers) + + pad_count = self.puzzle_emb_len * self.config.hidden_size - puzzle_embedding.shape[-1] + if pad_count > 0: + puzzle_embedding = F.pad(puzzle_embedding, (0, pad_count)) + + embedding = torch.cat((puzzle_embedding.view(-1, self.puzzle_emb_len, self.config.hidden_size), embedding), dim=-2) + + # Position embeddings + if self.config.pos_encodings == "learned": + # scale by 1/sqrt(2) to maintain forward variance + embedding = 0.707106781 * (embedding + self.embed_pos.embedding_weight.to(self.forward_dtype)) + + # Scale + return self.embed_scale * embedding + + def empty_carry(self, batch_size: int): + return TinyRecursiveReasoningModel_ACTV1InnerCarry( + z_H=torch.empty(batch_size, self.config.seq_len + self.puzzle_emb_len, self.config.hidden_size, dtype=self.forward_dtype), + z_L1=torch.empty(batch_size, self.config.seq_len + self.puzzle_emb_len, self.config.hidden_size, dtype=self.forward_dtype), + z_L2=torch.empty(batch_size, self.config.seq_len + self.puzzle_emb_len, self.config.hidden_size, dtype=self.forward_dtype), + z_L3=torch.empty(batch_size, self.config.seq_len + self.puzzle_emb_len, self.config.hidden_size, dtype=self.forward_dtype), + z_L4=torch.empty(batch_size, self.config.seq_len + self.puzzle_emb_len, self.config.hidden_size, dtype=self.forward_dtype), + z_L5=torch.empty(batch_size, self.config.seq_len + self.puzzle_emb_len, self.config.hidden_size, dtype=self.forward_dtype), + z_L6=torch.empty(batch_size, self.config.seq_len + self.puzzle_emb_len, self.config.hidden_size, dtype=self.forward_dtype), + ) + + def reset_carry(self, reset_flag: torch.Tensor, carry: TinyRecursiveReasoningModel_ACTV1InnerCarry): + return TinyRecursiveReasoningModel_ACTV1InnerCarry( + z_H=torch.where(reset_flag.view(-1, 1, 1), self.H_init, carry.z_H), + z_L1=torch.where(reset_flag.view(-1, 1, 1), self.L1_init, carry.z_L1), + z_L2=torch.where(reset_flag.view(-1, 1, 1), self.L2_init, carry.z_L2), + z_L3=torch.where(reset_flag.view(-1, 1, 1), self.L3_init, carry.z_L3), + z_L4=torch.where(reset_flag.view(-1, 1, 1), self.L4_init, carry.z_L4), + z_L5=torch.where(reset_flag.view(-1, 1, 1), self.L5_init, carry.z_L5), + z_L6=torch.where(reset_flag.view(-1, 1, 1), self.L6_init, carry.z_L6), + ) + + + def forward(self, carry: TinyRecursiveReasoningModel_ACTV1InnerCarry, batch: Dict[str, torch.Tensor]) -> Tuple[TinyRecursiveReasoningModel_ACTV1InnerCarry, torch.Tensor, Tuple[torch.Tensor, torch.Tensor]]: + seq_info = dict( + cos_sin=self.rotary_emb() if hasattr(self, "rotary_emb") else None, + ) + + # Input encoding + input_embeddings = self._input_embeddings(batch["inputs"], batch["puzzle_identifiers"]) + + # Forward iterations + it = 0 + z_H, z_L = carry.z_H, [carry.z_L1, carry.z_L2, carry.z_L3, carry.z_L4, carry.z_L5, carry.z_L6] + # H_cycles-1 without grad + with torch.no_grad(): + for _H_step in range(self.config.H_cycles-1): + for _L_step in range(self.config.L_cycles): + z_L_ = z_L[0] + z_L[1] + z_L[2] + z_L[3] + z_L[4] + z_L[5] + z_L[_L_step] = self.L_level(z_L_, z_H + input_embeddings, **seq_info) + z_L_ = z_L[0] + z_L[1] + z_L[2] + z_L[3] + z_L[4] + z_L[5] + z_H = self.L_level(z_H, z_L_, **seq_info) + # 1 with grad + for _L_step in range(self.config.L_cycles): + z_L_ = z_L[0] + z_L[1] + z_L[2] + z_L[3] + z_L[4] + z_L[5] + z_L[_L_step] = self.L_level(z_L_, z_H + input_embeddings, **seq_info) + z_L_ = z_L[0] + z_L[1] + z_L[2] + z_L[3] + z_L[4] + z_L[5] + z_H = self.L_level(z_H, z_L_, **seq_info) + + # LM Outputs + new_carry = TinyRecursiveReasoningModel_ACTV1InnerCarry(z_H=z_H.detach(), z_L1=z_L[0].detach(), z_L2=z_L[1].detach(), z_L3=z_L[2].detach(), z_L4=z_L[3].detach(), z_L5=z_L[4].detach(), z_L6=z_L[5].detach()) # New carry no grad + output = self.lm_head(z_H)[:, self.puzzle_emb_len:] + q_logits = self.q_head(z_H[:, 0]).to(torch.float32) # Q-head; uses the first puzzle_emb position + return new_carry, output, (q_logits[..., 0], q_logits[..., 1]) + + +class TinyRecursiveReasoningModel_ACTV1(nn.Module): + """ACT wrapper.""" + + def __init__(self, config_dict: dict): + super().__init__() + self.config = TinyRecursiveReasoningModel_ACTV1Config(**config_dict) + self.inner = TinyRecursiveReasoningModel_ACTV1_Inner(self.config) + + @property + def puzzle_emb(self): + return self.inner.puzzle_emb + + def initial_carry(self, batch: Dict[str, torch.Tensor]): + batch_size = batch["inputs"].shape[0] + + return TinyRecursiveReasoningModel_ACTV1Carry( + inner_carry=self.inner.empty_carry(batch_size), # Empty is expected, it will be reseted in first pass as all sequences are halted. + + steps=torch.zeros((batch_size, ), dtype=torch.int32), + halted=torch.ones((batch_size, ), dtype=torch.bool), # Default to halted + + current_data={k: torch.empty_like(v) for k, v in batch.items()} + ) + + def forward(self, carry: TinyRecursiveReasoningModel_ACTV1Carry, batch: Dict[str, torch.Tensor]) -> Tuple[TinyRecursiveReasoningModel_ACTV1Carry, Dict[str, torch.Tensor]]: + + # Update data, carry (removing halted sequences) + new_inner_carry = self.inner.reset_carry(carry.halted, carry.inner_carry) + + new_steps = torch.where(carry.halted, 0, carry.steps) + + new_current_data = {k: torch.where(carry.halted.view((-1, ) + (1, ) * (batch[k].ndim - 1)), batch[k], v) for k, v in carry.current_data.items()} + + # Forward inner model + new_inner_carry, logits, (q_halt_logits, q_continue_logits) = self.inner(new_inner_carry, new_current_data) + + outputs = { + "logits": logits, + "q_halt_logits": q_halt_logits, + "q_continue_logits": q_continue_logits + } + + with torch.no_grad(): + # Step + new_steps = new_steps + 1 + is_last_step = new_steps >= self.config.halt_max_steps + + halted = is_last_step + + # if training, and ACT is enabled + if self.training and (self.config.halt_max_steps > 1): + + # Halt signal + # NOTE: During evaluation, always use max steps, this is to guarantee the same halting steps inside a batch for batching purposes + + if self.config.no_ACT_continue: + halted = halted | (q_halt_logits > 0) + else: + halted = halted | (q_halt_logits > q_continue_logits) + + # Exploration + min_halt_steps = (torch.rand_like(q_halt_logits) < self.config.halt_exploration_prob) * torch.randint_like(new_steps, low=2, high=self.config.halt_max_steps + 1) + halted = halted & (new_steps >= min_halt_steps) + + if not self.config.no_ACT_continue: + # Compute target Q + # NOTE: No replay buffer and target networks for computing target Q-value. + # As batch_size is large, there're many parallel envs. + # Similar concept as PQN https://arxiv.org/abs/2407.04811 + _, _, (next_q_halt_logits, next_q_continue_logits), _, _ = self.inner(new_inner_carry, new_current_data) + outputs["target_q_continue"] = torch.sigmoid(torch.where(is_last_step, next_q_halt_logits, torch.maximum(next_q_halt_logits, next_q_continue_logits))) + + return TinyRecursiveReasoningModel_ACTV1Carry(new_inner_carry, new_steps, halted, new_current_data), outputs diff --git a/models/recursive_reasoning/trm_singlez.py b/models/recursive_reasoning/trm_singlez.py new file mode 100644 index 0000000..e5e1a7d --- /dev/null +++ b/models/recursive_reasoning/trm_singlez.py @@ -0,0 +1,294 @@ +from typing import Tuple, List, Dict, Optional +from dataclasses import dataclass +import math +import torch +import copy +import torch.nn.functional as F +from torch import nn +from pydantic import BaseModel +import random +from models.common import trunc_normal_init_ +from models.layers import rms_norm, LinearSwish, SwiGLU, Attention, RotaryEmbedding, CosSin, CastedEmbedding, CastedLinear +from models.sparse_embedding import CastedSparseEmbedding + +IGNORE_LABEL_ID = -100 + +@dataclass +class TinyRecursiveReasoningModel_ACTV1InnerCarry: + z_L: torch.Tensor + + + +@dataclass +class TinyRecursiveReasoningModel_ACTV1Carry: + inner_carry: TinyRecursiveReasoningModel_ACTV1InnerCarry + + steps: torch.Tensor + halted: torch.Tensor + + current_data: Dict[str, torch.Tensor] + + +class TinyRecursiveReasoningModel_ACTV1Config(BaseModel): + batch_size: int + seq_len: int + puzzle_emb_ndim: int = 0 + num_puzzle_identifiers: int + vocab_size: int + + H_cycles: int + L_cycles: int + + H_layers: int # ignored + L_layers: int + + # Transformer config + hidden_size: int + expansion: float + num_heads: int + pos_encodings: str + + rms_norm_eps: float = 1e-5 + rope_theta: float = 10000.0 + + # Halting Q-learning config + halt_max_steps: int + halt_exploration_prob: float + + forward_dtype: str = "bfloat16" + + # Alexia: added + mlp_t: bool = False # use mlp on L instead of transformer + puzzle_emb_len: int = 16 # if non-zero, its specified to this value + no_ACT_continue: bool = True # No continue ACT loss, only use the sigmoid of the halt which makes much more sense + +class TinyRecursiveReasoningModel_ACTV1Block(nn.Module): + def __init__(self, config: TinyRecursiveReasoningModel_ACTV1Config) -> None: + super().__init__() + + self.config = config + if self.config.mlp_t: + self.puzzle_emb_len = -(self.config.puzzle_emb_ndim // -self.config.hidden_size) if self.config.puzzle_emb_len == 0 else self.config.puzzle_emb_len + self.mlp_t = SwiGLU( + hidden_size=self.config.seq_len + self.puzzle_emb_len, # L + expansion=config.expansion, + ) + else: + self.self_attn = Attention( + hidden_size=config.hidden_size, + head_dim=config.hidden_size // config.num_heads, + num_heads=config.num_heads, + num_key_value_heads=config.num_heads, + causal=False + ) + self.mlp = SwiGLU( + hidden_size=config.hidden_size, + expansion=config.expansion, + ) + self.norm_eps = config.rms_norm_eps + + def forward(self, cos_sin: CosSin, hidden_states: torch.Tensor) -> torch.Tensor: + # B, L, D = hidden_states.shape + # Post Norm + if self.config.mlp_t: + hidden_states = hidden_states.transpose(1,2) + out = self.mlp_t(hidden_states) + hidden_states = rms_norm(hidden_states + out, variance_epsilon=self.norm_eps) + hidden_states = hidden_states.transpose(1,2) + else: + # Self Attention + hidden_states = rms_norm(hidden_states + self.self_attn(cos_sin=cos_sin, hidden_states=hidden_states), variance_epsilon=self.norm_eps) + # Fully Connected + out = self.mlp(hidden_states) + hidden_states = rms_norm(hidden_states + out, variance_epsilon=self.norm_eps) + return hidden_states + +class TinyRecursiveReasoningModel_ACTV1ReasoningModule(nn.Module): + def __init__(self, layers: List[TinyRecursiveReasoningModel_ACTV1Block]): + super().__init__() + self.layers = torch.nn.ModuleList(layers) + + def forward(self, hidden_states: torch.Tensor, **kwargs) -> torch.Tensor: + for layer in self.layers: + hidden_states = layer(hidden_states=hidden_states, **kwargs) + return hidden_states + + +class TinyRecursiveReasoningModel_ACTV1_Inner(nn.Module): + def __init__(self, config: TinyRecursiveReasoningModel_ACTV1Config) -> None: + super().__init__() + self.config = config + self.forward_dtype = getattr(torch, self.config.forward_dtype) + + # I/O + + self.embed_scale = math.sqrt(self.config.hidden_size) + embed_init_std = 1.0 / self.embed_scale + + self.embed_tokens = CastedEmbedding(self.config.vocab_size, self.config.hidden_size, init_std=embed_init_std, cast_to=self.forward_dtype) + self.lm_head = CastedLinear(self.config.hidden_size, self.config.vocab_size, bias=False) + self.q_head = CastedLinear(self.config.hidden_size, 2, bias=True) + + self.puzzle_emb_len = -(self.config.puzzle_emb_ndim // -self.config.hidden_size) if self.config.puzzle_emb_len == 0 else self.config.puzzle_emb_len # ceil div + if self.config.puzzle_emb_ndim > 0: + # Zero init puzzle embeddings + self.puzzle_emb = CastedSparseEmbedding(self.config.num_puzzle_identifiers, self.config.puzzle_emb_ndim, + batch_size=self.config.batch_size, init_std=0, cast_to=self.forward_dtype) + + # LM Blocks + if self.config.pos_encodings == "rope": + self.rotary_emb = RotaryEmbedding(dim=self.config.hidden_size // self.config.num_heads, + max_position_embeddings=self.config.seq_len + self.puzzle_emb_len, + base=self.config.rope_theta) + elif self.config.pos_encodings == "learned": + self.embed_pos = CastedEmbedding(self.config.seq_len + self.puzzle_emb_len, self.config.hidden_size, init_std=embed_init_std, cast_to=self.forward_dtype) + else: + pass + + # Reasoning Layers + self.L_level = TinyRecursiveReasoningModel_ACTV1ReasoningModule(layers=[TinyRecursiveReasoningModel_ACTV1Block(self.config) for _i in range(self.config.L_layers)]) + + # Initial states + self.L_init = nn.Buffer(trunc_normal_init_(torch.empty(self.config.hidden_size, dtype=self.forward_dtype), std=1), persistent=True) + + # Q head special init + # Init Q to (almost) zero for faster learning during bootstrapping + with torch.no_grad(): + self.q_head.weight.zero_() + self.q_head.bias.fill_(-5) # type: ignore + + def _input_embeddings(self, input: torch.Tensor, puzzle_identifiers: torch.Tensor): + # Token embedding + embedding = self.embed_tokens(input.to(torch.int32)) + + # Puzzle embeddings + if self.config.puzzle_emb_ndim > 0: + puzzle_embedding = self.puzzle_emb(puzzle_identifiers) + + pad_count = self.puzzle_emb_len * self.config.hidden_size - puzzle_embedding.shape[-1] + if pad_count > 0: + puzzle_embedding = F.pad(puzzle_embedding, (0, pad_count)) + + embedding = torch.cat((puzzle_embedding.view(-1, self.puzzle_emb_len, self.config.hidden_size), embedding), dim=-2) + + # Position embeddings + if self.config.pos_encodings == "learned": + # scale by 1/sqrt(2) to maintain forward variance + embedding = 0.707106781 * (embedding + self.embed_pos.embedding_weight.to(self.forward_dtype)) + + # Scale + return self.embed_scale * embedding + + def empty_carry(self, batch_size: int): + return TinyRecursiveReasoningModel_ACTV1InnerCarry( + z_L=torch.empty(batch_size, self.config.seq_len + self.puzzle_emb_len, self.config.hidden_size, dtype=self.forward_dtype), + ) + + def reset_carry(self, reset_flag: torch.Tensor, carry: TinyRecursiveReasoningModel_ACTV1InnerCarry): + return TinyRecursiveReasoningModel_ACTV1InnerCarry( + z_L=torch.where(reset_flag.view(-1, 1, 1), self.L_init, carry.z_L), + ) + + def forward(self, carry: TinyRecursiveReasoningModel_ACTV1InnerCarry, batch: Dict[str, torch.Tensor]) -> Tuple[TinyRecursiveReasoningModel_ACTV1InnerCarry, torch.Tensor, Tuple[torch.Tensor, torch.Tensor]]: + seq_info = dict( + cos_sin=self.rotary_emb() if hasattr(self, "rotary_emb") else None, + ) + + # Input encoding + input_embeddings = self._input_embeddings(batch["inputs"], batch["puzzle_identifiers"]) + + # Forward iterations + it = 0 + z_L = carry.z_L + # H_cycles-1 without grad + with torch.no_grad(): + for _H_step in range(self.config.H_cycles-1): + for _L_step in range(self.config.L_cycles): + z_L = self.L_level(z_L + input_embeddings, **seq_info) + z_L = self.L_level(z_L, **seq_info) + # 1 with grad + for _L_step in range(self.config.L_cycles): + z_L = self.L_level(z_L + input_embeddings, **seq_info) + z_L = self.L_level(z_L, **seq_info) + z_out = z_L + + # LM Outputs + new_carry = TinyRecursiveReasoningModel_ACTV1InnerCarry(z_L=z_L.detach()) # New carry no grad + output = self.lm_head(z_out)[:, self.puzzle_emb_len:] + q_logits = self.q_head(z_out[:, 0]).to(torch.float32) # Q-head; uses the first puzzle_emb position + return new_carry, output, (q_logits[..., 0], q_logits[..., 1]) + + +class TinyRecursiveReasoningModel_ACTV1(nn.Module): + """ACT wrapper.""" + + def __init__(self, config_dict: dict): + super().__init__() + self.config = TinyRecursiveReasoningModel_ACTV1Config(**config_dict) + self.inner = TinyRecursiveReasoningModel_ACTV1_Inner(self.config) + + @property + def puzzle_emb(self): + return self.inner.puzzle_emb + + def initial_carry(self, batch: Dict[str, torch.Tensor]): + batch_size = batch["inputs"].shape[0] + + return TinyRecursiveReasoningModel_ACTV1Carry( + inner_carry=self.inner.empty_carry(batch_size), # Empty is expected, it will be reseted in first pass as all sequences are halted. + + steps=torch.zeros((batch_size, ), dtype=torch.int32), + halted=torch.ones((batch_size, ), dtype=torch.bool), # Default to halted + + current_data={k: torch.empty_like(v) for k, v in batch.items()} + ) + + def forward(self, carry: TinyRecursiveReasoningModel_ACTV1Carry, batch: Dict[str, torch.Tensor]) -> Tuple[TinyRecursiveReasoningModel_ACTV1Carry, Dict[str, torch.Tensor]]: + + # Update data, carry (removing halted sequences) + new_inner_carry = self.inner.reset_carry(carry.halted, carry.inner_carry) + + new_steps = torch.where(carry.halted, 0, carry.steps) + + new_current_data = {k: torch.where(carry.halted.view((-1, ) + (1, ) * (batch[k].ndim - 1)), batch[k], v) for k, v in carry.current_data.items()} + + # Forward inner model + new_inner_carry, logits, (q_halt_logits, q_continue_logits) = self.inner(new_inner_carry, new_current_data) + + outputs = { + "logits": logits, + "q_halt_logits": q_halt_logits, + "q_continue_logits": q_continue_logits + } + + with torch.no_grad(): + # Step + new_steps = new_steps + 1 + is_last_step = new_steps >= self.config.halt_max_steps + + halted = is_last_step + + # if training, and ACT is enabled + if self.training and (self.config.halt_max_steps > 1): + + # Halt signal + # NOTE: During evaluation, always use max steps, this is to guarantee the same halting steps inside a batch for batching purposes + + if self.config.no_ACT_continue: + halted = halted | (q_halt_logits > 0) + else: + halted = halted | (q_halt_logits > q_continue_logits) + + # Exploration + min_halt_steps = (torch.rand_like(q_halt_logits) < self.config.halt_exploration_prob) * torch.randint_like(new_steps, low=2, high=self.config.halt_max_steps + 1) + halted = halted & (new_steps >= min_halt_steps) + + if not self.config.no_ACT_continue: + # Compute target Q + # NOTE: No replay buffer and target networks for computing target Q-value. + # As batch_size is large, there're many parallel envs. + # Similar concept as PQN https://arxiv.org/abs/2407.04811 + _, _, (next_q_halt_logits, next_q_continue_logits), _, _ = self.inner(new_inner_carry, new_current_data) + outputs["target_q_continue"] = torch.sigmoid(torch.where(is_last_step, next_q_halt_logits, torch.maximum(next_q_halt_logits, next_q_continue_logits))) + + return TinyRecursiveReasoningModel_ACTV1Carry(new_inner_carry, new_steps, halted, new_current_data), outputs diff --git a/models/sparse_embedding.py b/models/sparse_embedding.py new file mode 100644 index 0000000..f369205 --- /dev/null +++ b/models/sparse_embedding.py @@ -0,0 +1,132 @@ +from typing import Union + +import torch +from torch import nn +import torch.distributed as dist +from torch.optim.optimizer import Optimizer, ParamsT + +from models.common import trunc_normal_init_ + + +class CastedSparseEmbedding(nn.Module): + def __init__(self, num_embeddings: int, embedding_dim: int, batch_size: int, init_std: float, cast_to: torch.dtype): + super().__init__() + self.cast_to = cast_to + + # Real Weights + # Truncated LeCun normal init + self.weights = nn.Buffer( + trunc_normal_init_(torch.empty((num_embeddings, embedding_dim)), std=init_std), persistent=True + ) + + # Local weights and IDs + # Local embeddings, with gradient, not persistent + self.local_weights = nn.Buffer(torch.zeros(batch_size, embedding_dim, requires_grad=True), persistent=False) + # Local embedding IDs, not persistent + self.local_ids = nn.Buffer(torch.zeros(batch_size, dtype=torch.int32), persistent=False) + + def forward(self, inputs: torch.Tensor) -> torch.Tensor: + if not self.training: + # Test mode, no gradient + return self.weights[inputs].to(self.cast_to) + + # Training mode, fill puzzle embedding from weights + with torch.no_grad(): + self.local_weights.copy_(self.weights[inputs]) + self.local_ids.copy_(inputs) + + return self.local_weights.to(self.cast_to) + + +class CastedSparseEmbeddingSignSGD_Distributed(Optimizer): + def __init__( + self, + params: ParamsT, + + world_size: int, + lr: Union[float, torch.Tensor] = 1e-3, + weight_decay: float = 1e-2, + ): + if not 0.0 <= lr: + raise ValueError(f"Invalid learning rate: {lr}") + if not 0.0 <= weight_decay: + raise ValueError(f"Invalid weight_decay value: {weight_decay}") + + defaults = dict( + lr=lr, + weight_decay=weight_decay, + world_size=world_size + ) + super().__init__(params, defaults) + + @torch.no_grad + def step(self, closure=None): # type: ignore + for group in self.param_groups: + # Find the sparse embedding weights + local_weights_grad = None + local_ids = None + weights = None + + assert len(group["params"]) == 3 + for p in group["params"]: + if p.requires_grad: + local_weights_grad = p.grad + elif p.ndim == 1: + local_ids = p + elif p.ndim == 2: + weights = p + else: + assert False + + assert local_ids is not None + assert weights is not None + + # Apply SignSGD + # Adam ≈ SignSGD if gradient is very sparse + if local_weights_grad is not None: + _sparse_emb_signsgd_dist( + local_weights_grad, + local_ids, + weights, + + lr=group["lr"], + weight_decay=group["weight_decay"], + world_size=group["world_size"] + ) + + +def _sparse_emb_signsgd_dist( + local_weights_grad: torch.Tensor, + local_ids: torch.Tensor, + weights: torch.Tensor, + + lr: float, + weight_decay: float, + world_size: int +) -> None: + N, D = local_weights_grad.shape + + # All-gather + all_weights_grad = local_weights_grad + all_ids = local_ids + + if world_size > 1: + all_weights_grad = torch.empty((world_size * N, D), dtype=local_weights_grad.dtype, device=local_weights_grad.device) + all_ids = torch.empty(world_size * N, dtype=local_ids.dtype, device=local_ids.device) + + dist.all_gather_into_tensor(all_weights_grad, local_weights_grad) + dist.all_gather_into_tensor(all_ids, local_ids) + + # Unique + grad_ids, inv = all_ids.unique(return_inverse=True) + + grad = torch.zeros((grad_ids.shape[0], D), dtype=all_weights_grad.dtype, device=all_weights_grad.device) + grad.scatter_add_(0, inv.unsqueeze(-1).expand(-1, D), all_weights_grad) + + # SignSGD with decoupled weight decay + p = weights[grad_ids] + + p.mul_(1.0 - lr * weight_decay).add_(torch.sign(grad), alpha=-lr) + + # Write updated slices back + weights[grad_ids] = p diff --git a/pretrain.py b/pretrain.py new file mode 100644 index 0000000..b9072e2 --- /dev/null +++ b/pretrain.py @@ -0,0 +1,654 @@ +from typing import Optional, Any, Sequence, List +from dataclasses import dataclass +import os +import math +import yaml +import shutil +import copy + +import torch +import torch.distributed as dist +from torch import nn +from torch.utils.data import DataLoader + +import tqdm +import wandb +import coolname +import hydra +import pydantic +from omegaconf import DictConfig +from adam_atan2 import AdamATan2 + +from puzzle_dataset import PuzzleDataset, PuzzleDatasetConfig, PuzzleDatasetMetadata +from utils.functions import load_model_class, get_model_source_path +from models.sparse_embedding import CastedSparseEmbeddingSignSGD_Distributed +from models.ema import EMAHelper + + +class LossConfig(pydantic.BaseModel): + model_config = pydantic.ConfigDict(extra='allow') + name: str + + +class ArchConfig(pydantic.BaseModel): + model_config = pydantic.ConfigDict(extra='allow') + name: str + loss: LossConfig + + +class EvaluatorConfig(pydantic.BaseModel): + model_config = pydantic.ConfigDict(extra="allow") + name: str + + +class PretrainConfig(pydantic.BaseModel): + # Config + arch: ArchConfig + # Data + data_paths: List[str] + data_paths_test: List[str] = [] + # Evaluators + evaluators: List[EvaluatorConfig] = [] + + # Hyperparams + global_batch_size: int + epochs: int + + lr: float + lr_min_ratio: float + lr_warmup_steps: int + + weight_decay: float + beta1: float + beta2: float + + # Puzzle embedding + puzzle_emb_lr: float + puzzle_emb_weight_decay: float + + # Names + project_name: Optional[str] = None + run_name: Optional[str] = None + load_checkpoint: Optional[str] = None + checkpoint_path: Optional[str] = None + + # Extras + seed: int = 0 + checkpoint_every_eval: bool = False + eval_interval: Optional[int] = None + min_eval_interval: Optional[int] = 0 # when to start eval + eval_save_outputs: List[str] = [] + + ema: bool = False # use Exponential-Moving-Average + ema_rate: float = 0.999 # EMA-rate + freeze_weights: bool = False # If True, freeze weights and only learn the embeddings + +@dataclass +class TrainState: + model: nn.Module + optimizers: Sequence[torch.optim.Optimizer] + optimizer_lrs: Sequence[float] + carry: Any + + step: int + total_steps: int + + +def create_dataloader(config: PretrainConfig, split: str, rank: int, world_size: int, **kwargs): + dataset = PuzzleDataset(PuzzleDatasetConfig( + seed=config.seed, + dataset_paths=config.data_paths_test if len(config.data_paths_test)>0 and split=="test" else config.data_paths, + rank=rank, + num_replicas=world_size, + **kwargs + ), split=split) + dataloader = DataLoader( + dataset, + batch_size=None, + num_workers=1, + prefetch_factor=8, + pin_memory=True, + persistent_workers=True + ) + return dataloader, dataset.metadata + + +def create_model(config: PretrainConfig, train_metadata: PuzzleDatasetMetadata, rank: int, world_size: int): + model_cfg = dict( + **config.arch.__pydantic_extra__, # type: ignore + batch_size=config.global_batch_size // world_size, + vocab_size=train_metadata.vocab_size, + seq_len=train_metadata.seq_len, + num_puzzle_identifiers=train_metadata.num_puzzle_identifiers, + causal=False # Non-autoregressive + ) + + # Instantiate model with loss head + model_cls = load_model_class(config.arch.name) + loss_head_cls = load_model_class(config.arch.loss.name) + + with torch.device("cuda"): + model: nn.Module = model_cls(model_cfg) + print(model) + model = loss_head_cls(model, **config.arch.loss.__pydantic_extra__) # type: ignore + if "DISABLE_COMPILE" not in os.environ: + model = torch.compile(model) # type: ignore + + # Load checkpoint + if rank == 0: + load_checkpoint(model, config) + + # Broadcast parameters from rank 0 + if world_size > 1: + with torch.no_grad(): + for param in list(model.parameters()) + list(model.buffers()): + dist.broadcast(param, src=0) + + # Optimizers and lr + if config.arch.puzzle_emb_ndim == 0: + optimizers = [ + AdamATan2( + model.parameters(), + lr=0, # Needs to be set by scheduler + weight_decay=config.weight_decay, + betas=(config.beta1, config.beta2) + ) + ] + optimizer_lrs = [ + config.lr + ] + elif config.freeze_weights: + optimizers = [ + CastedSparseEmbeddingSignSGD_Distributed( + model.model.puzzle_emb.buffers(), # type: ignore + lr=0, # Needs to be set by scheduler + weight_decay=config.puzzle_emb_weight_decay, + world_size=world_size + ) + ] + optimizer_lrs = [ + config.puzzle_emb_lr + ] + else: + optimizers = [ + CastedSparseEmbeddingSignSGD_Distributed( + model.model.puzzle_emb.buffers(), # type: ignore + lr=0, # Needs to be set by scheduler + weight_decay=config.puzzle_emb_weight_decay, + world_size=world_size + ), + AdamATan2( + model.parameters(), + lr=0, # Needs to be set by scheduler + weight_decay=config.weight_decay, + betas=(config.beta1, config.beta2) + ) + ] + optimizer_lrs = [ + config.puzzle_emb_lr, + config.lr + ] + + return model, optimizers, optimizer_lrs + +def mix_weights_direct(device, alpha, net, nets): + sd = [] + for i in range(len(nets)): + sd += [nets[i].state_dict()] + sd_alpha = {} + for k in sd[0].keys(): + comb_net = alpha[0]*sd[0][k].to(device) + for i in range(1,len(nets)): + comb_net += alpha[i]*sd[i][k].to(device) + sd_alpha[k] = comb_net + net.load_state_dict(sd_alpha) + return net + +def cosine_schedule_with_warmup_lr_lambda( + current_step: int, *, base_lr: float, num_warmup_steps: int, num_training_steps: int, min_ratio: float = 0.0, num_cycles: float = 0.5 +): + if current_step < num_warmup_steps: + return base_lr * float(current_step) / float(max(1, num_warmup_steps)) + + progress = float(current_step - num_warmup_steps) / float(max(1, num_training_steps - num_warmup_steps)) + return base_lr * (min_ratio + max(0.0, (1 - min_ratio) * 0.5 * (1.0 + math.cos(math.pi * float(num_cycles) * 2.0 * progress)))) + + +def init_train_state(config: PretrainConfig, train_metadata: PuzzleDatasetMetadata, rank: int, world_size: int): + # Estimated total training steps + total_steps = int(config.epochs * train_metadata.total_groups * train_metadata.mean_puzzle_examples / config.global_batch_size) + + # Model + model, optimizers, optimizer_lrs = create_model(config, train_metadata, rank=rank, world_size=world_size) + + return TrainState( + step=0, + total_steps=total_steps, + + model=model, + optimizers=optimizers, + optimizer_lrs=optimizer_lrs, + carry=None + ) + + +def save_train_state(config: PretrainConfig, train_state: TrainState): + # FIXME: Only saved model. + if config.checkpoint_path is None: + return + + os.makedirs(config.checkpoint_path, exist_ok=True) + torch.save(train_state.model.state_dict(), os.path.join(config.checkpoint_path, f"step_{train_state.step}")) + + +def load_checkpoint(model: nn.Module, config: PretrainConfig): + if config.load_checkpoint is not None: + print(f"Loading checkpoint {config.load_checkpoint}") + + # Load state dict + state_dict = torch.load(config.load_checkpoint, map_location="cuda") + + # Resize and reset puzzle emb if needed + puzzle_emb_name = "_orig_mod.model.inner.puzzle_emb.weights" + expected_shape: torch.Size = model.model.puzzle_emb.weights.shape # type: ignore + if puzzle_emb_name in state_dict: + puzzle_emb = state_dict[puzzle_emb_name] + if puzzle_emb.shape != expected_shape: + print(f"Resetting puzzle embedding as shape is different. Found {puzzle_emb.shape}, Expected {expected_shape}") + # Re-initialize using mean + state_dict[puzzle_emb_name] = ( + torch.mean(puzzle_emb, dim=0, keepdim=True).expand(expected_shape).contiguous() + ) + model.load_state_dict(state_dict, assign=True) + + +def compute_lr(base_lr: float, config: PretrainConfig, train_state: TrainState): + return cosine_schedule_with_warmup_lr_lambda( + current_step=train_state.step, + base_lr=base_lr, + num_warmup_steps=round(config.lr_warmup_steps), + num_training_steps=train_state.total_steps, + min_ratio=config.lr_min_ratio + ) + + + +def create_evaluators(config: PretrainConfig, eval_metadata: PuzzleDatasetMetadata) -> List[Any]: + data_paths =config.data_paths_test if len(config.data_paths_test)>0 else config.data_paths + # Initialize evaluators + evaluators = [] + for cfg in config.evaluators: + for data_path in data_paths: + cls = load_model_class(cfg.name, "evaluators.")( + data_path=data_path, eval_metadata=eval_metadata, **cfg.__pydantic_extra__ + ) # type: ignore + evaluators.append(cls) + + return evaluators + +def train_batch(config: PretrainConfig, train_state: TrainState, batch: Any, global_batch_size: int, rank: int, world_size: int): + train_state.step += 1 + if train_state.step > train_state.total_steps: # At most train_total_steps + return + + # To device + batch = {k: v.cuda() for k, v in batch.items()} + + # Init carry if it is None + if train_state.carry is None: + with torch.device("cuda"): + train_state.carry = train_state.model.initial_carry(batch) # type: ignore + + # Forward + train_state.carry, loss, metrics, _, _ = train_state.model(carry=train_state.carry, batch=batch, return_keys=[]) + + ((1 / global_batch_size) * loss).backward() + + # Allreduce + if world_size > 1: + for param in train_state.model.parameters(): + if param.grad is not None: + dist.all_reduce(param.grad) + + # Apply optimizer + lr_this_step = None + for optim, base_lr in zip(train_state.optimizers, train_state.optimizer_lrs): + lr_this_step = compute_lr(base_lr, config, train_state) + + for param_group in optim.param_groups: + param_group['lr'] = lr_this_step + + optim.step() + optim.zero_grad() + + # Reduce metrics + if len(metrics): + assert not any(v.requires_grad for v in metrics.values()) + + metric_keys = list(sorted(metrics.keys())) # Sort keys to guarantee all processes use the same order. + # Reduce and reconstruct + metric_values = torch.stack([metrics[k] for k in metric_keys]) + if world_size > 1: + dist.reduce(metric_values, dst=0) + + if rank == 0: + metric_values = metric_values.cpu().numpy() + reduced_metrics = {k: metric_values[i] for i, k in enumerate(metric_keys)} + + # Postprocess + count = max(reduced_metrics["count"], 1) # Avoid NaNs + reduced_metrics = {f"train/{k}": v / (global_batch_size if k.endswith("loss") else count) for k, v in reduced_metrics.items()} + + reduced_metrics["train/lr"] = lr_this_step + return reduced_metrics + +def evaluate( + config: PretrainConfig, + train_state: TrainState, + eval_loader: torch.utils.data.DataLoader, + eval_metadata: PuzzleDatasetMetadata, + evaluators: List[Any], + rank: int, + world_size: int, + cpu_group: Optional[dist.ProcessGroup], +): + reduced_metrics = None + + with torch.inference_mode(): + return_keys = set(config.eval_save_outputs) + for evaluator in evaluators: + evaluator.begin_eval() + return_keys.update(evaluator.required_outputs) + + # Run evaluation + set_ids = {k: idx for idx, k in enumerate(eval_metadata.sets)} + + save_preds = {} + + metric_keys = [] + metric_values = None + + carry = None + processed_batches = 0 + + for set_name, batch, global_batch_size in eval_loader: + processed_batches += 1 + if rank == 0: + print(f"Processing batch {processed_batches}: {set_name}") + + # To device + batch = {k: v.cuda() for k, v in batch.items()} + with torch.device("cuda"): + carry = train_state.model.initial_carry(batch) # type: ignore + + # Forward + inference_steps = 0 + while True: + carry, loss, metrics, preds, all_finish = train_state.model( + carry=carry, batch=batch, return_keys=return_keys + ) + inference_steps += 1 + + if all_finish: + break + + if rank == 0: + print(f" Completed inference in {inference_steps} steps") + + for collection in (batch, preds): + for k, v in collection.items(): + if k in config.eval_save_outputs: + save_preds.setdefault(k, []) + save_preds[k].append(v.cpu()) # Move to CPU for saving GPU memory + + for evaluator in evaluators: + evaluator.update_batch(batch, preds) + + del carry, loss, preds, batch, all_finish + + # Aggregate metrics + set_id = set_ids[set_name] + + if metric_values is None: + metric_keys = list( + sorted(metrics.keys()) + ) # Sort keys to guarantee all processes use the same order. + metric_values = torch.zeros( + (len(set_ids), len(metrics.values())), dtype=torch.float32, device="cuda" + ) + + metric_values[set_id] += torch.stack([metrics[k] for k in metric_keys]) + + del metrics + + # concatenate save preds + save_preds = {k: torch.cat(v, dim=0) for k, v in save_preds.items()} + + # Save preds + if config.checkpoint_path is not None and len(save_preds): + # Each rank save predictions independently + os.makedirs(os.path.dirname(config.checkpoint_path), exist_ok=True) + torch.save( + save_preds, os.path.join(config.checkpoint_path, f"step_{train_state.step}_all_preds.{rank}") + ) + + del save_preds + + # Reduce to rank 0 + if metric_values is not None: + if world_size > 1: + dist.reduce(metric_values, dst=0) + + if rank == 0: + reduced_metrics = metric_values.cpu().numpy() + reduced_metrics = { + set_name: { + metric_name: reduced_metrics[set_id, metric_id] + for metric_id, metric_name in enumerate(metric_keys) + } + for set_id, set_name in enumerate(set_ids) + } + + # Postprocess + for set_name, m in reduced_metrics.items(): + count = m.pop("count") + reduced_metrics[set_name] = {k: v / count for k, v in m.items()} + + # Run evaluators + if rank == 0: + print(f"\nRunning {len(evaluators)} evaluator(s)...") + + for i, evaluator in enumerate(evaluators): + if rank == 0: + print(f"Running evaluator {i+1}/{len(evaluators)}: {evaluator.__class__.__name__}") + + # Path for saving + evaluator_save_path = None + if config.checkpoint_path is not None: + evaluator_save_path = os.path.join( + config.checkpoint_path, + f"evaluator_{evaluator.__class__.__name__}_step_{train_state.step}", + ) + os.makedirs(evaluator_save_path, exist_ok=True) + + # Run and log + metrics = evaluator.result(evaluator_save_path, rank=rank, world_size=world_size, group=cpu_group) + if rank == 0 and metrics is not None: + if reduced_metrics is None: + reduced_metrics = {} + + reduced_metrics.update(metrics) + print(f" Completed {evaluator.__class__.__name__}") + + if rank == 0: + print("All evaluators completed!") + + return reduced_metrics + +def save_code_and_config(config: PretrainConfig): + if config.checkpoint_path is None or wandb.run is None: + return + + os.makedirs(config.checkpoint_path, exist_ok=True) + + # Copy code + code_list = [ + get_model_source_path(config.arch.name), + get_model_source_path(config.arch.loss.name) + ] + for code_file in code_list: + if code_file is not None: + code_name = os.path.basename(code_file) + + shutil.copy(code_file, os.path.join(config.checkpoint_path, code_name)) + + # Dump config as yaml + config_file = os.path.join(config.checkpoint_path, "all_config.yaml") + with open(config_file, "wt") as f: + yaml.dump(config.model_dump(), f) + + # Log code + wandb.run.log_code(config.checkpoint_path) + + +def load_synced_config(hydra_config: DictConfig, rank: int, world_size: int) -> PretrainConfig: + objects = [None] + if rank == 0: + config = PretrainConfig(**hydra_config) # type: ignore + + # Naming + if config.project_name is None: + config.project_name = f"{os.path.basename(config.data_paths[0]).capitalize()}-ACT-torch" + if config.run_name is None: + config.run_name = f"{config.arch.name.split('@')[-1]} {coolname.generate_slug(2)}" + if config.checkpoint_path is None: + config.checkpoint_path = os.path.join("checkpoints", config.project_name, config.run_name) + + objects = [config] + + if world_size > 1: + dist.broadcast_object_list(objects, src=0) + + return objects[0] # type: ignore + + +@hydra.main(config_path="config", config_name="cfg_pretrain", version_base=None) +def launch(hydra_config: DictConfig): + RANK = 0 + WORLD_SIZE = 1 + CPU_PROCESS_GROUP = None + + # Initialize distributed training if in distributed environment (e.g. torchrun) + if "LOCAL_RANK" in os.environ: + # Initialize distributed, default device and dtype + dist.init_process_group(backend="nccl") + + RANK = dist.get_rank() + WORLD_SIZE = dist.get_world_size() + + torch.cuda.set_device(int(os.environ["LOCAL_RANK"])) + + # CPU GLOO process group + CPU_PROCESS_GROUP = dist.new_group(backend="gloo") + assert ( + dist.get_rank(CPU_PROCESS_GROUP) == RANK and dist.get_world_size(CPU_PROCESS_GROUP) == WORLD_SIZE + ) + + # Load sync'ed config + config = load_synced_config(hydra_config, rank=RANK, world_size=WORLD_SIZE) + + # Seed RNGs to ensure consistency + torch.random.manual_seed(config.seed + RANK) + + # Dataset + train_epochs_per_iter = config.eval_interval if config.eval_interval is not None else config.epochs + total_iters = config.epochs // train_epochs_per_iter + + assert config.epochs % train_epochs_per_iter == 0, "Eval interval must be a divisor of total epochs." + + train_loader, train_metadata = create_dataloader(config, "train", test_set_mode=False, epochs_per_iter=train_epochs_per_iter, global_batch_size=config.global_batch_size, rank=RANK, world_size=WORLD_SIZE) + try: + eval_loader, eval_metadata = create_dataloader(config, "test", test_set_mode=True, epochs_per_iter=1, global_batch_size=config.global_batch_size, rank=RANK, world_size=WORLD_SIZE) + except: + print("NO EVAL DATA FOUND") + eval_loader = eval_metadata = None + + try: + evaluators = create_evaluators(config, eval_metadata) + except: + print("No evaluator found") + evaluators = [] + + # Train state + train_state = init_train_state(config, train_metadata, rank=RANK, world_size=WORLD_SIZE) + + # Progress bar and logger + progress_bar = None + ema_helper = None + if RANK == 0: + progress_bar = tqdm.tqdm(total=train_state.total_steps) + wandb.init(project=config.project_name, name=config.run_name, config=config.model_dump(), settings=wandb.Settings(_disable_stats=True)) # type: ignore + wandb.log({"num_params": sum(x.numel() for x in train_state.model.parameters())}, step=0) + save_code_and_config(config) + if config.ema: + print('Setup EMA') + ema_helper = EMAHelper(mu=config.ema_rate) + ema_helper.register(train_state.model) + + # Training Loop + for _iter_id in range(total_iters): + print (f"[Rank {RANK}, World Size {WORLD_SIZE}]: Epoch {_iter_id * train_epochs_per_iter}") + + ############ Train Iter + if RANK == 0: + print("TRAIN") + train_state.model.train() + for set_name, batch, global_batch_size in train_loader: + metrics = train_batch(config, train_state, batch, global_batch_size, rank=RANK, world_size=WORLD_SIZE) + + if RANK == 0 and metrics is not None: + wandb.log(metrics, step=train_state.step) + progress_bar.update(train_state.step - progress_bar.n) # type: ignore + if config.ema: + ema_helper.update(train_state.model) + + if _iter_id >= config.min_eval_interval: + ############ Evaluation + if RANK == 0: + print("EVALUATE") + if config.ema: + print("SWITCH TO EMA") + train_state_eval = copy.deepcopy(train_state) + train_state_eval.model = ema_helper.ema_copy(train_state_eval.model) + else: + train_state_eval = train_state + train_state_eval.model.eval() + metrics = evaluate(config, + train_state_eval, + eval_loader, + eval_metadata, + evaluators, + rank=RANK, + world_size=WORLD_SIZE, + cpu_group=CPU_PROCESS_GROUP) + + if RANK == 0 and metrics is not None: + wandb.log(metrics, step=train_state.step) + + ############ Checkpointing + if RANK == 0: + print("SAVE CHECKPOINT") + if RANK == 0 and (config.checkpoint_every_eval or (_iter_id == total_iters - 1)): + save_train_state(config, train_state_eval) + + if config.ema: + del train_state_eval + + # finalize + if dist.is_initialized(): + dist.destroy_process_group() + wandb.finish() + + +if __name__ == "__main__": + launch() diff --git a/puzzle_dataset.py b/puzzle_dataset.py new file mode 100644 index 0000000..16cf292 --- /dev/null +++ b/puzzle_dataset.py @@ -0,0 +1,250 @@ +import os +import json +from typing import Tuple, List, Dict, Optional +import numpy as np +import pydantic + +import torch +from torch.utils.data import IterableDataset, get_worker_info + +from models.losses import IGNORE_LABEL_ID +from dataset.common import PuzzleDatasetMetadata + +from argdantic import ArgParser +from pydantic import BaseModel + +def _sample_batch(rng: np.random.Generator, group_order: np.ndarray, puzzle_indices: np.ndarray, group_indices: np.ndarray, start_index: int, global_batch_size: int): + # Pack examples into a full batch + batch = [] + batch_puzzle_indices = [] + current_size = 0 + + while (start_index < group_order.size) and (current_size < global_batch_size): + # Pick a group and a puzzle from that group + group_id = group_order[start_index] + puzzle_id = rng.integers(group_indices[group_id], group_indices[group_id + 1]) + start_index += 1 + + # Get range of the puzzle + puzzle_start = puzzle_indices[puzzle_id] + puzzle_size = int(puzzle_indices[puzzle_id + 1] - puzzle_start) + + append_size = min(puzzle_size, global_batch_size - current_size) + + # Put into batch + batch_puzzle_indices.append(np.full(append_size, puzzle_id, dtype=np.int32)) + batch.append(puzzle_start + np.random.choice(puzzle_size, append_size, replace=False)) + + current_size += append_size + + return start_index, np.concatenate(batch), np.concatenate(batch_puzzle_indices) + + +class PuzzleDatasetConfig(pydantic.BaseModel): + seed: int + dataset_paths: List[str] + global_batch_size: int + test_set_mode: bool + epochs_per_iter: int # Batch X epochs in an iteration to reduce overhead. + rank: int + num_replicas: int + +class PuzzleDataset(IterableDataset): + def __init__(self, config: PuzzleDatasetConfig, split: str = "train"): + super().__init__() + self.config = config + self.split = split + + # Merge multiple metadata + prev_seq_len = None + prev_vocab_size = None + prev_pad_id = None + prev_ignore_label_id = None + prev_blank_identifier_id = None + prev_sets = None + prev_num_identifiers = None + mean_puzzle_examples = 0 + total_puzzles = 0 + total_groups = 0 + num_identifiers = 0 + for dataset_path in config.dataset_paths: + current_metadata = self._load_metadata(dataset_path) + if prev_seq_len is None: + prev_seq_len = current_metadata.seq_len + prev_vocab_size = current_metadata.vocab_size + prev_pad_id = current_metadata.pad_id + prev_ignore_label_id = current_metadata.ignore_label_id + prev_blank_identifier_id = current_metadata.blank_identifier_id + prev_sets = current_metadata.sets + prev_num_identifiers = current_metadata.num_puzzle_identifiers + else: + assert prev_seq_len == current_metadata.seq_len + assert prev_vocab_size == current_metadata.vocab_size + assert prev_pad_id == current_metadata.pad_id + assert prev_ignore_label_id == current_metadata.ignore_label_id + assert prev_blank_identifier_id == current_metadata.blank_identifier_id + assert prev_sets == current_metadata.sets + assert prev_num_identifiers == current_metadata.num_puzzle_identifiers + mean_puzzle_examples += current_metadata.mean_puzzle_examples*current_metadata.total_puzzles + total_puzzles += current_metadata.total_puzzles + total_groups += current_metadata.total_groups + num_identifiers += current_metadata.num_puzzle_identifiers + mean_puzzle_examples = mean_puzzle_examples / total_puzzles + + self.metadata = PuzzleDatasetMetadata( + seq_len=prev_seq_len, + vocab_size=prev_vocab_size, + pad_id=prev_pad_id, + ignore_label_id=prev_ignore_label_id, + blank_identifier_id=prev_blank_identifier_id, + num_puzzle_identifiers=num_identifiers, + total_groups=total_groups, + mean_puzzle_examples=mean_puzzle_examples, + total_puzzles=total_puzzles, + sets=prev_sets + ) + + # Checks + assert self.config.global_batch_size % self.config.num_replicas == 0, f"Global batch size {self.config.global_batch_size} must be multiples of nodes {self.config.num_replicas}." + self.local_batch_size = self.config.global_batch_size // self.config.num_replicas + + # State + self._data = None + self._iters = 0 + + def _load_metadata(self, dataset_path) -> PuzzleDatasetMetadata: + with open(os.path.join(dataset_path, self.split, "dataset.json"), "r") as f: + return PuzzleDatasetMetadata(**json.load(f)) + + def _lazy_load_dataset(self): + if self._data is not None: + return + + field_mmap_modes = { + "inputs": "r", + "labels": "r", + + # Keep indices in memory + "puzzle_identifiers": None, + "puzzle_indices": None, + "group_indices": None + } + + # Load data + self._data = {} + for set_name in self.metadata.sets: # Load subset + for i, dataset_path in enumerate(self.config.dataset_paths): + if i > 0: + set_name_ = set_name + str(i) + else: + set_name_ = set_name + self._data[set_name_] = { + field_name: np.load(os.path.join(dataset_path, self.split, f"{set_name}__{field_name}.npy"), mmap_mode=mmap_mode) + for field_name, mmap_mode in field_mmap_modes.items() + } + + + def _collate_batch(self, batch): + # Convert dtype + batch = {k: v.astype(np.int32) for k, v in batch.items()} + + # Convert ignore label IDs + if self.metadata.ignore_label_id is not None: + batch["labels"][batch["labels"] == self.metadata.ignore_label_id] = IGNORE_LABEL_ID + + # Pad + if batch["puzzle_identifiers"].size < self.local_batch_size: + pad_size = self.local_batch_size - batch["puzzle_identifiers"].size + pad_values = { + "inputs": self.metadata.pad_id, + "labels": IGNORE_LABEL_ID, + "puzzle_identifiers": self.metadata.blank_identifier_id + } + batch = {k: np.pad(v, ((0, pad_size), ) + ((0, 0), ) * (v.ndim - 1), constant_values=pad_values[k]) for k, v in batch.items()} + + # To tensor + return {k: torch.from_numpy(v) for k, v in batch.items()} + + def _iter_test(self): + for set_i, (set_name, dataset) in enumerate(self._data.items()): # type: ignore + total_examples = len(dataset["inputs"]) + + # Load examples one by one + start_index = 0 + while start_index < total_examples: + # Compute indices + end_index = min(total_examples, start_index + self.config.global_batch_size) + + local_start = start_index + self.config.rank * self.local_batch_size + local_end = min(start_index + (self.config.rank + 1) * self.local_batch_size, end_index) + + # Get batch of examples, and also puzzle IDs + puzzle_indices = [] + puzzle_index = np.searchsorted(dataset["puzzle_indices"], local_start, side="right") - 1 + for i in range(local_start, local_end): + while puzzle_index + 1 < len(dataset["puzzle_indices"]) and i >= dataset["puzzle_indices"][puzzle_index + 1]: + puzzle_index += 1 + + puzzle_indices.append(puzzle_index) + + batch = self._collate_batch({ + "inputs": dataset["inputs"][local_start: local_end], + "labels": dataset["labels"][local_start: local_end], + "puzzle_identifiers": dataset["puzzle_identifiers"][puzzle_indices] + }) + + yield set_name, batch, end_index - start_index + + # Advance to next batch + start_index += self.config.global_batch_size + + def _iter_train(self): + for set_name, dataset in self._data.items(): # type: ignore + # Increase epoch count + self._iters += 1 + + # Randomly shuffle groups + rng = np.random.Generator(np.random.Philox(seed=self.config.seed + self._iters)) + + group_order = np.concatenate([rng.permutation(dataset["group_indices"].size - 1) for _i in range(self.config.epochs_per_iter)]) + start_index = 0 + + while start_index < group_order.size: + start_index, batch_indices, batch_puzzle_indices = _sample_batch( + rng, + group_order=group_order, + puzzle_indices=dataset["puzzle_indices"], + group_indices=dataset["group_indices"], + start_index=start_index, + global_batch_size=self.config.global_batch_size, + ) + + # Select current rank and collate + global_effective_batch_size = batch_puzzle_indices.size # Global effective batch size, excluding pads + + # Drop last batch + if global_effective_batch_size < self.config.global_batch_size: + break + + batch_indices = batch_indices [self.config.rank * self.local_batch_size: (self.config.rank + 1) * self.local_batch_size] + batch_puzzle_indices = batch_puzzle_indices[self.config.rank * self.local_batch_size: (self.config.rank + 1) * self.local_batch_size] + batch = self._collate_batch({ + "inputs": dataset["inputs"][batch_indices], + "labels": dataset["labels"][batch_indices], + "puzzle_identifiers": dataset["puzzle_identifiers"][batch_puzzle_indices] + }) + + yield set_name, batch, global_effective_batch_size + + def __iter__(self): + worker_info = get_worker_info() + assert worker_info is None or worker_info.num_workers == 1, "Multithreaded data loading is not currently supported." + + self._lazy_load_dataset() + + # Iterate using specified mode + if self.config.test_set_mode: + yield from self._iter_test() + else: + yield from self._iter_train() + diff --git a/requirements.txt b/requirements.txt new file mode 100644 index 0000000..cea0f55 --- /dev/null +++ b/requirements.txt @@ -0,0 +1,20 @@ +torch +adam-atan2 +einops +tqdm +coolname +pydantic +argdantic +wandb +omegaconf +hydra-core +huggingface_hub +packaging +ninja +wheel +setuptools +setuptools-scm +pydantic-core +huggingface_hub +numba +triton \ No newline at end of file diff --git a/utils/functions.py b/utils/functions.py new file mode 100644 index 0000000..b123636 --- /dev/null +++ b/utils/functions.py @@ -0,0 +1,19 @@ +import importlib +import inspect + + +def load_model_class(identifier: str, prefix: str = "models."): + module_path, class_name = identifier.split('@') + + # Import the module + module = importlib.import_module(prefix + module_path) + cls = getattr(module, class_name) + + return cls + + +def get_model_source_path(identifier: str, prefix: str = "models."): + module_path, class_name = identifier.split('@') + + module = importlib.import_module(prefix + module_path) + return inspect.getsourcefile(module)