import json import logging import os import random from functools import partial from itertools import accumulate from logging import Logger from pathlib import Path from typing import Any import fire import numpy as np import numpy.typing as npt import pyrootutils from abstract_algebra.finite_algebras import ( Group, generate_cyclic_group, generate_symmetric_group, ) from dotenv import load_dotenv from tqdm import tqdm PROJECT_ROOT: Path = pyrootutils.find_root( search_from=__file__, indicator=".project-root" ) DATA_DIR: Path = PROJECT_ROOT / "data" load_dotenv(PROJECT_ROOT / ".env") logging.basicConfig( format="%(asctime)s - %(levelname)s - %(name)s - %(message)s", datefmt="%Y-%d-%m %H:%M:%S", level=logging.INFO, ) log: Logger = logging.getLogger(__name__) def _set_all_seeds(seed: int): os.environ["PYTHONHASHSEED"] = str(seed) np.random.seed(seed) random.seed(seed) log.info(f"Set all seeds to {seed}") def _create_group(g: tuple[str, int]) -> Group: """ Create a group based on the input string. """ if g[0] == "S": return generate_symmetric_group(g[1]) elif g[0] == "A": s_n: Group = generate_symmetric_group(g[1]) a_n: Group = s_n.commutator_subalgebra() a_n.name = f"A{g[1]}" return a_n elif g[0] == "Z": return generate_cyclic_group(g[1]) else: raise ValueError(f"Unknown group type: {g[0]}") def generate_data( max_sequence_length: int = 100, samples_per_group: int = 100_000, seed: int | None = None, groups: list[str] = [ "S2", "S3", "S4", "S5", "S6", # symmetric groups "A3", "A4", "A5", "A6", # alternating groups "Z6", "Z12", "Z24", "Z60", "Z120", "Z360", "Z720", # cyclic groups ], ): """ Generates datasets of sequences of group elements and their products. By default, we generate 1 million samples per group, with a maximum sequence length of 100. We generate samples from 5 symmetric groups (S2, S3, S4, S5, S6), 4 alternating groups (A3, A4, A5, A6), and 7 cyclic groups (Z6, Z12, Z24, Z60, Z120, Z360, Z720). The cyclic groups are chosen to correspond to the order of the symmetric and alternating groups: - S2: 2 - S3: 6 - S4: 24 - S5: 120 - S6: 720 - A3: 3 == Z3 - A4: 12 - A5: 60 - A6: 360 - Z6: 6 - Z12: 12 - Z24: 24 - Z60: 60 - Z120: 120 - Z360: 360 - Z720: 720 """ def _group_reduce(lhs: str | int, rhs: int, G: Group) -> int: if isinstance(lhs, str): prod: str = G.op(lhs, G.elements[rhs]) else: prod: str = G.op(G.elements[lhs], G.elements[rhs]) return G.elements.index(prod) if seed is not None: log.info("Using seed from argument") _set_all_seeds(seed) elif os.environ.get("DATA_SEED") is not None: log.info("Using seed from environment variable `DATA_SEED`") seed: int = int(os.environ["DATA_SEED"]) _set_all_seeds(seed) else: log.info("Using random seed") seed: int = np.random.randint(0, 2**32 - 1) _set_all_seeds(seed) for group_name in tqdm(groups, position=0): log.info( f"Generating {samples_per_group} samples with a max sequence length of {max_sequence_length} from {group_name}" ) group_type: str = group_name[0] group_num: int = int(group_name[1:]) G: Group = _create_group((group_type, group_num)) num_elements: int = len(G.elements) samples: list[dict[str, Any]] = [] for _ in tqdm(range(samples_per_group), position=1): s_len: int = np.random.randint(1, max_sequence_length + 1) s_elts: npt.ArrayLike[np.int_] = np.random.choice( num_elements, size=s_len, replace=True ).tolist() scanned: list[int] = list( accumulate(s_elts, partial(_group_reduce, G=G), initial=0) ) product: int = scanned[-1] samples.append( { "sequence": s_elts, "intermediate_products": scanned, "product": product, "sequence_length": s_len, "group": group_name, } ) dataset_path: Path = DATA_DIR / f"{group_name}.jsonl" if not dataset_path.parent.exists(): dataset_path.parent.mkdir(parents=True, exist_ok=True) log.info(f"Writing dataset to {dataset_path}") with open(dataset_path, "w") as f: for sample in samples: f.write(json.dumps(sample, separators=(",", ":")) + "\n") del samples del G if __name__ == "__main__": fire.Fire(generate_data)