jowenpetty/monoids-100

Monoids

Sequences of elements from various monoids along with their products. Contains data from monoids over symmetric groups (S2, S3, S4, S5, and S6); alternating groups (A3, A4, A5, and A6); and several cyclic groups chosen to match the order of the symmetric and alternating groups (Z6, Z12, Z24, Z60, Z120, Z360, and Z720).

Each group has its own eponymous split; each split contains 100,000 records of 5 features:

• sequence: list[int] A sequence of elements in in the range 0...order(group), of length at most 100;
• intermediate_products: list[int] The kth value corresponds to the product of the first k elements, with the 0th value equal to sequence[0];
• product: int The product of the entire sequence, equal to intermediate_products[-1];
• sequence_len: int The length of the sequence;
• group: str The group from which the sequence is drawn.

Generating data

We also provide a script to generate new data. Install dependencies provided in pyproject.toml (e.g., with ev) and then run:

uv run generate_data.py [--max_sequence_length: int] [--samples_per_group: int] [--seed: int | None] [--groups: list[str]]

Arguments have the following uses: - max_sequence_length: The maximum length of the sequences to generate (default: 100). - samples_per_group: The number of samples to generate for each group (default: 100_000). - seed: The random seed to use for reproducibility (default: None; will attempt to load DATA_SEED from environment; if this is not set, will use a random seed). - groups: A list of groups to generate data for (default: all groups in the dataset). Valid groups are symmetric groups (S#), alternating groups (A#), and cyclic groups (Z#).