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monoids-100

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add generating code

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Files changed (5) hide show
  1. .python-version +1 -0
  2. README.md +15 -1
  3. generate_data.py +175 -0
  4. pyproject.toml +17 -0
  5. uv.lock +407 -0
.python-version ADDED
@@ -0,0 +1 @@
 
 
1
+ 3.13
README.md CHANGED
@@ -47,4 +47,18 @@ Each group has its own eponymous split; each split contains 100,000 records of 5
47
  - `intermediate_products: list[int]` The `k`th value corresponds to the product of the first `k` elements, with the 0th value equal to `sequence[0]`;
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  - `product: int` The product of the entire sequence, equal to `intermediate_products[-1]`;
49
  - `sequence_len: int` The length of the sequence;
50
- - `group: str` The group from which the sequence is drawn.
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
47
  - `intermediate_products: list[int]` The `k`th value corresponds to the product of the first `k` elements, with the 0th value equal to `sequence[0]`;
48
  - `product: int` The product of the entire sequence, equal to `intermediate_products[-1]`;
49
  - `sequence_len: int` The length of the sequence;
50
+ - `group: str` The group from which the sequence is drawn.
51
+
52
+ ## Generating data
53
+
54
+ We also provide a script to generate new data. Install dependencies provided in `pyproject.toml` (e.g., with `ev`) and then run:
55
+
56
+ ```bash
57
+ uv run generate_data.py [--max_sequence_length: int] [--samples_per_group: int] [--seed: int | None] [--groups: list[str]]
58
+ ```
59
+
60
+ Arguments have the following uses:
61
+ - `max_sequence_length`: The maximum length of the sequences to generate (default: 100).
62
+ - `samples_per_group`: The number of samples to generate for each group (default: 100_000).
63
+ - `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).
64
+ - `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#`).
generate_data.py ADDED
@@ -0,0 +1,175 @@
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1
+ import json
2
+ import logging
3
+ import os
4
+ import random
5
+ from functools import partial
6
+ from itertools import accumulate
7
+ from logging import Logger
8
+ from pathlib import Path
9
+ from typing import Any
10
+
11
+ import fire
12
+ import numpy as np
13
+ import numpy.typing as npt
14
+ import pyrootutils
15
+ from abstract_algebra.finite_algebras import (
16
+ Group,
17
+ generate_cyclic_group,
18
+ generate_symmetric_group,
19
+ )
20
+ from dotenv import load_dotenv
21
+ from tqdm import tqdm
22
+
23
+ PROJECT_ROOT: Path = pyrootutils.find_root(
24
+ search_from=__file__, indicator=".project-root"
25
+ )
26
+ DATA_DIR: Path = PROJECT_ROOT / "data"
27
+
28
+ load_dotenv(PROJECT_ROOT / ".env")
29
+
30
+ logging.basicConfig(
31
+ format="%(asctime)s - %(levelname)s - %(name)s - %(message)s",
32
+ datefmt="%Y-%d-%m %H:%M:%S",
33
+ level=logging.INFO,
34
+ )
35
+
36
+ log: Logger = logging.getLogger(__name__)
37
+
38
+
39
+ def _set_all_seeds(seed: int):
40
+ os.environ["PYTHONHASHSEED"] = str(seed)
41
+ np.random.seed(seed)
42
+ random.seed(seed)
43
+
44
+ log.info(f"Set all seeds to {seed}")
45
+
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+
47
+ def _create_group(g: tuple[str, int]) -> Group:
48
+ """
49
+ Create a group based on the input string.
50
+ """
51
+ if g[0] == "S":
52
+ return generate_symmetric_group(g[1])
53
+ elif g[0] == "A":
54
+ s_n: Group = generate_symmetric_group(g[1])
55
+ a_n: Group = s_n.commutator_subalgebra()
56
+ a_n.name = f"A{g[1]}"
57
+ return a_n
58
+ elif g[0] == "Z":
59
+ return generate_cyclic_group(g[1])
60
+ else:
61
+ raise ValueError(f"Unknown group type: {g[0]}")
62
+
63
+
64
+ def generate_data(
65
+ max_sequence_length: int = 100,
66
+ samples_per_group: int = 100_000,
67
+ seed: int | None = None,
68
+ groups: list[str] = [
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+ "S2",
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+ "S3",
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+ "S4",
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+ "S5",
73
+ "S6", # symmetric groups
74
+ "A3",
75
+ "A4",
76
+ "A5",
77
+ "A6", # alternating groups
78
+ "Z6",
79
+ "Z12",
80
+ "Z24",
81
+ "Z60",
82
+ "Z120",
83
+ "Z360",
84
+ "Z720", # cyclic groups
85
+ ],
86
+ ):
87
+ """
88
+ Generates datasets of sequences of group elements and their products.
89
+
90
+ By default, we generate 1 million samples per group, with a maximum sequence
91
+ length of 100. We generate samples from 5 symmetric groups (S2, S3, S4, S5, S6),
92
+ 4 alternating groups (A3, A4, A5, A6), and 7 cyclic groups (Z6, Z12, Z24, Z60,
93
+ Z120, Z360, Z720). The cyclic groups are chosen to correspond to the order of
94
+ the symmetric and alternating groups:
95
+ - S2: 2
96
+ - S3: 6
97
+ - S4: 24
98
+ - S5: 120
99
+ - S6: 720
100
+ - A3: 3 == Z3
101
+ - A4: 12
102
+ - A5: 60
103
+ - A6: 360
104
+ - Z6: 6
105
+ - Z12: 12
106
+ - Z24: 24
107
+ - Z60: 60
108
+ - Z120: 120
109
+ - Z360: 360
110
+ - Z720: 720
111
+ """
112
+
113
+ def _group_reduce(lhs: str | int, rhs: int, G: Group) -> int:
114
+ if isinstance(lhs, str):
115
+ prod: str = G.op(lhs, G.elements[rhs])
116
+ else:
117
+ prod: str = G.op(G.elements[lhs], G.elements[rhs])
118
+ return G.elements.index(prod)
119
+
120
+ if seed is not None:
121
+ log.info("Using seed from argument")
122
+ _set_all_seeds(seed)
123
+ elif os.environ.get("DATA_SEED") is not None:
124
+ log.info("Using seed from environment variable `DATA_SEED`")
125
+ seed: int = int(os.environ["DATA_SEED"])
126
+ _set_all_seeds(seed)
127
+ else:
128
+ log.info("Using random seed")
129
+ seed: int = np.random.randint(0, 2**32 - 1)
130
+ _set_all_seeds(seed)
131
+
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+ for group_name in tqdm(groups, position=0):
133
+ log.info(
134
+ f"Generating {samples_per_group} samples with a max sequence length of {max_sequence_length} from {group_name}"
135
+ )
136
+
137
+ group_type: str = group_name[0]
138
+ group_num: int = int(group_name[1:])
139
+ G: Group = _create_group((group_type, group_num))
140
+ num_elements: int = len(G.elements)
141
+
142
+ samples: list[dict[str, Any]] = []
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+ for _ in tqdm(range(samples_per_group), position=1):
144
+ s_len: int = np.random.randint(1, max_sequence_length + 1)
145
+ s_elts: npt.ArrayLike[np.int_] = np.random.choice(
146
+ num_elements, size=s_len, replace=True
147
+ ).tolist()
148
+ scanned: list[int] = list(
149
+ accumulate(s_elts, partial(_group_reduce, G=G), initial=0)
150
+ )
151
+ product: int = scanned[-1]
152
+ samples.append(
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+ {
154
+ "sequence": s_elts,
155
+ "intermediate_products": scanned,
156
+ "product": product,
157
+ "sequence_length": s_len,
158
+ "group": group_name,
159
+ }
160
+ )
161
+
162
+ dataset_path: Path = DATA_DIR / f"{group_name}.jsonl"
163
+ if not dataset_path.parent.exists():
164
+ dataset_path.parent.mkdir(parents=True, exist_ok=True)
165
+ log.info(f"Writing dataset to {dataset_path}")
166
+ with open(dataset_path, "w") as f:
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+ for sample in samples:
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+ f.write(json.dumps(sample, separators=(",", ":")) + "\n")
169
+
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+ del samples
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+ del G
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+
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+
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+ if __name__ == "__main__":
175
+ fire.Fire(generate_data)
pyproject.toml ADDED
@@ -0,0 +1,17 @@
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1
+ [project]
2
+ name = "monoids-100"
3
+ version = "1.0.0"
4
+ description = "Sequences of elements from various monoids along with their products."
5
+ readme = "README.md"
6
+ requires-python = ">=3.13"
7
+ dependencies = [
8
+ "abstract-algebra",
9
+ "fire>=0.7.0",
10
+ "numpy>=2.2.6",
11
+ "pyrootutils>=1.0.4",
12
+ "python-dotenv>=1.1.0",
13
+ "tqdm>=4.67.1",
14
+ ]
15
+
16
+ [tool.uv.sources]
17
+ abstract-algebra = { git = "https://github.com/jopetty/abstract_algebra" }
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+ revision = 2
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