reasoning-gym/README.md

Reasoning Gym

We are building a python library of procedural dataset generators and algorithmically verifiable reasoning environments for training Reasoning Models with reinforcement learning (RL).

The goal is to generate virtually infinite data with adjustable complexity.

Task Overview

Algebra Tasks

• SimpleEquationsDataset: Generate linear equations with one variable to solve (e.g. "3*x + 2 = 14")

Arithmetic Tasks

• BasicArithmeticDataset: Generate arithmetic expressions with configurable complexity and operators (+, -, *)
• ChainSum: Generate addition/subtraction chains with configurable length and digit counts
• FractionSimplificationDataset: Generate fraction simplification tasks with configurable complexity
• GCDDataset: Generate Greatest Common Divisor problems with configurable number of integers
• LCMDataset: Generate Least Common Multiple problems with configurable number of integers
• LegCountingDataset: Generate animal leg counting word problems with various animals
• PrimeFactorizationDataset: Generate prime factorization tasks with configurable number ranges

Algorithmic Tasks

• BaseConversionDataset: Convert numbers between different bases (binary, hex, etc.)
• LetterCountingDataset: Count letter occurrences in text spans
• NumberFilteringDataset: Filter numbers based on comparison with threshold
• NumberSortingDataset: Sort lists of numbers in ascending or descending order
• WordReversalDataset: Reverse word order in text spans

Cognition Tasks

• NumberSequenceDataset: Generate number sequences with discoverable patterns

Logic Tasks

• PropositionalLogicDataset: Generate propositional logic reasoning problems

Relationship Tasks

• FamilyRelationshipsDataset: Generate family relationship reasoning tasks with family trees

Game Tasks

• SudokuDataset: Generate 9x9 Sudoku puzzles with configurable number of empty cells
• MiniSudokuDataset: Generate 4x4 Mini Sudoku puzzles with configurable difficulty

Available Generators

Basic Arithmetic

Generates arithmetic problems with configurable complexity:

from reasoning_gym.arithmetic import BasicArithmeticDataset, BasicArithmeticDatasetConfig

config = BasicArithmeticDatasetConfig(
    min_terms=2,        # Minimum number of terms in expression
    max_terms=4,        # Maximum number of terms
    min_digits=1,       # Minimum digits per number
    max_digits=2,       # Maximum digits per number
    allow_parentheses=True,  # Include nested expressions
    size=5,            # Number of problems to generate
    seed=42            # For reproducibility
)

dataset = BasicArithmeticDataset(config)
for item in dataset:
    print(item)

Example output:

{'question': '-1 + -5   * 8 + -8 =', 'answer': '-49', 'metadata': {'num_terms': 4, 'num_digits': 1, 'expression': '-1 + -5   * 8 + -8'}}
{'question': '19 - 17 =', 'answer': '2', 'metadata': {'num_terms': 2, 'num_digits': 2, 'expression': '19 - 17'}}
{'question': '3 + -6 * -9 =', 'answer': '57', 'metadata': {'num_terms': 3, 'num_digits': 1, 'expression': '3 + -6 * -9'}}
{'question': '-22 - -94 + -97 =', 'answer': '-25', 'metadata': {'num_terms': 3, 'num_digits': 2, 'expression': '-22 - -94 + -97'}}
{'question': '51 * 63 =', 'answer': '3213', 'metadata': {'num_terms': 2, 'num_digits': 2, 'expression': '51 * 63'}}

Chain Sum

Generates addition/subtraction problems with configurable complexity:

from reasoning_gym.arithmetic import ChainSum, ChainSumConfig

config = ChainSumConfig(
    min_terms=2,        # Minimum numbers to add/subtract
    max_terms=6,        # Maximum numbers
    min_digits=1,       # Minimum digits per number
    max_digits=4,       # Maximum digits per number
    allow_negation=True, # Allow negative numbers
    size=5,             # Number of problems
    seed=42             # For reproducibility
)

dataset = ChainSum(config)
for item in dataset:
    print(item)

Example data:

{
    "question": "426 + 562 =",
    "answer": "988",
    "metadata": { "num_terms": 2, "num_digits": 3, "expression": "426 + 562" },
}
{
    "question": "426 + 562 =",
    "answer": "988",
    "metadata": { "num_terms": 2, "num_digits": 3, "expression": "426 + 562" }
}

Sequence Completion

Generates number sequence completion tasks with dynamic pattern generation:

from reasoning_gym.cognition import NumberSequenceDataset, NumberSequenceConfig

config = NumberSequenceConfig(
    min_terms=4,        # Minimum visible terms
    max_terms=8,        # Maximum visible terms
    min_value=-100,     # Minimum allowed number
    max_value=100,      # Maximum allowed number
    max_complexity=3,   # Maximum operations to combine
    size=5,            # Number of sequences
    seed=42            # For reproducibility
)

dataset = NumberSequenceDataset(config)
for item in dataset:
    print(item)

Example data:

{
    "question": "3, 6, 12, 24, 48, 96, 192, 384, ?",
    "answer": "768",
    "metadata": {"rule": "double", "complexity": 3, "sequence": [3, 6, 12, 24, 48, 96, 192, 384, 768]},
}
{
    "question": "8, 14, 20, 26, 32, 38, 44, ?",
    "answer": "50",
    "metadata": {"rule": "add 6", "complexity": 1, "sequence": [8, 14, 20, 26, 32, 38, 44, 50]},
}

Propositional Logic

Generates logical reasoning tasks with configurable complexity:

from reasoning_gym.logic import PropositionalLogicDataset, PropositionalLogicConfig

config = PropositionalLogicConfig(
    min_vars=2,         # Minimum number of variables
    max_vars=4,         # Maximum number of variables
    min_statements=2,   # Minimum number of given statements
    max_statements=4,   # Maximum number of statements
    max_complexity=3,   # Maximum operator depth
    size=5,            # Number of problems to generate
    seed=42            # For reproducibility
)

dataset = PropositionalLogicDataset(config)
for item in dataset:
    print(item)

Example data:

{
    "question": "Given:\n1. R\n2. Q\nWhat can we conclude?",
    "answer": "(P ∨ Q)",
    "metadata": {"premises": ["R", "Q"], "variables": ["P", "Q", "R", "S"], "complexity": 3},
}
{
    "question": "Given:\n1. ((Q → P) ∨ (Q → P))\n2. ((Q ↔ Q) → (P → P))\n3. P\nWhat can we conclude?",
    "answer": "(P → P)",
    "metadata": {
        "premises": ["((Q → P) ∨ (Q → P))", "((Q ↔ Q) → (P → P))", "P"],
        "variables": ["P", "Q"],
        "complexity": 3,
    },
}

Future Generator Ideas

• More complex math tasks (algebra, geometry)
• Algorithmic tasks (counting, sorting, re-ordering)
• Logic riddles
• Logic inductive programming tasks
• ARC-AGI synthetic riddles

Call for Contributions

If you have ideas for additional procedural dataset generators or please create an issue here.

Or contact us in the #arc-agi-2 channel of the GPU-Mode discord server.