Emulated-Inc/procedural-reasoning-training-pool

Procedural reasoning training pool

Reasoning questions from 101 procedural generators, each of which writes a question, computes its own answer and ships a verifier that scores an attempt at it, plus a collection of solved Sudoku puzzles. Every answer is short and exactly checkable, so a trained model can be marked against the key by a program and no judge is needed. Laid out twice. Train on either layer or on both.

pool.jsonl

Every generator rewritten into one shape, 161495 rows, one JSON object per line, with these fields.

Field	What it holds
id	a row identifier unique within this file
generator	the generator that wrote the row, one of those listed below
family	the package of the library the generator belongs to
part	core for the twenty drawn deeply, wider for the rest, collected for the downloaded puzzles
question	the question, exactly as its generator wrote it
answer	the generator's own answer, or null
worked_answer	a worked answer or an accepted answer where the generator records one
worked_answer_field	which of its metadata fields that came from
metadata	the generator's own record for the row, which its verifier reads
source	the directory under sources/ the row came from
source_seed	the seed the row was drawn under
provenance_class	how the row came to exist
licence	the licence of the part it came from

158999 rows carry an answer and 70182 carry a worked answer. The answer is the generator's own answer field. Five generators write no answer at all, because any response that satisfies the puzzle is correct and their verifier checks the response rather than compares it. Three of them record an acceptable answer in their metadata, which is what worked_answer holds for those rows, and 1001 rows hold neither an answer nor a worked answer and are a prompt with a verifier and no key. The verifier for a row is the generator named in its generator field, reached through the library at version 0.1.25: create that generator and hand it the answer together with the row's own question, answer and metadata. Several verifiers give partial credit for a near miss, so read the score rather than only its sign. Every shipped key was read by the verifier of the generator that wrote the row, exactly as that verifier reads a model's answer, and a row whose own key it did not score at 1.0 is not here. 6 rows were dropped that way.

Worth knowing about that version. The library's own __version__ string still reads 0.1.19 in this release, so the distribution version is what is pinned. Install reasoning-gym==0.1.25 and read the version back from the distribution metadata rather than from the module.

Rows are written one generator after another. One row per canonical question within a generator, the canonical form being the question with runs of whitespace collapsed. Repeats are skipped during the draw rather than removed afterwards. Within a generator a question appears once.

sources/

The same items untouched, 776495 rows. The library's own entries as drawn, one jsonl file per generator under the directory of the library package it belongs to, with only the dropped rows taken out, and the downloaded collection under its own directory in the parquet files and with the columns its repository publishes. Nothing here was renamed, reshaped, reordered or deduplicated, so use this layer if you want to pose the questions yourself, or want a column the rewritten rows drop, such as the printed grid the Sudoku collection carries beside its flat one.

The generators

20 generators were drawn at 5000 items each under seed 40260912, and 81 at 500 items each under seed 50260912. A generator whose question space is narrower than the count asked for contributed what it had, and no question on the held-out list named under Filtering comes from a generator of the second group. Rows in the rewritten layer per generator, with the package it belongs to.

Generator	Family	Part	Rows	With an answer	With a worked answer
basic_arithmetic	arithmetic	core	4975	4975	4975
calendar_arithmetic	arithmetic	core	4985	4985	0
chain_sum	arithmetic	core	4994	4994	4994
gcd	arithmetic	core	4998	4998	0
time_intervals	arithmetic	core	5000	5000	0
complex_arithmetic	algebra	core	4959	4959	0
polynomial_multiplication	algebra	core	5000	5000	0
simple_equations	algebra	core	5000	5000	0
aiw	logic	core	4940	4940	0
knights_knaves	logic	core	5000	5000	5000
self_reference	logic	core	2698	2698	0
family_relationships	graphs	core	5000	5000	0
shortest_path	graphs	core	5000	5000	3174
mini_sudoku	games	core	4999	4999	4999
color_cube_rotation	cognition	core	5000	5000	0
number_sequence	cognition	core	4711	4711	4711
palindrome_generation	algorithmic	core	4995	4995	0
sentence_reordering	algorithmic	core	4974	4974	0
spell_backward	algorithmic	core	4993	4993	0
word_sequence_reversal	algorithmic	core	5000	5000	0
ab	algorithmic	wider	500	500	0
acre	induction	wider	500	500	0
advanced_geometry	geometry	wider	500	500	0
base_conversion	algorithmic	wider	499	499	0
bf	code	wider	500	500	0
binary_alternation	algorithmic	wider	500	500	500
binary_matrix	algorithmic	wider	500	500	500
bitwise_arithmetic	arithmetic	wider	500	500	0
boxnet	games	wider	500	0	0
caesar_cipher	algorithmic	wider	500	500	0
circuit_logic	logic	wider	500	500	500
coin_flip	probability	wider	258	258	0
count_bits	arithmetic	wider	500	500	500
count_primes	algorithmic	wider	500	500	500
countdown	games	wider	500	500	500
course_schedule	graphs	wider	500	500	500
cryptarithm	algorithmic	wider	500	500	0
decimal_arithmetic	arithmetic	wider	500	500	0
decimal_chain_sum	arithmetic	wider	500	500	500
dice	arithmetic	wider	500	500	0
emoji_mystery	games	wider	500	500	0
figlet_font	cognition	wider	500	500	0
fraction_simplification	arithmetic	wider	500	500	0
futoshiki	games	wider	500	500	500
game_of_life	algorithmic	wider	500	500	0
game_of_life_halting	algorithmic	wider	500	500	0
graph_color	algorithmic	wider	500	0	500
group_anagrams	algorithmic	wider	500	500	500
gsm_symbolic	arithmetic	wider	499	499	0
intermediate_integration	algebra	wider	500	500	0
isomorphic_strings	algorithmic	wider	500	500	500
jugs	algorithmic	wider	500	500	0
kakurasu	games	wider	500	500	500
knight_swap	games	wider	500	500	402
largest_island	graphs	wider	500	500	500
lcm	arithmetic	wider	500	500	0
leg_counting	arithmetic	wider	500	500	0
letter_counting	algorithmic	wider	500	500	0
letter_jumble	algorithmic	wider	500	500	0
list_functions	induction	wider	500	500	0
mahjong_puzzle	games	wider	500	500	500
manipulate_matrix	algorithmic	wider	500	500	500
maze	games	wider	500	500	0
modulo_grid	cognition	wider	500	500	0
n_queens	games	wider	500	500	500
needle_haystack	cognition	wider	500	500	0
number_filtering	algorithmic	wider	500	500	0
number_format	arithmetic	wider	500	500	500
number_sorting	algorithmic	wider	500	500	0
palindrome_partitioning	algorithmic	wider	500	500	500
path_star	graphs	wider	500	500	0
polynomial_equations	algebra	wider	500	500	0
pool_matrix	algorithmic	wider	500	500	500
power_function	arithmetic	wider	500	500	500
prime_factorization	arithmetic	wider	500	500	0
products	arithmetic	wider	500	500	500
propositional_logic	logic	wider	496	0	496
puzzle24	games	wider	500	500	0
quantum_lock	graphs	wider	500	500	0
ransom_note	algorithmic	wider	500	500	500
rectangle_count	cognition	wider	500	500	500
rotate_matrix	algorithmic	wider	500	500	500
rotten_oranges	algorithmic	wider	500	500	500
rubiks_cube	cognition	wider	500	0	499
rush_hour	games	wider	500	0	0
simple_geometry	geometry	wider	500	500	0
simple_integration	algebra	wider	500	500	0
sokoban	games	wider	500	500	0
spiral_matrix	algorithmic	wider	500	500	500
string_insertion	algorithmic	wider	500	500	500
string_manipulation	algorithmic	wider	500	500	500
string_splitting	algorithmic	wider	216	216	216
string_synthesis	algorithmic	wider	216	216	216
sudoku	games	wider	500	500	500
survo	games	wider	500	500	500
syllogism	logic	wider	500	500	0
tower_of_hanoi	games	wider	90	90	0
tsumego	games	wider	500	500	0
word_ladder	algorithmic	wider	500	500	0
word_sorting	algorithmic	wider	500	500	0
zebra_puzzles	logic	wider	500	500	0
sudoku	sudoku_puzzles	collected	25000	25000	25000

The sources

sources/algebra

The 6 generators the library keeps in its algebra package, drawn from version 0.1.25 of the reasoning-gym library under seeds 40260912, 50260912. 16459 rows in 6 files, all of which also appear in pool.jsonl. Provenance class rule-generated, licence cc-by-4.0. Every line is one of the library's own entries, whose keys are question, answer and metadata.

sources/algorithmic

The 34 generators the library keeps in its algorithmic package, drawn from version 0.1.25 of the reasoning-gym library under seeds 40260912, 50260912. 34393 rows in 34 files, all of which also appear in pool.jsonl. Provenance class rule-generated, licence cc-by-4.0. Every line is one of the library's own entries, whose keys are question, answer and metadata.

sources/arithmetic

The 18 generators the library keeps in its arithmetic package, drawn from version 0.1.25 of the reasoning-gym library under seeds 40260912, 50260912. 31451 rows in 18 files, all of which also appear in pool.jsonl. Provenance class rule-generated, licence cc-by-4.0. Every line is one of the library's own entries, whose keys are question, answer and metadata.

sources/code

The 1 generator the library keeps in its code package, drawn from version 0.1.25 of the reasoning-gym library under seed 50260912. 500 rows in 1 file, all of which also appear in pool.jsonl. Provenance class rule-generated, licence cc-by-4.0. Every line is one of the library's own entries, whose keys are question, answer and metadata.

sources/cognition

The 7 generators the library keeps in its cognition package, drawn from version 0.1.25 of the reasoning-gym library under seeds 40260912, 50260912. 12211 rows in 7 files, all of which also appear in pool.jsonl. Provenance class rule-generated, licence cc-by-4.0. Every line is one of the library's own entries, whose keys are question, answer and metadata.

sources/games

The 17 generators the library keeps in its games package, drawn from version 0.1.25 of the reasoning-gym library under seeds 40260912, 50260912. 12589 rows in 17 files, all of which also appear in pool.jsonl. Provenance class rule-generated, licence cc-by-4.0. Every line is one of the library's own entries, whose keys are question, answer and metadata.

sources/geometry

The 2 generators the library keeps in its geometry package, drawn from version 0.1.25 of the reasoning-gym library under seed 50260912. 1000 rows in 2 files, all of which also appear in pool.jsonl. Provenance class rule-generated, licence cc-by-4.0. Every line is one of the library's own entries, whose keys are question, answer and metadata.

sources/graphs

The 6 generators the library keeps in its graphs package, drawn from version 0.1.25 of the reasoning-gym library under seeds 40260912, 50260912. 12000 rows in 6 files, all of which also appear in pool.jsonl. Provenance class rule-generated, licence cc-by-4.0. Every line is one of the library's own entries, whose keys are question, answer and metadata.

sources/induction

The 2 generators the library keeps in its induction package, drawn from version 0.1.25 of the reasoning-gym library under seed 50260912. 1000 rows in 2 files, all of which also appear in pool.jsonl. Provenance class rule-generated, licence cc-by-4.0. Every line is one of the library's own entries, whose keys are question, answer and metadata.

sources/logic

The 7 generators the library keeps in its logic package, drawn from version 0.1.25 of the reasoning-gym library under seeds 40260912, 50260912. 14634 rows in 7 files, all of which also appear in pool.jsonl. Provenance class rule-generated, licence cc-by-4.0. Every line is one of the library's own entries, whose keys are question, answer and metadata.

sources/probability

The 1 generator the library keeps in its probability package, drawn from version 0.1.25 of the reasoning-gym library under seed 50260912. 258 rows in 1 file, all of which also appear in pool.jsonl. Provenance class rule-generated, licence cc-by-4.0. Every line is one of the library's own entries, whose keys are question, answer and metadata.

sources/sudoku_puzzles

A published collection of 9x9 Sudoku puzzles with their solutions, in five files of falling clue counts from 63 down to 17. From abatilo/sudokubench at revision 8efe5b22131f4d9720126822e910cf11bfb347db, files kids.parquet, easy.parquet, medium.parquet, hard.parquet, insane.parquet. 640000 rows here, of which 25000 also appear in pool.jsonl: 5000 rows of each file, drawn under seed 40260912, rewritten into the shape the library's own Sudoku generator uses so that the same verifier scores them. Provenance class rule-generated, licence apache-2.0. Its own fields are starting_cells, puzzle, puzzle_pretty, solution, solution_pretty.

Worth knowing. The puzzles were made by a program, like the drawn rows, so the class is the same. What the collection adds is a wider clue range and a much larger stock of puzzles than a draw of one generator, in its own files

Provenance and licences

Every row here is rule-generated, which is the honest headline for this pool. A program wrote each question from a template over values it drew, computed the answer as it built the item, and ships the code that checks an attempt. No row was written by a person and no row was written by a language model.

Worth knowing before training on this. A model trained on the output of a generator can learn the generator rather than the rule behind it, and here the generator is what made every item. The generators are public and unbounded, so more rows of any of them can be drawn at any seed, and the value of this file is that it is a fixed, decontaminated, verifiable draw rather than that it is the only one available.

The pool as a whole is offered under cc-by-4.0. The drawn rows come out of the reasoning-gym library (github.com/open-thought/reasoning-gym), which is released under apache-2.0 and is credited here as the author of every question and every verifier. The Sudoku collection is apache-2.0. Each row carries its own licence in the licence field and each directory under sources/ is one part, so a subset under a single licence can be selected.

Filtering

391 rows were removed before publication, from both layers alike, because their question repeated a question on a held-out list word for word once whitespace was collapsed, and 191 more because one single held-out question accounted for four fifths or more of the row's word 8-grams. The list is not distributed here. 6 further rows went for the reason given above, their own verifier not accepting their own key. Nothing else was filtered: no generator, no length and no difficulty was selected for or against, so every generator contributes as many rows as its draw left, and the generator and family fields are how to select what you want.