nltower-env

The nl_tower environment data: six 1,024-question test sets and the RL prompt pools from which every level's RL prompt mix was drawn. Each row carries the puzzle, the gold answer and the generator's structured metadata (solution, clues, step patterns, number of held-out steps).

This repository is part of the nl_tower (100M) collection on the Hugging Face Hub (5 CPT models, 6 SFT models, the base model and 4 datasets).

nl_tower in brief

nl_tower is a synthetic reasoning task. Each puzzle places 6-12 people on distinct floors (1-40) of a tower. The prompt lists the occupied floors, each person's best friend, and clues that relate the floors of two terms ("greater than", "k floors above", sums, parity, "twice", highest/lowest). Many clues refer to people indirectly, for example "the best friend of the person on the second-highest floor"; such a clue becomes usable only after other clues have pinned part of the answer. Each puzzle has a unique solution that a step-by-step solver reaches without guessing.

The study asks whether reinforcement learning can teach reasoning compositions that the imitation data never shows:

• Covered patterns (shown in the mid-training traces): friend ("Ava's best friend"), friend2 ("the best friend of Ava's best friend"), order ("the person directly above Ava"), rankn ("the person on the second-highest floor"), dfriend_occ ("the best friend of the person on floor 19").
• Held-out patterns (appear only in RL prompts and tests): dfriend_rank ("the best friend of the person on the highest floor"), dfriend_above ("the best friend of the person directly above Ava"), and nested (two-level references).

Test rungs: easy (nltw_e, 6-7 people, covered only), covered mid (nltw_m0, 8-9 people, covered only), held-out mid (nltw_m, 8-9 people, 2-4 held-out steps), hard (nltw_h, 9-10 people, 4-6 held-out steps), size-only hard (nltw_hb, 10-11 people, 2-4 held-out steps) and 12 people (nltw_hb12, test only).

Rungs

All rungs use floors 1-40 and 2 noise clues. "Held-out steps" counts the solving steps that need a held-out pattern; this is what makes a rung hard for a model that has only imitated covered patterns.

rung	people	step patterns	held-out steps	test (1,024)	RL pool
nltw_e easy	6-7	covered only	0	yes	-
nltw_m0 covered mid	8-9	covered only	0	yes	m0 (10,000)
nltw_m held-out mid	8-9	all 8	2-4	yes	m (20,000)
nltw_h hard	9-10	all 8, held-out weighted up	4-6	yes	h (10,000)
nltw_h9 hard, 9 people	9	as hard	4-6	9-person half of the nltw_h test (501)	h9 (10,000)
nltw_hb size-only hard	10-11	all 8	2-4	yes	hb (10,000)
nltw_hb12 12 people	12	all 8	2-4	yes	-

Size and held-out-step distributions (from the files):

split	rows	people	held-out steps
tests/nltw_e	1,024	6: 529, 7: 495	0: 1,024
tests/nltw_m0	1,024	8: 518, 9: 506	0: 1,024
tests/nltw_m	1,024	8: 529, 9: 495	2: 365, 3: 358, 4: 301
tests/nltw_h	1,024	9: 501, 10: 523	4: 365, 5: 394, 6: 265
tests/nltw_hb	1,024	10: 542, 11: 482	2: 373, 3: 307, 4: 344
tests/nltw_hb12	1,024	12: 1,024	2: 344, 3: 348, 4: 332
rl_pools/m0	10,000	8: 5,083, 9: 4,917	0: 10,000
rl_pools/m	20,000	8: 9,873, 9: 10,127	2: 7,075, 3: 6,853, 4: 6,072
rl_pools/h	10,000	9: 4,726, 10: 5,274	4: 3,888, 5: 3,469, 6: 2,643
rl_pools/h9	10,000	9: 10,000	4: 4,025, 5: 3,486, 6: 2,489
rl_pools/hb	10,000	10: 5,003, 11: 4,997	2: 3,310, 3: 3,436, 4: 3,254

Seeds and exclusions

• Tests nltw_e, nltw_m0, nltw_m, nltw_h: the first 1,024 unique questions of the generator stream with seed 20260921.
• RL pools m0, m, h: seed 777, excluding the test sets and the trace questions that existed at the time.
• RL pool h9: seed 1008, 9-person hard puzzles, excluding the four tests above and the 6,000-question hard generator pool. It did not exclude pool h: 3,522 of its 10,000 prompts also appear in pool h.
• nltw_hb: seed 1012, pool of 10,000 plus the 1,024-question test, excluding the four tests above, the 6,000-question hard generator pool and pool h9.
• nltw_hb12: seed 1013, test only, built after nltw_hb.
• Apart from the h/h9 overlap, all test sets and pools are pairwise disjoint (checked by exact question text for this release).
• The trace corpus sfanm/nltower-traces-tw1X (built 2026-09-26) was drawn excluding the four tests above and pools m0, m, h, and audited at 0 overlap. The later sets (h9, nltw_hb, nltw_hb12) all need held-out steps, which no trace question has, so they cannot coincide with trace questions.

Fields

field	meaning
qid	question id (16 hex characters)
spec	rung name
prompt	question + "\n\nAnswer: ", the exact model input
question	the puzzle text, ending with the answer-format instruction
answer	gold assignment Name=floor, ...
n_people	number of people
n_held	number of held-out steps
n_deferred	number of steps that need an already-pinned floor's occupant (covered dfriend_occ included)
patterns	JSON string: the step patterns used by the puzzle
metadata	JSON string: the generator's full metadata (names, floors, friends, solution, clues, statements, patterns, counters)

Scoring

A completion is correct when it contains \boxed{...} and every Name=floor pair inside matches answer exactly (order-insensitive). The study reports pass@k from 64 samples per question at temperature 1.0 (unbiased estimator) and greedy accuracy; see sfanm/nltower-results.

from datasets import load_dataset
test = load_dataset("sfanm/nltower-env", "tests", split="nltw_h")
nine_person_half = test.filter(lambda r: r["n_people"] == 9)   # the 501-question level-2.5 test
pools = load_dataset("sfanm/nltower-env", "rl_pools")

Source files

The splits were converted to parquet from the original JSONL files (the nested metadata dict was serialised to a JSON string; nothing else changed). md5 of the original JSONL files: test_nltw_e 2422c3d1fc99bb8f70d48607e190f91a, test_nltw_m0 0d9e5adf9c9cda0df46af1544aa437ec, test_nltw_m 2da059c5645bc02ce92a6a32afb106ea, test_nltw_h bf23c4dc0a8044cf5a2f2c50c78b798e, test_nltw_hb 4df30cc23bd5cfa18171243ae0e79e5f, test_nltw_hb12 394d7964ff508cffc44977a3515da2e6, pool_m0 2ee3dfa7ee28a1b2cac338bdc98e4e14, pool_m 0a8e311cf7cfcec57375b424e31d181d, pool_h 4aab5d22427b12d7b4985f780c686259, pool_h9 b9357e206a318b2299d1d3c6b7679110, pool_hb 8914e7cdfd0c6ee5dcb4648bca8c5a22.

Code

Code: the environment generator, solver, data builders, training recipes and evaluator are not public yet.

License

Apache-2.0, matching the code repository. All content is generated by the authors' own code (puzzle generator and solver); no third-party text is included.

Authors and citation

Authors and citation: to be added.

This release (files and this card) was prepared with AI assistance (Claude, an Anthropic model) and is being reviewed by the authors.