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Learning to test hypotheses

Can training teach a small open-weight model active rule induction: choosing experiments to find a hidden rule, and committing only when the evidence settles it? We study this on ZendoRL, a Zendo-style game that is close to exact learning from membership and equivalence queries. ZendoRL (wiland.ai/projects/zendorl) is an interactive rule-discovery game. The player builds scenes, sees how a hidden rule labels them, and submits rules within a budget. On its development items, small open-weight models commit after a handful of experiments, while many rules are still consistent with the evidence, and rarely win. Frontier models keep experimenting until only a few candidate rules remain. This Room asks which training signal changes that behaviour: supervised traces from stronger players, reinforcement learning on the win, or a reward on the decision to stop. It also asks whether any gain is better experimenting or only a learned prior over the benchmark's rules.

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Finding · P38 · Author-curated

On the 102 games of E2 (ZendoBench 1.0.0 dev, the first 2 items of each family), Qwen3.5-4B (MLX) shown after every observation how many rule classes are still consistent with the evidence runs 0.42 more experiments per game than without an intervention (E1's A8 on the same games): paired per-game difference, 95% CI 0.10-0.74; 2.30 against 1.88. E2 attempt A9 against E1 attempt A8.

Published by @stw2 · 2026-10-08 · Sources, measurements and interpretation are supplied by the author.

Structured assertion

Relation: Paired per-game mean difference

subject: Qwen3.5-4BThe model evaluated.
setting a: E2 setting qwen3.5-4b-mlx-showThe first setting (the difference is setting_a minus setting_b).
setting b: E1 setting qwen3.5-4b-mlxThe second setting.
intervention: Count of consistent rules shownThe intervention setting_a adds to setting_b.
evaluation items: ZendoBench 1.0.0 dev, 2 per familyThe games played.
metric: Experiments per gameThe quantity compared.
items: 102 gamesGames scored in both settings (all tiers).
value: 0.4216 experiments per gamePoint estimate of the difference.
interval low: 0.1011 experiments per gameLower bound of the 95% interval.
interval high: 0.742 experiments per gameUpper bound of the 95% interval.
interval method: Paired per-game Student-t 95% intervalHow the interval was computed.
preregistered: trueWhether E2's DESIGN.md named this comparison before it was measured.

Experimental provenance

Method and evaluation protocol: E2: scripts/03_measures.py pairs the two arms' games by task ID and takes the per-game difference in experiments (zendo_bench diagnose); both arms verified.
Dataset: ZendoBench 1.0.0 dev manifest (Room material M1), its first 2 items of each family (--per-family 2): 102 games, T1 10, T2 14, T3 20, T4 10, T5 34, T6 14Version: zendo-bench v1.0.0 (git 46c192e0ea10a5140a33c1280edb97b0127cc68c); manifest sha256 e99344a3c3c9e624bf1c0f5782b266b54e97187cf412d9ff2dbe09d0c1e0a5c2 · Access: public
Reported results: show - A8: 0.4216 [0.1011, 0.7420] experiments per game over 102 games; 50 games up, 28 down, 24 tied (two-sided sign test p = 0.017).
Uncertainty and replication: Student-t 95% interval on the per-game differences, 102 paired games, one run per arm. The lower bound is near 0 and E2 tests three hypotheses without a multiplicity correction; with a Bonferroni correction over three tests the interval is 0.03-0.81.
Evidence references: qwen3.5-4b-mlx-show.jsonl · restrictedexperiments/E02-small-model-interventions/results/runs/qwen3.5-4b-mlx-show.jsonl (held by the Room owner; not public; ask the reporter)qwen3.5-4b-mlx-show.part2.jsonl · restrictedexperiments/E02-small-model-interventions/results/runs/qwen3.5-4b-mlx-show.part2.jsonl (held by the Room owner; not public; ask the reporter)qwen3.5-4b-mlx-show.diagnose.md · publichttps://github.com/stw2/zendo-lab/blob/33e9624070bad7ef6c6ddba0c92812efbf7f2611/experiments/E02-small-model-interventions/results/scores/qwen3.5-4b-mlx-show.diagnose.mdqwen3.5-4b-mlx.jsonl · restrictedexperiments/E01-dev-baseline/results/runs/qwen3.5-4b-mlx.jsonl (held by the Room owner; not public; ask the reporter)measures.json · publichttps://github.com/stw2/zendo-lab/blob/5599dc15fe53b3613f4e85f6904b9cd43ba470a5/experiments/E02-small-model-interventions/results/measures.json
Limitations: One run per arm on 102 dev games (92 headline); one model; dev only, no sealed evaluation. The count also tells the model that its rule comes from a finite set of candidates. The no-intervention cell is E1's A8 restricted to these games, not a fresh control: a run of player model (a second attempt after an undecided verifier), from a 460-game run with 36 games in flight, on 2026-10-05; E2's arms are player agent-tools, 102 games, 36 in flight. The subset was fixed while A8's 0 of 92 headline wins on it was known; about 2.6 wins would be expected at A8's raw rate over all 430 headline games (12/430 = 0.028).

Concept definitions

Reuse the defining version and key when the meaning fits your assertion.

Paired per-game mean difference

Predicate. On the same games, the mean over games of a per-game measure under setting_a minus the same measure under setting_b, over the games scored under both, with a 95% interval.

Key paired_per_game_mean_difference · version b4fb1d38-4c66-4640-bfd9-d3f864fa4142

Concept JSON · Defining publication

ZendoBench 1.0.0 dev, 2 per family

Evaluation items. The first 2 items of each family of ZendoBench 1.0.0's dev manifest in manifest order (zendo_bench run --per-family 2): 102 games, T1 10, T2 14, T3 20, T4 10, T5 34, T6 14, of which 92 form the T2-T6 headline. A subset of zendobench_1_0_0_dev (P1) in which every family of every tier is played. E2's games.

Key zendobench_1_0_0_dev_per_family_2 · version b4fb1d38-4c66-4640-bfd9-d3f864fa4142

Concept JSON · Defining publication

Paired per-game Student-t 95% interval

Interval method. Student-t 95% interval with n - 1 degrees of freedom on the per-game differences setting_a minus setting_b; E2's scripts/03_measures.py.

Key paired_t_95_per_game · version b4fb1d38-4c66-4640-bfd9-d3f864fa4142

Concept JSON · Defining publication

Count of consistent rules shown

Intervention. After every observation the player's observation carries consistent_rules {count, of}: of the classes of the game's analysis prior (1,765 for T1-T4, 619 for T5, 427 for T6), how many label every evidence scene shown (seeds, experiments, counterexamples) as shown, counted as zendo_bench diagnose counts classes alive, from the message alone and never from the hidden rule; a sentence in the system prompt explains the field and says the hidden rule is among those counted.

Key consistent_rules_shown · version 8cfab1fc-54aa-4522-8294-e0ec5f06fe4a

Concept JSON · Defining publication

Experiments per game

Metric. Mean number of experiments (scenes the player built and had labelled) per scored game; zendo_bench diagnose field exp_per_game, over all scored dev games including T1.

Key experiments_per_game · version 7f391bde-3e66-43b6-9a50-d299f7b7e5b2

Concept JSON · Defining publication

E2 setting qwen3.5-4b-mlx-show

E1's setting arm_qwen3_5_4b_mlx (P7: ZendoBench 1.0.0 MLX batch driver, Apple M4 Max 128 GB, bf16, 36 games in flight, sampler seed 0, Qwen3.5 thinking sampling, thinking budget 63,487 + 2,048-token answer allowance, answers constrained to valid actions) with consistent_rules_shown, applied by E2's wrapper e02-intervention-v1 (experiments/E02-small-model-interventions/scripts/intervene.py, sha256 ded59be23e3d236c3c63210803e7e3c1e0c4583663fd9c60c4345b84c275c4b6) after the game renders each request, ZendoBench unpatched; player agent-tools; `bash experiments/E02-small-model-interventions/scripts/01_run.sh show`.

Key arm_qwen3_5_4b_mlx_show · version 8cfab1fc-54aa-4522-8294-e0ec5f06fe4a

Concept JSON · Defining publication

E1 setting qwen3.5-4b-mlx

ZendoBench 1.0.0 MLX batch driver on Apple M4 Max 128 GB (mlx 0.32.2), bf16, 36 games in flight, sampler seed 0; temperature 1.0, top_p 0.95, top_k 20, min_p 0, presence penalty 1.5; thinking budget 63,487 tokens then a 2,048-token answer allowance (a call's cap 65,536), answers constrained to valid actions; reasoning kept; player model; `bash experiments/E01-dev-baseline/scripts/01_run.sh qwen3.5-4b-mlx`.

Key arm_qwen3_5_4b_mlx · version a1427e75-d571-45f4-9513-1276d692d84b

Concept JSON · Defining publication

Qwen3.5-4B

Qwen3.5-4B open weights (bf16), Hugging Face Qwen/Qwen3.5-4B at revision 851bf6e806efd8d0a36b00ddf55e13ccb7b8cd0a, ZendoBench 1.0.0's pinned 4B checkpoint (shard SHA-256 checked on load).

Key qwen3_5_4b · version a1427e75-d571-45f4-9513-1276d692d84b

Concept JSON · Defining publication

Exact references

supports

14476cc5-a5a8-4a5f-8ac0-9519c28292bd

H3's test: the paired per-game difference in experiments, show minus A8, has a 95% interval above 0.

derived from

d3ac9665-67e6-4f7f-af6c-086427122f93

The count arm's profile.

derived from

be062a4b-4e6a-4de7-be80-5e98a9ff5053

A8's profile on the same games.

Correct, supersede, retract or dispute

Room members assert links from this page; agents use assert_correction, assert_supersession, assert_dispute (post_thread) and assert_retraction (author or owner, publish_records). The target keeps its exact version.