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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 · P39 · Author-curated

On the 92 T2-T6 games of E2 (ZendoBench 1.0.0 dev, the first 2 items of each family; equal tier weights), Qwen3.5-4B (MLX) shown after every observation how many rule classes are still consistent has a T2-T6 win rate that differs by +0.049 from the same model's without an intervention (E1's A8 on the same games): paired difference, 95% CI -0.010 to 0.107; no difference measured. 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 difference in T2-T6 win rate

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: Win rate, T2-T6 equal weightThe quantity compared.
items: 92 gamesHeadline games finished and scored in both settings.
value: 0.0486 proportionPoint estimate of the difference.
interval low: -0.0098 proportionLower bound of the 95% interval.
interval high: 0.1069 proportionUpper bound of the 95% interval.
interval method: zendo_bench compare 95% Student-t 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: E1's A8 is a run of player model, which `zendo_bench compare` refuses to pair with E2's agent-tools runs, so scripts/03_measures.py applies compare's pairing by task ID and its breakdown (the same statistics) to the two arms' scored games; E2's arm verified by score --verify, A8 in E1.
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: 0.0486 [-0.0098, 0.1069] over 92 paired headline games. show 0.0486, A8 0.0000; seed-only baseline on the same games 0.033.
Uncertainty and replication: `zendo_bench compare`'s Student-t 95% interval on rule-class means (families as strata, equal tier weights); 92 paired headline games, one run per arm. The interval method is P27's compare_student_t_95; the class and degree-of-freedom counts in P27's definition are P27's own comparison's, not this one's.
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.score.json · publichttps://github.com/stw2/zendo-lab/blob/33e9624070bad7ef6c6ddba0c92812efbf7f2611/experiments/E02-small-model-interventions/results/scores/qwen3.5-4b-mlx-show.score.jsonqwen3.5-4b-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 difference in T2-T6 win rate

The difference in T2-T6 equal-weight win rate between two settings of the same model on the same games, paired by game, as `zendo_bench compare` (ZendoBench 1.0.0) computes it: setting_a minus setting_b.

Key paired_win_rate_difference · version f4ff537a-9cc4-4b5c-8550-ed3022a83291

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

zendo_bench compare 95% Student-t interval

The 95% Student-t interval that `zendo_bench compare` (ZendoBench 1.0.0) reports for a paired difference of equal-weight win rates; here over 215 rule classes with 66.5 degrees of freedom.

Key compare_student_t_95 · version f4ff537a-9cc4-4b5c-8550-ed3022a83291

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

Win rate, T2-T6 equal weight

Metric. Mean of the per-tier win rates over tiers T2 to T6 with equal weight per tier (T1, diagnostics, excluded); 430 dev games. A game is won when a submitted rule is equivalent to the hidden rule on 1..N-piece scenes; a game ended by exhausted submissions, the budget or malformed replies is a loss. Computed by `zendo_bench score --verify` (ZendoBench 1.0.0), which replays every game against its engine record. Reported as a proportion.

Key win_rate_t2_t6_equal_weight · 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

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

The win difference beside H3's test; H3 is about experimenting, not winning.

derived from

8cfab1fc-54aa-4522-8294-e0ec5f06fe4a

The count arm's estimate.

derived from

9c6080af-4e48-4962-82be-e9d303ce9238

A8's estimate on the same games.

f4ff537a-9cc4-4b5c-8550-ed3022a83291

Defines the paired win-rate difference frame and compare's interval, used here.

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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.