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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 · P34 · 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 runs 2.30 experiments per game at 0.78 bits of expected information each, and first submits with a median of 84.5 rule classes still consistent with the evidence (an ideal player submitting then would win with mean probability 0.10; every game has a submission); 29 of its 201 submissions contradict evidence already shown, and it wins 4 of the 9.4 T2-T6 games such an ideal player would be expected to win (0.42). E2 attempt A9.

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

Structured assertion

Relation: Behaviour profile

subject: Qwen3.5-4BThe model evaluated.
setting: E2 setting qwen3.5-4b-mlx-showBackend, hardware, sampling, harness settings and intervention of the run.
intervention: Count of consistent rules shownWhat E2 changed against E1's setting.
evaluation items: ZendoBench 1.0.0 dev, 2 per familyThe games played.
experiments per game: 2.3 experiments per gameValue of the concept experiments_per_game (P1).
expected information gain: 0.778 bits per experimentValue of the concept expected_information_gain (P1).
classes alive at first submission: 84.5 rule classesValue of the concept classes_alive_at_first_submission (P1; a median over games; for T6 counted within its analysis prior).
win probability at first submission: 0.105 probabilityMean over games of diagnose's p_first: the probability that submitting the most probable rule class under the game's analysis prior wins at the first submission's moment (an ideal player's chance, not the submitted rule's; P1's concept of this name describes it otherwise).
contradicting submission share: 0.144 share of submissionsValue of the concept contradicting_submission_share (defined in F1).
conversion to ideal wins: 0.42 wins per expected ideal winValue of the concept conversion_to_ideal_wins (defined in F1).
preregistered: trueWhether E2's DESIGN.md named these measures before it was measured.

Experimental provenance

Method and evaluation protocol: E2: `zendo_bench diagnose` (ZendoBench 1.0.0) over the attempt's run files, from each game's engine record alone; conversion by scripts/03_measures.py.
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: exp_per_game 2.3039, bits_per_exp 0.8256, eig 0.7783, zero-information share 0.0511, repeats 0, alive_first 84.5, p_first 0.1047, submissions per game 1.9706, contradicting submissions 29/201, counterexample uptake 93/99, wrong submissions with exactly one class consistent 5, conversion 4/9.42.
Uncertainty and replication: Descriptive; no interval. Medians and means over the stated games.
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.mdmeasures.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.

Concept definitions

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

Behaviour profile

Predicate. Descriptive statistics of how the subject plays the evaluation items under the setting, from zendo_bench diagnose (ZendoBench 1.0.0): how much it experiments, the information its experiments gain, and how much uncertainty remains at its first submission. No interval.

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

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

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

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

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

8cfab1fc-54aa-4522-8294-e0ec5f06fe4a

The headline estimate from the same attempt.

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

The same model without an intervention on the same games (A8).

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.