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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 · P29 · 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 with the evidence has a T2-T6 win rate of 0.049 (95% Korn-Graubard CI 0.017-0.215); the seed-only baseline on the same games is 0.033. E2 attempt A9.

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

Structured assertion

Relation: Evaluation estimate

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.
metric: Win rate, T2-T6 equal weightThe quantity estimated.
items: 92 gamesHeadline games finished and scored.
value: 0.0486 proportionPoint estimate.
interval low: 0.0168 proportionLower bound of the 95% interval.
interval high: 0.2154 proportionUpper bound of the 95% interval.
interval method: Korn-Graubard 95% interval (MOVER)How the interval was computed.
preregistered: trueWhether E2's DESIGN.md named this measure before it was measured.

Experimental provenance

Method and evaluation protocol: E2: `zendo_bench score --verify` (ZendoBench 1.0.0) over the attempt's run files; every game replayed from its recorded replies.
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: T2-T6 0.0486 [0.0168, 0.2154]; wins T1 5/10, T2 2/14, T3 2/20, T4 0/10, T5 0/34, T6 0/14; 0 unscored; every game verified. Seed-only baseline on the same games 0.033. Pooled w0 bands: w0=0 0.051 (45 classes); w0>=0.5 0.000 (3 classes; too few for an interval). Malformed rate (headline) 0.0000. 436 calls; 0 reached the thinking budget (none was cut at the 65,536-token cap); 0 ended inside the thought without an answer.
Uncertainty and replication: 95% Korn-Graubard intervals per tier with rule classes as clusters, combined over T2-T6 by MOVER; 92 headline games, one run.
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.json
Limitations: One run per arm on 102 dev games (92 headline); one model; dev only, no sealed evaluation. The wrapper changes the prompt after the game renders it, so the run is labelled player agent-tools. 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.

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

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

Evaluation estimate

Predicate. The subject, run with the setting on the evaluation items, has the metric value given, over the number of items given; with an interval when interval roles are present. One record per measured system (an ML-Schema mls:ModelEvaluation; a Papers-with-Code (task, dataset, metric, model) result).

Key evaluation_estimate · 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

Korn-Graubard 95% interval (MOVER)

Interval method. 95% confidence interval from `zendo_bench score` (ZendoBench 1.0.0): per tier, a Korn-Graubard interval with an effective sample size for games clustered by rule class; the equal-weight headline combines the tier intervals by MOVER (score.json ci_method korn-graubard-mover).

Key korn_graubard_mover_95 · version 7f391bde-3e66-43b6-9a50-d299f7b7e5b2

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

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

a1427e75-d571-45f4-9513-1276d692d84b

E1's estimate for the same model and base setting, on all 430 headline games.

b4fb1d38-4c66-4640-bfd9-d3f864fa4142

Defines E2's games and vocabulary; the forced arm 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.