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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 · P20 · Author-curated

On ZendoBench 1.0.0 dev (460 games), GPT-6.1 Sol (reasoning high, Codex CLI, no tools) runs 18.10 experiments per game at 0.37 bits of expected information each, and first submits with a median of 1 rule class still consistent with the evidence (mean win probability 0.73; 460 games with a submission). E3 attempt A14.

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

Structured assertion

Relation: Behaviour profile

subject: GPT-6.1 SolThe model evaluated.
setting: E3 setting gpt-6.1-sol-codex-highHarness, sampling and isolation settings of the run.
evaluation items: ZendoBench 1.0.0 devThe games played.
games: 460 gamesScored games described (all tiers, T1 included).
experiments per game: 18.10 experiments per gameValue of the concept experiments_per_game (defined in the seed-only finding).
expected information gain: 0.368 bits per experimentValue of the concept expected_information_gain.
classes alive at first submission: 1 rule classesValue of the concept classes_alive_at_first_submission (a median).
win probability at first submission: 0.732 probabilityValue of the concept win_probability_at_first_submission (a mean).
games with a submission: 460 gamesGames over which the two first-submission statistics are taken.
preregistered: trueWhether DESIGN.md (E3) named these measures before measuring (as descriptive measures).

Experimental provenance

Method and evaluation protocol: E3: `zendo_bench diagnose` (ZendoBench 1.0.0) over the attempt's run files, from each game's engine record alone.
Dataset: ZendoBench 1.0.0 dev manifest: 460 games (T1 30, T2 60, T3 150, T4 60, T5 100, T6 60), Room material M1Version: zendo-bench v1.0.0 (git 46c192e0ea10a5140a33c1280edb97b0127cc68c); manifest sha256 e99344a3c3c9e624bf1c0f5782b266b54e97187cf412d9ff2dbe09d0c1e0a5c2 · Access: public
Reported results: exp_per_game 18.0978, bits_per_exp 0.3859, eig 0.3683, zero-information share 0.5698, alive_first 1, p_first 0.7318, submissions per game 1.3957, contradicting submissions 7/642, counterexample uptake 182/182, games with a submission 460/460.
Uncertainty and replication: Descriptive; no interval. Medians and means over the stated games.
Evidence references: gpt-6.1-sol-codex-high.jsonl · restrictedexperiments/E03-codex-frontier/results/runs/gpt-6.1-sol-codex-high.jsonl (run file; held by the Room owner; not public; ask the reporter)gpt-6.1-sol-codex-high.diagnose.md · publichttps://github.com/stw2/zendo-lab/blob/408e42697dd9637e60d1fde3c887e0e18c58e0d9/experiments/E03-codex-frontier/results/scores/gpt-6.1-sol-codex-high.diagnose.md
Limitations: One run per system on the dev split, not sealed. Played through the Codex CLI with no tools at reasoning effort high: Codex sets no output cap and its own sampling defaults (temperature 1.0, top_p 0.98, verbosity low), and the model version is whatever OpenAI served to Codex on the dates stated, neither pinned nor reported. Through Codex, GPT-6 Luna wins 0.087 less than through OpenRouter on the same games (E3's harness check), so comparisons with E1's HTTP arms carry that difference. Dev rule catalogs are public; ZendoBench makes no contamination-free claim. Covers all 460 games including T1, while the headline covers T2-T6.

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

Evaluation items. The 460 games of ZendoBench 1.0.0's dev manifest (T1 30, T2 60, T3 150, T4 60, T5 100, T6 60), file sha256 e99344a3c3c9e624bf1c0f5782b266b54e97187cf412d9ff2dbe09d0c1e0a5c2 (Room material M1), from github.com/stw2/zendo-bench tag v1.0.0, commit 46c192e. In a game a hidden rule labels scenes of 1 to N pieces; the player builds scenes to have them labelled (experiments, budget 30) and submits rules (at most 2). Close to exact learning from membership and equivalence queries.

Key zendobench_1_0_0_dev · version 7f391bde-3e66-43b6-9a50-d299f7b7e5b2

Concept JSON · Defining publication

E3 setting gpt-6.1-sol-codex-high

The Codex CLI 0.160.0 (`codex exec`) with no tools in the request, one stateless call per decision (ZendoBench's system prompt as Codex's instructions, its user message as the prompt, the last agent message as the reply), reasoning effort high, reasoning summary detailed, Codex's defaults otherwise (temperature 1.0, top_p 0.98, verbosity low, no output cap), default service tier, 12 calls in flight, each call in a new empty folder under a macOS sandbox closing the repositories and run files; player model, ZendoBench 1.0.0; run by `bash experiments/E03-codex-frontier/scripts/01_run.sh gpt-6.1-sol-codex-high` (github.com/stw2/zendo-lab).

Key arm_gpt_6_1_sol_codex_high · version 8117a6b7-ce4c-46c7-9cfc-1b2fe62afcd9

Concept JSON · Defining publication

GPT-6.1 Sol

GPT-6.1 Sol (Codex model slug gpt-6.1-sol), a closed OpenAI model reached through the Codex CLI under a ChatGPT sign-in, accessed 2026-10-07; the version is whatever OpenAI served to Codex on those dates, neither pinned nor reported by the caller.

Key gpt_6_1_sol · version 8117a6b7-ce4c-46c7-9cfc-1b2fe62afcd9

Concept JSON · Defining publication

Exact references

8117a6b7-ce4c-46c7-9cfc-1b2fe62afcd9

The headline estimate from the same attempt.

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.