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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 · P9 · Author-curated

On ZendoBench 1.0.0 dev (460 games), GPT-6 Luna (reasoning high, OpenRouter) runs 16.70 experiments per game at 0.39 bits of expected information each, and first submits with a median of 2 rule classes still consistent with the evidence (mean win probability 0.62; 431 games with a submission). E1 attempt A2.

Published by @stw2 · 2026-10-06 · Sources, measurements and interpretation are supplied by the author.

Structured assertion

Relation: Behaviour profile

subject: GPT-6 LunaThe model evaluated.
setting: E1 setting gpt-6-luna-openrouter-highBackend, hardware, sampling and harness 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: 16.70 experiments per gameValue of the concept experiments_per_game (defined in the seed-only finding).
expected information gain: 0.391 bits per experimentValue of the concept expected_information_gain.
classes alive at first submission: 2 rule classesValue of the concept classes_alive_at_first_submission (a median).
win probability at first submission: 0.622 probabilityValue of the concept win_probability_at_first_submission (a mean).
games with a submission: 431 gamesGames over which the two first-submission statistics are taken.
preregistered: trueWhether DESIGN.md (E1) named these measures before measuring (as descriptive measures).

Experimental provenance

Method and evaluation protocol: E1: `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 16.7022, bits_per_exp 0.3957, eig 0.3910, zero-information share 0.5213, alive_first 2, p_first 0.6220, submissions per game 1.3696, contradicting submissions 55/630, counterexample uptake 198/199.
Uncertainty and replication: Descriptive; no interval. Medians and means over the stated games.
Evidence references: gpt-6-luna-openrouter-high.jsonl · restrictedexperiments/E01-dev-baseline/results/runs/gpt-6-luna-openrouter-high.jsonl (held by the Room owner; not public; ask the reporter)gpt-6-luna-openrouter-high.part2.jsonl · restrictedexperiments/E01-dev-baseline/results/runs/gpt-6-luna-openrouter-high.part2.jsonl (held by the Room owner; not public; ask the reporter)gpt-6-luna-openrouter-high.diagnose.md · publichttps://github.com/stw2/zendo-lab/blob/3a25d59f04e9084f4cecf84f124d67c647c5e903/experiments/E01-dev-baseline/results/scores/gpt-6-luna-openrouter-high.diagnose.md
Limitations: One run per system on the dev split, not sealed. Each system runs at its publisher's recommended sampling and reasoning effort, so settings differ between systems. 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

E1 setting gpt-6-luna-openrouter-high

HTTP chat completions to OpenRouter, default provider routing (the provider was not recorded per call), reasoning effort high, max_tokens 65,536, 64 calls in flight, reasoning text kept; player model, ZendoBench 1.0.0; run by `bash experiments/E01-dev-baseline/scripts/01_run.sh gpt-6-luna-openrouter-high` (github.com/stw2/zendo-lab).

Key arm_gpt_6_luna_openrouter_high · version 4afb1318-33ab-4d14-9f47-5bbeb4c6e769

Concept JSON · Defining publication

GPT-6 Luna

GPT-6 Luna (openai/gpt-6-luna), closed model reached through OpenRouter (OpenAI as provider), accessed 2026-10-04/05; the version is whatever OpenAI served on those dates, not pinned by the caller.

Key gpt_6_luna · version 4afb1318-33ab-4d14-9f47-5bbeb4c6e769

Concept JSON · Defining publication

Exact references

4afb1318-33ab-4d14-9f47-5bbeb4c6e769

The headline estimate from the same attempt.

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