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FALSIFYBENCH: Evaluating Inductive Reasoning in LLMs with Rule Discovery Games

T0 review · 2 major / 2 minor · reviewed 2026-06-28 · grok-4.3

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Pith's one-line read LLMs that seek to falsify hypotheses outperform those seeking confirmation in rule discovery games.

desk verdict FALSIFYBENCH adapts the Wason task into an iterative benchmark and links better LLM performance to negative testing, though the evidence for deliberate falsification is indirect. read the letter →

arxiv 2606.04751 v1 pith:KDNPIUSL submitted 2026-06-03 cs.AI

Leonardo Bertolazzi , Katya Tentori , Raffaella Bernardi This is my paper · ORCID
classification cs.AI
keywords inductivereasoninglargelanguagemodelshypothesistestingrulediscoveryfalsificationnegativescientificbeliefrevision
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper introduces FALSIFYBENCH, a benchmark where language models discover hidden semantic rules by proposing examples and revising beliefs from feedback. It tests twelve models across families and scales, showing reasoning models generally surpass instruction-tuned ones. The main driver of success is negative testing, in which models actively propose examples that would disprove their current hypothesis rather than only seek confirming cases. Failures trace to identifiable patterns in how models explore the space of possible rules.

What carries the argument

FALSIFYBENCH, an iterative evaluation game in which agents propose examples to uncover hidden semantic properties and receive feedback indicating whether each example fits the rule.

What would settle it

A side-by-side test measuring whether the same models that excel at negative testing on FALSIFYBENCH also generate better hypotheses when given real experimental data from a scientific domain.

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Extended reading notes

Core claim

The central claim is that the capacity for negative testing drives success on the FALSIFYBENCH task. Models that generate examples intended to falsify their hypotheses discover the hidden semantic rules more reliably than models focused on confirmation. Although reasoning models outperform instruction-tuned models, no system reaches optimal performance, and turn-level analysis links most failures to specific navigation patterns in the hypothesis space.

Load-bearing premise

That performance on this semantic rule-discovery game meaningfully predicts an LLM's ability to engage in hypothesis-driven reasoning for real scientific discovery tasks.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

2 major / 2 minor

Summary. The paper introduces FALSIFYBENCH, a benchmark framework inspired by the Wason 2-4-6 task, in which LLMs act as agents that iteratively propose examples to discover hidden semantic rules and receive binary feedback. It evaluates 12 models across families and scales, finding that reasoning models outperform instruction-tuned models (though none approach optimal performance), that success is primarily driven by the capacity for negative testing (actively seeking disconfirming evidence), and that turn-level analysis reveals identifiable failure patterns in hypothesis-space navigation.

Significance. If the central empirical patterns hold, the work supplies a controlled, falsification-oriented benchmark that isolates hypothesis generation, evidence gathering, and belief revision—elements relevant to scientific discovery agents. The emphasis on negative testing as a performance driver offers a concrete, testable hypothesis for future agent design. The absence of machine-checked proofs or parameter-free derivations is expected for an empirical benchmark paper; the contribution lies in the task design and the fine-grained behavioral analysis.

major comments (2)
  1. [§4 (turn-level analysis)] §4 (or the section presenting the turn-level analysis): the claim that 'the primary driver of success is the capacity for negative testing' is load-bearing yet rests on post-hoc inference from the proportion and pattern of negative-labeled proposals. Without an explicit requirement that models state their current hypothesis before each proposal, negative feedback could equally result from broad exploration, post-hoc revision, or sampling variance rather than targeted disconfirmation of a held belief. A concrete test (e.g., correlation between pre-proposal hypothesis statements and subsequent negative examples) is needed to isolate the mechanism.
  2. [Methods / Evaluation protocol] Evaluation protocol (methods section describing the iterative loop): the benchmark does not record or condition on whether a model articulates an explicit hypothesis before proposing an example. This design choice makes it impossible to distinguish deliberate falsification attempts from other sources of negative feedback, directly weakening the causal attribution in the abstract and §5.
minor comments (2)
  1. [Figure 3] Figure 3 (or the figure showing model performance by negative-testing rate): axis labels and legend should explicitly state whether the x-axis is the fraction of negative proposals or a normalized score; current presentation risks conflating volume of negative feedback with strategic intent.
  2. [Table 1] Table 1 (model list): include the exact prompting template and temperature settings used for each model family so that the negative-testing metric can be reproduced.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments, which help clarify the evidential basis for our claims about negative testing. We respond to each major comment below.

read point-by-point responses

  1. Referee: [§4 (turn-level analysis)] §4 (or the section presenting the turn-level analysis): the claim that 'the primary driver of success is the capacity for negative testing' is load-bearing yet rests on post-hoc inference from the proportion and pattern of negative-labeled proposals. Without an explicit requirement that models state their current hypothesis before each proposal, negative feedback could equally result from broad exploration, post-hoc revision, or sampling variance rather than targeted disconfirmation of a held belief. A concrete test (e.g., correlation between pre-proposal hypothesis statements and subsequent negative examples) is needed to isolate the mechanism.

    Authors: We agree that the evidence linking negative testing to success is correlational, derived from the observed relationship between the rate of negatively labeled proposals and task success in the turn-level analysis. The benchmark follows the standard Wason 2-4-6 protocol without mandating explicit hypothesis statements to preserve ecological validity. We will revise §4 to more explicitly define negative testing via proposal labels, discuss alternative explanations such as exploration variance, and qualify the abstract and §5 claims as correlational rather than mechanistic. A direct correlation test with pre-proposal hypotheses would require a protocol change and is noted as future work. revision: partial

  2. Referee: [Methods / Evaluation protocol] Evaluation protocol (methods section describing the iterative loop): the benchmark does not record or condition on whether a model articulates an explicit hypothesis before proposing an example. This design choice makes it impossible to distinguish deliberate falsification attempts from other sources of negative feedback, directly weakening the causal attribution in the abstract and §5.

    Authors: The iterative loop is deliberately unconditioned on explicit hypotheses to study models' spontaneous inductive behavior. We will update the methods section to document this design decision and its consequences for interpreting negative feedback. This revision will temper causal language in the abstract and §5 to emphasize observed correlations between negative proposal rates and performance. revision: yes

Circularity Check

0 steps flagged · score 0.0 of 10

Empirical benchmark evaluation with no derivation chain or fitted inputs

full rationale

The paper introduces FALSIFYBENCH as an empirical evaluation framework for LLM inductive reasoning via a rule-discovery game. All claims, including the role of negative testing, are derived from observed performance metrics across 12 models on the benchmark tasks. There are no equations, parameter fits, uniqueness theorems, or self-citations that reduce the central results to their own inputs by construction. The work is self-contained as a standard benchmark study whose findings rest on external model evaluations rather than internal redefinitions or renamings.

Assumptions & free parameters 0 free parameters · 0 assumptions · 0 invented entities

Abstract supplies no information on free parameters, axioms, or invented entities.

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Cite this review

Pith. "Pith review of FALSIFYBENCH: Evaluating Inductive Reasoning in LLMs with Rule Discovery Games." pith.science (2026). https://pith.science/paper/KDNPIUSL

@misc{pith2026260604751,
  author       = {Pith},
  title        = {Pith review of: FALSIFYBENCH: Evaluating Inductive Reasoning in LLMs with Rule Discovery Games},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/KDNPIUSL}},
  note         = {Machine review of arXiv:2606.04751}
}
read the original abstract

Large language models (LLMs) are increasingly deployed as autonomous agents in scientific tasks. Yet whether these systems can effectively engage in forms of inductive reasoning relevant to scientific discovery remains an open question. In this work, we introduce FALSIFYBENCH, an evaluation framework for hypothesis-driven reasoning inspired by the classic Wason 2-4-6 task, in which agents must discover hidden semantic properties by iteratively proposing examples and receiving feedback. This task captures key elements of scientific reasoning: hypothesis generation, evidence gathering, and belief revision in response to both confirming and disconfirming evidence. Our evaluation of 12 LLMs across model families and scales shows that reasoning models are generally stronger scientific reasoners than instruction-tuned models, although no model comes close to optimal performance. The primary driver of success is the capacity for negative testing: models that actively seek to falsify their hypotheses consistently outperform those that primarily seek confirmation. Moreover, a fine-grained turn-level analysis, neglected in previous work, reveals that failure is tied to identifiable patterns in how models navigate the hypothesis space.

Figures

Figures reproduced from arXiv: 2606.04751 by the authors.

Figure 1
Figure 1. FALSIFYBENCH game structure. The player is given three items (e.g., pocketed bat, skimmer, and tarsius glis) and must identify their shared hidden target rule (e.g., “they are animals”) by proposing additional test triples and receiving feedback from the oracle (“Conform” vs. “Do not conform”). Before proposing a test triple, the player makes explicit the hypothesis about the hidden rule being tested. In positive te… view at source ↗
Figure 2
Figure 2. Experimental results for 12 LLMs on FALSIFYBENCH. Models to the left of the vertical black line are instruction-tuned variants, while models to the right are reasoning variants. Top-left: Success rate represents the percentage of correctly identified target rules. Bottom-left: Confirmation bias measures the proportion of queries that confirm rather than falsify the current hypothesis (lower is better). Top-right: Or… view at source ↗
Figure 3
Figure 3. Results of the Bayesian mixed-effects logistic regression ( [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figures from the paper (10 more)
Figure 4
Figure 4. Figure 4: Distribution of relations between the current [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]
Figure 5
Figure 5. Figure 5: Top: Average conclusive falsification rate per model: the proportion of Test turns that yield a conclusive falsification given the relation between H and R at that turn. Models to the left of the vertical black line are instruction-tuned variants; models to the right a…
Figure 6
Figure 6. Figure 6: Left: Mean gap (in percentage points) in the proportion of Disjoint and Partial Overlap Test turns between failed and successful games, per model. Positive values indicate a configuration is more prevalent in failed games. Asterisks denote statistically significant dif…
Figure 7
Figure 7. Figure 7: Raw match count between surface-level lin [PITH_FULL_IMAGE:figures/full_fig_p014_7.png]
Figure 8
Figure 8. Figure 8: Left: The average number of turns required to correctly identify the target rule R, computed over successful games only. Right: The average number of Guess actions performed per game. In both plots, models to the left of the vertical black line are instruction-tuned va…
Figure 9
Figure 9. Figure 9: Distribution of relations between H and R across Test turns, split by outcome. Left: Successful games only. Right: Failed games only. Successful games are dominated by the H ⊂ R configuration (blue) reflecting coherent upward revision. Failed games show a substantially…
Figure 10
Figure 10. Figure 10: Top: success rate. Center: average Confirmation bias. Bottom: average conclusive falsification rate. All metrics are decomposed by target rule [PITH_FULL_IMAGE:figures/full_fig_p017_10.png]
Figure 11
Figure 11. Figure 11: Top: average turns to solution. Bottom: average guesses per game. All metrics are decomposed by target rule. Empty cells in the turns heatmap indicate zero successful games for that model-target rule combination [PITH_FULL_IMAGE:figures/full_fig_p018_11.png]
Figure 12
Figure 12. Figure 12: Oracle accuracy and agreement with human annotator decomposed by target rule. [PITH_FULL_IMAGE:figures/full_fig_p018_12.png]
Figure 13
Figure 13. Figure 13: Results decomposed by game outcome (Succeeded vs. Failed). [PITH_FULL_IMAGE:figures/full_fig_p019_13.png]

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. DiG-bench: Discovery in Games

    cs.AI 2026-08 conditional novelty 6.0 of 10

    A 70-game interactive benchmark where agents must discover hidden rules and objectives, with human beatability on every game and frontier models failing on the hardest tiers.

Reference graph

Works this paper leans on

16 extracted references · 1 canonical work pages · cited by 1 Pith paper

  1. [1]

    The AI Scientist: Towards Fully Automated Open-Ended Scientific Discovery

    Evaluating the inductive abilities of large language models: Why chain-of-thought reasoning sometimes hurts more than helps. InThe Thirty-ninth Annual Conference on Neural Information Process- ing Systems. Joshua Klayman and Young Whee Ha. 1987. Confirma- tion, disconfirmation, and informa-tion in hypothesis testing. Brenden Lake and Marco Baroni. 2018. G...

    work page Pith review arXiv 1987

  2. [2]

    Oracle’s judgment: CONFORM

    and one failed (Table 9) complete game trace pro- duced by GPT-5.2-Chat. In each trace the player’s strategy in Test turns is labeled withpositivefor positive tests andnegativefor negative tests. F Use of Generative AI Tools We used GitHub Copilot and Claude Code as as- sistant tools for parts of the project’s source code development, while ChatGPT was us...

  3. [3]

    Propose 3 new items to test your current hypothesis

  4. [4]

    action":

    Make a guess of the property if you think you know it. The purpose of testing is to gather information to refine your hypothesis. Once you believe you have enough information, you can make a guess. If your guess is correct, you win. If it’s incorrect, you can keep testing and guessing until you find the right property or run out of turns. Your response mu...

  5. [5]

    {{initial_examples[0]}}

  6. [6]

    {{initial_examples[1]}}

  7. [7]

    {{target_property}}

    {{initial_examples[2]}} What is your first move? Respond with JSON only. Table 5: System prompt and first user role interaction provided to the player. The system prompt specifies the rules of the game and is provided once at the start of each game; the initial message introduces the three initial examples. Double curly-brace placeholders are filled befor...

  8. [8]

    {{target_property}}

    {{items[2]}} Do ALL three items conform to the property “{{target_property}}”? Respond with ONLY a JSON object: { "conforms": true or false, "explanation": "brief explanation of your judgment" } Classify player’s test strategy You are an oracle in a property discovery game. The property to evaluate is: “{{property_hypothesis}}” The player has proposed the...

Show all 16 references
  1. [9]

    {{property_hypothesis}}

    {{items[2]}} Player’s current hypothesis: “{{property_hypothesis}}” Player’s reasoning for choosing these items: “{{player_reasoning}}” Tasks:

  2. [10]

    confirm" = they expect all three items to conform to their hypothesis -

    Infer the player’s *intention* for this Test based on their hypothesis and reasoning. - "confirm" = they expect all three items to conform to their hypothesis - "falsify" = they expect at least one item to NOT conform to their hypothesis

  3. [11]

    intention

    Separately, judge whether all three items actually conform to the hypothesis. Respond with ONLY a JSON object: { "intention": "confirm" or "falsify", "expected_conforms": true or false, "conforms": true or false, "explanation": "brief explanation" } JudgeGuessagainst the targe...

  4. [12]

    animal” | Hypothesis: “animal

    Target: “animal” | Hypothesis: “animal” -> identical

  5. [13]

    animal” | Hypothesis: “mammal

    Target: “animal” | Hypothesis: “mammal” -> hypothesis_included_in_target

  6. [14]

    animal” | Hypothesis: “living thing

    Target: “animal” | Hypothesis: “living thing” -> target_included_in_hypothesis

  7. [15]

    animal” | Hypothesis: “carnivore

    Target: “animal” | Hypothesis: “carnivore” -> partial_overlap

  8. [16]

    animal” | Hypothesis: “mineral

    Target: “animal” | Hypothesis: “mineral” -> disjoint Now annotate this case. target rule: “{{target_property}}” Current hypothesis: “{{hypothesis}}” Respond with JSON only in this format: { "relation": "one of identical, disjoint, partial_overlap, hypothesis_included_in_target...

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