SciGame: Let Agents Play the Scientific Discovery Games in the Real and Counterfactual World

AI summary

Overview

Research area: AI for scientific discovery, specifically benchmark design for LLM agents that infer scientific laws from evidence.

Technical level: Intermediate — readers should be comfortable with LLM agents, benchmark/evaluation design, and basic notions of symbolic regression, but no domain physics background is required.

Scope: The paper introduces SciGame, a controlled benchmark that pairs real scientific relations ("Original") with dimensionally consistent altered versions ("Counterfactual") under an identical task interface, and uses it to test whether LLM agents follow evidence or fall back on memorized priors.

What This Paper Is About

LLM agents are increasingly used to do scientific discovery, but existing benchmarks blur law inference together with programming, reward fitting to given data rather than prediction on unseen inputs, and never cleanly separate what an agent actually learned from the environment versus what it already memorized from pretraining. SciGame addresses this by distilling scientific papers into structured "scientific cards," each of which spawns two matched environments — one implementing the real published relation, one implementing a systematically mutated but dimensionally consistent version — so researchers can see whether an agent reasons from evidence or simply recites familiar laws.

Key Contributions

1. A paired Original/Counterfactual benchmark. Every task family yields two environments sharing the same controllable inputs, ranges, observables, and experimental constraints, differing only in the relation that generates observations. The authors verify the pairing works by checking that each environment's ground-truth equation fails prediction evaluation on its counterpart's observations.

2. A live, knowledge-cutoff-aware Temporal collection. Alongside 20 Historical task families of canonical laws, the paper builds 24 Temporal task families from 23 papers published between 30 April and 15 September 2026, using a rerunnable pipeline that keeps only papers whose journal and first-preprint dates both fall after the evaluated model's reported cutoff, with LLM extraction and independent LLM review of each card.

3. A unified framework crossing two task settings with three protocols. Identification (agent picks among candidate relations combined via a hidden parameter s) and Discovery (no candidates given) are each run under Prior-only (no observations), Fixed (a preset batch, B = 4 in the main table), and Adaptive (agent queries an Oracle sequentially and decides when to stop), scored with three metrics rather than one.

4. Three-metric evaluation that separates prediction from explanation. A prediction score on hidden inputs, a hierarchical episode success rate (weak tolerance-based and strict exact-expression standards), and a rubric-based scientific explanation score judged post hoc by an LLM.

Main Findings

• Familiar priors become a liability under counterfactual laws. Under Fixed, Original Discovery averages 58.6% ESR on Historical and 21.3% on Temporal across all nine LLMs. On Historical counterfactuals, strict ESR drops to zero for every LLM; on Temporal counterfactuals it averages 8.9%. Under Adaptive, the top model reaches 16.7% on Temporal counterfactuals but only 1.7% on Historical ones.

• Adaptive experimentation helps strong models and hurts weaker ones. GPT-6 Astra rises from 9.7% to 16.7% ESR on Temporal Counterfactual Discovery; Qwen3.7 Plus stays flat at 6.9%; GPT-5.6 Terra falls from 8.3% to 1.4%. On Temporal Original Discovery, GPT-5.6 Terra drops from 20.8% to 6.9% and Qwen3.7 Plus from 13.9% to 6.9%.

• Passive observation struggles specifically on altered laws. Under Fixed, Temporal Counterfactual Discovery averages 8.9% versus 21.3% for Temporal Original Discovery, with all models bunched between 5.6% and 12.5%. Four observations suffice to fit many original laws but not to resolve counterfactual forms.

• Good explanations can hide wrong predictors. Multiple model/protocol/condition combinations have strict ESR below 12.0% while scoring above 0.700 on the explanation score. GPT-5.6 Terra on Adaptive Temporal Counterfactual Discovery reaches SES 0.815 with ESR 1.4% and PS 0.060; DeepSeek-V4 Flash reaches SES 0.723 with ESR 11.1%.

• Exact symbolic recovery is the main bottleneck. Agents can often interpret evidence correctly and still fail to return the exact functional form. For GPT-6 Astra, 48% of failures are cases where the exact equation is not symbolically recovered; for GPT-5.5 and GPT-5.6 Sol, incorrect relations account for about half of failures.

• Adaptive Discovery has a cold start; Adaptive Identification saturates immediately. In Adaptive Discovery, success stays near zero for the first two queries and rises mainly after step four. In Adaptive Identification, GPT-6 Astra solves over 95% of both Original and Counterfactual episodes at step one and stays flat up to B = 8.

• Preset observations beat sequential search at small budgets. In Counterfactual Discovery at B = 8, Fixed reaches 47.2%–65.3% across three models while Adaptive reaches only 27.8%–34.7%; for GPT-6 Astra the gap is 65.3% (Fixed) versus 30.6% (Adaptive).

• The strongest model appears to generalize rather than memorize. On Temporal Counterfactual Discovery, GPT-6 Astra solves more tasks from papers released up to September 2026, unlike GPT-5.5 and GPT-5.6 Sol, which the authors read as evidence of generalization rather than training-data recall.

Methodology in Plain English

The authors turn published science into "cards." A card records a relation, its parameter values, variable definitions and units, a valid input domain, and the conditions under which the relation holds. Each card is then instantiated twice: once as the Original environment using the published relation, and once as a Counterfactual environment using a mutated version. The mutations follow the NewtonBench approach — adjusting coefficients and exponents, applying nonlinear transformations that preserve dimensional consistency, and adding cross-input interactions — with every affected variable updated across all related equations. Because both environments share the same inputs, units, ranges, and constraints, any performance difference must come from the agent's reasoning rather than from a changed interface.

An episode is one run of an agent (the "Player") on one task under one protocol. In Prior-only, the agent gets no data at all and must answer from the task description plus its pretrained knowledge. In Fixed, it receives a preset batch of observations it cannot choose or repeat. In Adaptive, it proposes experiments to an Oracle step by step; the Oracle checks each proposal against the constraints, returns simulated observations for accepted proposals (quantized to the declared measurement resolution, with no injected noise) or diagnostic feedback for rejected ones. To keep the agent honest, each Adaptive step must report at least two hypotheses with nonnegative confidence scores summing to one, plus a numerical forecast under every hypothesis for every requested input and observable; the loop ends when the top hypothesis's confidence exceeds a threshold τ, and violating the stopping rule automatically fails the episode.

The Identification setting hands the agent a parametric blend of the true and mutated expressions, with a hidden switch s set to 0 (Original) or 1 (Counterfactual), so the task reduces to choosing among candidates and using experiments to check. Discovery hands over no candidates, so the agent must construct the relation from scratch. In both, the agent submits executable predictors — represented as pure arithmetic expression trees with a fixed operator set, capped at 1024 total nodes and depth 64, rather than arbitrary code — plus a written explanation and applicability conditions.

Scoring uses three lenses. The prediction score compares the submitted expressions against simulator outputs on hidden inputs, normalizing absolute error by declared absolute and relative tolerances. The episode success rate counts episodes where every prediction error stays within tolerance (weak) or where the expression also matches exactly (strict). The explanation score is assigned by a fixed LLM judge on three criteria — correct description of input–observable effects, a valid controlled comparison or scaling consequence, and staying within supported evidence — each scored 0, 0.5, or 1.

Why This Matters

Impact on research. The paper argues that benchmark design has been conflating things that should be measured separately: whether an agent can infer a law, whether it can predict unseen inputs, and whether it is reasoning or recalling. The Original/Counterfactual pairing gives the field a clean instrument for measuring prior interference, and the Temporal collection with a moving date window offers a repeatable way to reduce contamination instead of merely acknowledging it.

Real-world applications.

• Automated discovery of governing relations in experimental physics and chemistry, where the agent must design the next measurement rather than analyze a supplied dataset.
• Materials and process engineering, where a model's job is to predict behavior outside the tested region, not to interpolate within it.
• Any setting where legacy intuition is wrong — new regimes, engineered or synthetic systems, unusual conditions — and a model that defaults to textbook laws will confidently mispredict.
• Auditing AI-generated scientific claims: the finding that explanations can look excellent while predictions are wrong is directly relevant to review workflows that read prose explanations as evidence of understanding.

Industry relevance. For teams deploying LLM agents in lab automation or simulation-driven R&D, the budget results matter: sequential self-directed experimentation only pays off for the strongest models and only with more than about four to eight interaction steps, whereas a fixed batch of observations is often the better default for weaker systems.

Future Directions

• Scale and diversify the evaluation. The authors note the study covers a small set of models, mostly from the GPT family, run through a single agent harness, with 44 task families (most from physics) and three repetitions per condition — making small cell differences uncertain.
• Add realistic measurement noise. All environments are deterministic simulators with no stochastic noise, and Temporal relations simplify what the papers actually report; noisy simulators would test robustness the current setup cannot.
• Broaden counterfactual generation. Counterfactual relations come from a limited set of synthetic mutations, and the Historical and Temporal collections use different mutation schemes — unifying and expanding these is an open design question.
• Attack the symbolic-recovery bottleneck directly. Since wrong functional form dominates failures — especially for the strongest model, where 48% of failures are failures of exact symbolic recovery — methods that bridge accurate evidence interpretation to exact equation induction (rather than polynomial curve-fitting) are the clearest next target.
• Reduce judge circularity. Card curation and explanation scoring both rely on LLMs, and the judge is itself one of the evaluated models, so independent or human verification remains open.

Target Audience

Researchers building and evaluating LLM agents for scientific reasoning; benchmark designers interested in contamination-resistant, counterfactual evaluation; AI-for-science practitioners in physics, chemistry, and engineering who want agents to design experiments rather than fit supplied data; and industry teams assessing whether an agent should be allowed to choose its own experiments under a limited budget.

Authors’ abstract

Large language model agents are increasingly used for scientific discovery. However, existing benchmarks mix law inference with programming, score data fitting instead of prediction on unseen inputs, and do not separate empirical evidence from pretrained priors. We introduce SciGame, a controlled benchmark that converts scientific literature into structured scientific cards. Each card yields a pair of Original and dimensionally consistent Counterfactual environments with the same task interface. SciGame contains a Historical collection of canonical laws and a live Temporal collection curated from papers published after model knowledge cutoffs. It evaluates agents in candidate-guided Identification and open-ended Discovery settings. Each setting runs under Prior-only, Fixed, and Adaptive protocols. Experiments on five frontier models yield three findings. First, familiar priors hurt performance once the governing relation is altered. Second, adaptive experimentation helps the strongest models but harms weaker ones under limited budgets. Third, good explanations can hide quantitative failures. Recovering the exact symbolic form remains the main bottleneck, even when agents interpret evidence correctly. Current agents can investigate systems actively, but inducing exact laws in unfamiliar settings remains an open challenge.