Bethe Ansatz with a Large Language Model

Beyond math and code, Large language models (LLMs) are beginning to tackle problems that have traditionally required substantial training for theoretical physicists, but it remains unclear how far this capability extends and where it might break. As a first step toward pushing LLMs in high-energy theoretical physics, we introduce QFT-Bench, a benchmark of 75 graduate- to research-level problems requiring extensive reasoning and derivation across core Quantum Field Theory (QFT) subareas. Each question has a well-defined target and closed-form reference answer. Evaluation combines symbolic verification with LLM-based judge. Across 39 proprietary and open-source models, frontier models already demonstrate substantial capabilities on nontrivial QFT calculations, with the strongest models exceeding 95% accuracy. At the same time, clear gaps remain. Even strong models still make errors in calculations, conventions, and instruction following, while weaker models often fail at the level of physical concepts or derivations. We further monitor models' CoTs and show that current models exhibit nontrivial reasoning unfaithfulness, i.e., they could reach correct answers but the reasoning itself does not justify and logically support them. These results provide a quantitative assessment of current LLM capabilities in QFT and a first step toward broader evaluation in high-energy theoretical physics.

Current large-language-model (LLM) physics benchmarks are usually scored by answer accuracy, which cannot distinguish genuine reasoning from recall of familiar problem patterns and reveals little about where a model's reasoning breaks down. We introduce an auditable four-stage diagnostic that evaluates whether an LLM can reason inside an unfamiliar physics framework through induction, formulation, prediction, and review. The diagnostic combines locked pre-registrations, fresh sessions between stages, dual-LLM judging, and a human-audit pathway, and we apply it to three parallel physics worlds: a single-equation counterfactual world ($F=mv$), a historical framework (Aristotelian mechanics), and a four-domain counterfactual world (Decay World). Across Claude Opus 4.7, GPT-5.5, and Gemini 3.1 Pro, the three worlds yield composite PASS rates are 6/15, 6/15, and 0/15 respectively (content $\land$ structural for $F=mv$ and Aristotelian, content axis only for Decay World where the structural axis is out of scope). The most pointed empirical pattern is a qualitative-versus-quantitative asymmetry: in Decay World, models almost never predict the wrong direction of change, but frequently compute the wrong ratio by slipping back to standard-physics relations. The protocol also surfaces two methodology findings: LLM-judge reliability does not transfer across frameworks, and Stage 4 self-review is weak in every framework, with the model's own review wrongly reporting no earlier error in at least two-thirds of the trials that actually contained one. We release the full prompts, responses, verdicts, and audit records.

With the growing popularity of Large Reasoning Models and their results in solving mathematical problems, it becomes crucial to measure their capabilities. We introduce a pipeline for both automatic and interactive verification as a more accurate alternative to only checking the answer which is currently the most popular approach for benchmarks. The pipeline can also be used as a generator of correct solutions both in formal and informal languages. 3 AI agents, which can be chosen for the benchmark accordingly, are included in the structure. The key idea is the use of prompts to obtain the solution in the specific form which allows for easier verification using proof assistants and possible use of small models ($\le 8B$). Experiments on several datasets suggest low probability of False Positives. The open-source implementation with instructions on setting up a server is available at https://github.com/LogicEnj/lean4_verification_pipeline.