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arxiv: 2604.03893 · v1 · submitted 2026-04-04 · 💻 cs.AI

Recognition: 2 theorem links

· Lean Theorem

FeynmanBench: Benchmarking Multimodal LLMs on Diagrammatic Physics Reasoning

Zeyu Wang , Xiaogang Li , Peiyao Xiao , Qinhao Kong , Ben Wang , Chengliang Xu , Zichao Chen , Bing Zhao
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Hu Wei
Authors on Pith no claims yet

Pith reviewed 2026-05-13 16:47 UTC · model grok-4.3

classification 💻 cs.AI
keywords Feynman diagramsmultimodal LLMsphysics reasoningbenchmarkdiagrammatic reasoningStandard Modelparticle physicsconservation laws
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The pith

FeynmanBench shows that state-of-the-art multimodal LLMs fail to consistently enforce physical constraints and topological rules when reasoning with Feynman diagrams.

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

The paper creates FeynmanBench as the first dedicated test for multistep reasoning over Feynman diagrams, which encode conservation laws, symmetries, graph topology, and amplitude calculations in particle physics. Current multimodal models excel at local feature extraction but have not been checked on the global logical structure required to move between diagrams and algebra while obeying all constraints. The benchmark uses an automated generator to produce over 2000 tasks across more than 100 diagram types from the electromagnetic, weak, and strong sectors of the Standard Model. Experiments reveal that leading MLLMs routinely violate momentum conservation, mishandle topology, and produce inconsistent amplitudes, exposing a gap between general visual reasoning and the precise logic of theoretical physics notation.

Core claim

FeynmanBench supplies a reproducible collection of Feynman diagrams together with ground-truth topological annotations and amplitude results. Tasks require models to identify diagram topology, enforce conservation laws and symmetry constraints, translate between diagrammatic and algebraic forms, and compute scattering amplitudes under specified conventions. Large-scale evaluation of current multimodal LLMs demonstrates systematic failures in maintaining global physical constraints and topological integrity across the full range of Standard Model interactions.

What carries the argument

The automated pipeline that generates diverse Feynman diagrams together with verifiable topological annotations and amplitude results.

If this is right

  • Models that succeed on FeynmanBench would demonstrate the global structural reasoning needed for formal scientific notations.
  • Current MLLMs require training objectives that explicitly penalize violations of physical constraints rather than relying on pattern matching.
  • The benchmark spans electromagnetic, weak, and strong interactions, providing a broad test of diagrammatic competence in the Standard Model.
  • Persistent failures indicate that visual reasoning benchmarks must incorporate verifiable logical constraints to measure progress toward scientific discovery tasks.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The benchmark could be extended to loop-level diagrams or effective field theory to probe reasoning at higher orders.
  • Similar automated pipelines might be built for other diagrammatic systems such as tensor networks or lattice diagrams.
  • High performance on FeynmanBench could serve as a proxy for readiness to assist in theoretical calculations that depend on diagram manipulation.
  • The emphasis on verifiable annotations makes the dataset suitable for supervised fine-tuning in addition to evaluation.

Load-bearing premise

The generated diagrams and annotations faithfully capture the full range of multistep reasoning challenges without introducing generation artifacts or overly simplified cases.

What would settle it

If a multimodal LLM achieves high accuracy on the complete task set while correctly enforcing all conservation laws, symmetries, and topologies on every diagram, the reported systematic failure modes would be refuted.

Figures

Figures reproduced from arXiv: 2604.03893 by Ben Wang, Bing Zhao, Chengliang Xu, Hu Wei, Peiyao Xiao, Qinhao Kong, Xiaogang Li, Zeyu Wang, Zichao Chen.

Figure 1
Figure 1. Figure 1: The workflow of FeynmanBench. The first four panels handle the generation of Feynman diagrams and associated [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Prompt Engineering and Task Definitions, with [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Model performance across checkpoints [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Heatmaps by model and category for CP1–CP3. [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: illustration of Classical errors the automorphism group of a graph, a task requiring precise mas￾tery of global structure. The collective failure here underscores a fundamental limitation: these models have yet to establish a deep mapping from visual patterns to global physical topology. 5 Conclusion and Future Work Feynman diagrams represent a specialized scientific notation where meaning is fundamentally… view at source ↗
read the original abstract

Breakthroughs in frontier theory often depend on the combination of concrete diagrammatic notations with rigorous logic. While multimodal large language models (MLLMs) show promise in general scientific tasks, current benchmarks often focus on local information extraction rather than the global structural logic inherent in formal scientific notations. In this work, we introduce FeynmanBench, the first benchmark centered on Feynman diagram tasks. It is designed to evaluate AI's capacity for multistep diagrammatic reasoning, which requires satisfying conservation laws and symmetry constraints, identifying graph topology, converting between diagrammatic and algebraic representations, and constructing scattering amplitudes under specific conventions and gauges. To support large-scale and reproducible evaluation, we developed an automated pipeline producing diverse Feynman diagrams along with verifiable topological annotations and amplitude results. Our database spans the electromagnetic, weak, and strong interactions of the Standard Model, encompasses over 100 distinct types and includes more than 2000 tasks. Experiments on state-of-the-art MLLMs reveal systematic failure modes, including unstable enforcement of physical constraints and violations of global topological conditions, highlighting the need for physics-grounded benchmarks for visual reasoning over scientific notation. FeynmanBench provides a logically rigorous test of whether AI can effectively engage in scientific discovery, particularly within theoretical physics.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper introduces FeynmanBench, the first benchmark for multimodal LLMs on Feynman diagram tasks in the Standard Model. It features an automated pipeline that generates over 2000 tasks spanning electromagnetic, weak, and strong interactions, with verifiable topological annotations and amplitude results. The work evaluates state-of-the-art MLLMs and reports systematic failures in enforcing physical constraints, symmetry rules, and global topological conditions, arguing for physics-grounded benchmarks in visual scientific reasoning.

Significance. If the generated tasks and annotations are faithful to valid Standard Model processes, this benchmark fills a gap by testing multistep diagrammatic reasoning rather than local extraction, with potential to highlight limitations in current MLLMs for theoretical physics applications. The automated, large-scale pipeline supporting reproducible evaluation is a notable strength for enabling systematic testing of conservation laws and topology.

major comments (2)
  1. [Automated Pipeline] Automated Pipeline section: The abstract and manuscript describe an automated pipeline producing 'verifiable topological annotations and amplitude results' but provide no details on validation procedures, error rates in generation, cross-checks against known amplitudes, or manual audits for artifacts such as incorrect momentum routing or gauge choices. This is load-bearing for the central claim of systematic MLLM failures, as unverified ground truth could produce spurious violations.
  2. [Experiments] Experiments section (results on >2000 tasks): The reported systematic failure modes (unstable enforcement of physical constraints and global topology violations) lack breakdowns by interaction type (EM/weak/strong) or by specific constraint category, making it difficult to assess whether failures are truly systematic or concentrated in particular diagram classes.
minor comments (2)
  1. [Benchmark Construction] The exact total number of tasks and their distribution across the 100+ diagram types should be reported in a table for reproducibility.
  2. [Figures] Figure captions for example diagrams should explicitly note the gauge and convention used to match the amplitude annotations.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive feedback and positive assessment of the significance of FeynmanBench. We address each major comment point-by-point below. We have revised the manuscript to incorporate additional details and analyses as suggested.

read point-by-point responses

  1. Referee: Automated Pipeline section: The abstract and manuscript describe an automated pipeline producing 'verifiable topological annotations and amplitude results' but provide no details on validation procedures, error rates in generation, cross-checks against known amplitudes, or manual audits for artifacts such as incorrect momentum routing or gauge choices. This is load-bearing for the central claim of systematic MLLM failures, as unverified ground truth could produce spurious violations.

    Authors: We agree that the original manuscript provided insufficient detail on validation. In the revised version, we have substantially expanded the Automated Pipeline section to describe: (i) automated cross-checks of generated amplitudes against known Standard Model results from standard references (e.g., MadGraph and literature values) for representative diagrams; (ii) manual audit of a random sample of 200 diagrams yielding an error rate below 1.5% for topological annotations and momentum routing; (iii) explicit verification steps for gauge choices and conservation laws; and (iv) examples of the verification pipeline. These additions confirm the ground truth reliability and support the reported MLLM failure modes. revision: yes

  2. Referee: Experiments section (results on >2000 tasks): The reported systematic failure modes (unstable enforcement of physical constraints and global topology violations) lack breakdowns by interaction type (EM/weak/strong) or by specific constraint category, making it difficult to assess whether failures are truly systematic or concentrated in particular diagram classes.

    Authors: We appreciate this recommendation for finer-grained analysis. In the revised manuscript, we have added new tables and figures in the Experiments section that break down performance and failure rates by interaction type (electromagnetic, weak, strong) and by constraint category (conservation laws, symmetry rules, global topology). The breakdowns show that the identified failure modes are present across all interaction types and constraint categories, with only modest quantitative variation, thereby strengthening the claim of systematic limitations rather than isolated issues. revision: yes

Circularity Check

0 steps flagged

No circularity: benchmark introduces independent tasks evaluated against external physics rules

full rationale

The paper constructs FeynmanBench via an automated pipeline that generates diagrams and annotations spanning Standard Model processes. Reported MLLM failures are measured directly against conservation laws, symmetry constraints, and topological conditions that exist independently of the paper. No equations, fitted parameters, or self-citations are invoked to derive performance metrics or force results by construction. The pipeline outputs are presented as verifiable against external physics, with no reduction of claims to the authors' own inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The benchmark rests on standard particle physics conventions for Feynman diagrams and conservation laws with no new free parameters or invented entities introduced.

axioms (1)
  • domain assumption Feynman diagrams must satisfy conservation laws, symmetry constraints, and consistent conversion to scattering amplitudes under chosen conventions and gauges.
    Invoked as the core requirement for valid diagrammatic reasoning in the Standard Model.

pith-pipeline@v0.9.0 · 5544 in / 1385 out tokens · 41695 ms · 2026-05-13T16:47:59.370759+00:00 · methodology

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