DualityCert: Verifier-Gated Language-Model Repair of Broken Duality Claims in Quantum Field Theory

Dualities play an important role in establishing both microscopic and emergent phenomena in a wide range of physical systems. In practice, though, it can often be computationally challenging to establish when two systems are dual, even when all of the "rules of the game" are well-known. Said differently, when confronted with two systems, how can one efficiently establish that they are in fact dual? In this paper we use machine learning methods to address this question for Seiberg dualities of supersymmetric quiver gauge theories. Mathematically, this involves establishing mutations of quivers, which is in turn a variation on the theme of "learning to unknot". On the one hand, this leads us to a practical tool for establishing the computational complexity of different dualities. On the other hand, it also allows us to study how different network architectures learn how to trace Seiberg dualities. We find that for quivers with a modest number of quiver nodes (of order $10$), different network architectures consisting of transformers and multi-layer perceptrons tend to outperform deterministic algorithms. Supplementing the network by well-established pathfinder algorithms (essentially "Google Maps for quivers") leads to an additional improvement in the efficiency and accuracy of the search strategy. We anticipate that this class of questions can serve as a useful benchmark for frontier AI models applied to theoretical physics.

Verifier reliability is not portable across tasks. A verifier-guided self-DPO pipeline with genuine held-out gains on MathVista (+9.6 points on self-training data, +8.0 held out) can be harmful on MMMU. The failure is invisible from the target-task self-training signal: over six learner-verifier configurations, MMMU self-training performance still improves by +3.52 points while held-out performance drops by 1.42 points. We call this silent negative transfer: a verifier validated as useful before can still show signatures of successful self-training after its induced update stops transferring to unseen data. Downstream failure alone cannot diagnose this: poor generalization may mean the verifier induces a wrong learning direction, or that the correct direction itself does not generalize beyond the self-training distribution. We separate these effects via gradient fidelity F, the alignment between verifier-induced and correct training directions, and gradient transferability T, the alignment between correct and held-out directions, giving a conservative Safe-Transfer Margin: positive first-order held-out alignment is certified when arccos(F) + arccos(T) < pi/2. We then introduce Asymmetric Acceptance Gating (AAG), a precision-first filter selecting preference pairs by the verifier's absolute confidence in the response receiving the positive update. On MMMU, AAG raises fidelity from 0.29 to 0.42. In a same-cell analysis, the correct direction stays positively aligned with the held-out direction (T = 0.31), yet raw verification rotates the induced update to negative held-out alignment (-0.13); AAG restores positive alignment (+0.22). Across all six MMMU configurations, AAG beats raw verifier-guided training. Verifier reliability thus means not that it worked before, but that it induces the right update on the task at hand and that this update stays useful beyond the data that generated it.

Large language models confabulate chemical objects (molecular formulas, space groups, formation energies) in fluent reasoning traces, concentrated on long-tail entities where confidence is least trustworthy. Deterministic, database-grounded verification can catch and repair such errors without the coverage cost of blanket retrieval; the binding constraint, we find, is detection, not repair. Our tiered verifier extracts each checkable claim, checks it against authoritative databases and physics, and feeds the reference into a gated correction loop. Across four models and 528 condition-pinned prompts, gated correction cuts committed-formula error from 22% to 4% at $3.2\times$ fewer retrievals than blanket augmentation, beating a conversational oracle. Repair succeeds wherever a flag fires (80--97%); the bottleneck is in-loop detection recall. Grounding improves the final answer only when the verifier's scope reaches the deliverable (83% to 90%), and the lift appears only where extractable long-tail error exists: absent on near-ceiling physical constants, large on isotope half-lives (11% to 0%).