[2604.05034] Learning to Unscramble Feynman Loop Integrals with SAILIR

High Energy Physics - Phenomenology arXiv:2604.05034 (hep-ph) [Submitted on 6 Apr 2026] Title:Learning to Unscramble Feynman Loop Integrals with SAILIR Authors:David Shih View a PDF of the paper titled Learning to Unscramble Feynman Loop Integrals with SAILIR, by David Shih View PDF HTML (experimental) Abstract:Integration-by-parts (IBP) reduction of Feynman integrals to master integrals is a key computational bottleneck in precision calculations in high-energy physics. Traditional approaches based on the Laporta algorithm require solving large systems of equations, leading to memory consumption that grows rapidly with integral complexity. We present SAILIR (Self-supervised AI for Loop Integral Reduction), a new machine learning approach in which a transformer-based classifier guides the reduction of integrals one step at a time in a fully online fashion. The classifier is trained in an entirely self-supervised manner on synthetic data generated by a scramble/unscramble procedure: known reduction identities are applied in reverse to build expressions of increasing complexity, and the classifier learns to undo these steps. When combined with beam search and a highly parallelized, asynchronous, single-episode reduction strategy, SAILIR can reduce integrals of arbitrarily high weight with bounded memory. We benchmark SAILIR on the two-loop triangle-box topology, comparing against the state-of-the-art IBP reduction code Kira across 16 integrals of varying complexity. While SAI...