A self-supervised transformer learns to unscramble Feynman integrals for online IBP reduction, delivering bounded memory use on complex two-loop topologies while matching Kira's speed on the hardest cases tested.
Learning to Unscramble: Simplifying Symbolic Expressions via Self-Supervised Oracle Trajectories
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abstract
We present a new self-supervised machine learning approach for symbolic simplification of complex mathematical expressions. Training data is generated by scrambling simple expressions and recording the inverse operations, creating oracle trajectories that provide both goal states and explicit paths to reach them. A permutation-equivariant, transformer-based policy network is then trained on this data step-wise to predict the oracle action given the input expression. We demonstrate this approach on two problems in high-energy physics: dilogarithm reduction and spinor-helicity scattering amplitude simplification. In both cases, our trained policy network achieves near perfect solve rates across a wide range of difficulty levels, substantially outperforming prior approaches based on reinforcement learning and end-to-end regression. When combined with contrastive grouping and beam search, our model achieves a 100\% full simplification rate on a representative selection of 5-point gluon tree-level amplitudes in Yang-Mills theory, including expressions with over 200 initial terms.
years
2026 3verdicts
UNVERDICTED 3representative citing papers
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Learning to Unscramble Feynman Loop Integrals with SAILIR
A self-supervised transformer learns to unscramble Feynman integrals for online IBP reduction, delivering bounded memory use on complex two-loop topologies while matching Kira's speed on the hardest cases tested.
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When Does Critique Improve AI-Assisted Theoretical Physics? SCALAR: Structured Critic--Actor Loop for Agentic Reasoning
Structured critic-actor loops improve AI performance on theoretical physics reasoning tasks, with benefits strongest in asymmetric model pairings using constructive feedback.
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