Learning to Unscramble: Simplifying Symbolic Expressions via Self-Supervised Oracle Trajectories

TL;DR

This paper introduces a self-supervised learning method using oracle trajectories and transformer networks to effectively simplify complex symbolic mathematical expressions, outperforming prior approaches.

Contribution

The authors develop a novel self-supervised approach with oracle trajectories and transformer policies for symbolic expression simplification, applied successfully to physics problems.

Findings

Near-perfect solve rates on high-energy physics problems.

Outperforms reinforcement learning and regression methods.

Achieves 100% full simplification on complex amplitudes.

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.