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

arXiv: https://arxiv.org/abs/2603.11164 · HTML: https://mlsanity.com/paper/2603.11164/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 0 of its 9 references that are in the map.
- First posted on arXiv 11 Mar 2026.

## Built on by (most cited first, 4 of 4)

- [Learning to Unscramble Feynman Loop Integrals with SAILIR](https://mlsanity.com/paper/2604.05034/) (2026)
- [When Does Critique Improve AI-Assisted Theoretical Physics? SCALAR: Structured Critic--Actor Loop for Agentic Reasoning](https://mlsanity.com/paper/2605.06772/) (2026)
- [Efficient AI-Inspired Reduction of Feynman Integrals via Tube Seeding](https://mlsanity.com/paper/2606.10698/) (2026)
- [Machine learning for the LHC physics program: a 2025-2026 stocktake](https://mlsanity.com/paper/2609.32874/) (2026)

## Abstract (arXiv)

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.