Learning advanced mathematical computations from examples

2020/06/11 by François Charton, Charton, François, Amaury Hayat +3
Computer Science · Physics and Astronomy · #Computation and Language (cs.CL) #Computational Physics and Python Applications #FOS: Computer and information sciences #Machine Learning (cs.LG) #Model Reduction and Neural Networks #Neural Networks and Applications

paper · pdf · doi:10.48550/arxiv.2006.06462

openalex publication_date 2020/06/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Using transformers over large generated datasets, we train models to learn mathematical properties of differential systems, such as local stability, behavior at infinity and controllability. We achieve near perfect prediction of qualitative characteristics, and good approximations of numerical features of the system. This demonstrates that neural networks can learn to perform complex computations, grounded in advanced theory, from examples, without built-in mathematical knowledge.

Citations

• Learning to Execute
• Long Short-Term Memory
• Sequence to Sequence Learning with Neural Networks
• Neural-network methods for boundary value problems with irregular boundaries
• Learning a SAT Solver from Single-Bit Supervision

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