Learning advanced mathematical computations from examples

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.

Authors

• François Charton
• Amaury Hayat
• Guillaume Lample

Keywords

• differential equations
• computation
• transformers
• deep learning