Determining the stability properties of differential systems is a challenging task that involves very advanced symbolic and numeric mathematical manipulations. This paper shows that given enough training data, a simple language model with no underlying knowledge of mathematics can learn to solve these problems with remarkably high accuracy.
OUTLINE:
0:00 – Intro & Overview
3:15 – Differential System Tasks
11:30 – Datasets & Models
15:15 – Experiments
21:00 – Discussion & My Comments
Paper:
My Video on Deep Learning for Symbolic Mathematics:
Abstract:
Can advanced mathematical computations be learned from examples? Using transformers over large generated datasets, we train models to learn properties of differential systems, such as local stability, behavior at infinity and controllability. We achieve near perfect estimates of qualitative characteristics of the systems, and good approximations of numerical quantities, demonstrating that neural networks can learn advanced theorems and complex computations without built-in mathematical knowledge.
Authors: François Charton, Amaury Hayat, Guillaume Lample
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