Deep Differential System Stability - Learning advanced computations from examples (Paper Explained)

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: https://ift.tt/3foFILU My Video on Deep Learning for Symbolic Mathematics: https://youtu.be/p3sAF3gVMMA 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 Links: YouTube: https://www.youtube.com/c/yannickilcher Twitter: https://twitter.com/ykilcher Discord: https://ift.tt/3dJpBrR BitChute: https://ift.tt/38iX6OV Minds: https://ift.tt/37igBpB