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

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Switzerland Yannic Kilcher
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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://arxiv.org/abs/2006.06462
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

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Tags:
deep learning
machine learning
arxiv
explained
neural networks
ai
artificial intelligence
paper
math
derivative
ode
pde
solution
integral
gradient
jacobian
mathematics
language model
transformer
symbolic
numeric
stability
equilibrium
attention
tokens
dataset
abstract