Landscapes of large scale problems with applications to machine learning

Abstract

Nonconvex optimization is at the heart of modern machine learning. We believe that studying the structure of these models and the repartition of critical values of associated nonconvex functions is fundamental to understand and reduce the computational complexity of learning tasks. Our proposal addresses these issues along three lines: ? Counting critical values using powerful algebraic geometry results. ? Identify equivalent critical points using symmetries and invariances of learning models. ? Algorithmic theory and design: obtain new complexity estimates and more efficient algorithms. Modern machine learning techniques such as deep learning, nonnegative matrix factorization or clustering constitute very natural applications with potentially high practical implications since they are used on a daily basis in industry and within the Air Force community.

Document Details

Document Type
DoD Grant Award
Publication Date
Jan 14, 2022
Source ID
FA95501917026

Entities

People

  • Jerome Bolte

Organizations

  • Air Force Office of Scientific Research
  • Toulouse School of Economics
  • United States Air Force

Tags

Fields of Study

  • Computer science

Readers

  • Artificial Intelligence
  • Economics
  • Operations Research

Technology Areas

  • AI & ML
  • AI & ML - DoD AI Strategy
  • AI & ML - Machine Learning Algorithms
  • AI & ML - Neural Networks