Explore machine learning techniques for computing tensor rank in this insightful lecture from the Workshop on Tensors: Quantum Information, Complexity and Combinatorics. Delve into the challenges of tensor rank computation and discover a novel approach using deep reinforcement learning. Learn how the problem is reframed as a single-player game and how AI agents, similar to those used in Chess and Go, are adapted for this mathematical challenge. Examine the groundbreaking AlphaTensor agent and its application in finding new efficient matrix multiplication algorithms. Gain insights into the action space, training process, and architectural components of the system. Discuss the implications of this research, including performance improvements, limitations, and potential applications in algorithmic discovery. Understand the significance of this work in advancing fields such as mathematics, computer science, and signal processing.
Overview
Syllabus
Introduction
Machine learning has revolutionized many fields
Can we use machine learning to find new algorithms
What are the challenges of machine learning
Outline
Matrix multiplication tensor
Matrix multiplication algorithm
Improving asymptotic complexity
Math problem
Model
Challenges
Action Space
Alpha Zero
Training
Synthetic data
Tensor rank
architecture
attention
machine learning architecture
overall system
results
example
open source
bilinear algorithm
rewards function
performance improvements
limitations
applications
why
possible
inference TPU
Algorithmic Discovery
Taught by
Centre de recherches mathématiques - CRM
