Matrix shapes from special lagrangian geometry link to deep learning models
Special Lagrangian cones in Deep Learning
Machine Learning
Summary
The paper finds a new way to describe special shapes called special Lagrangian manifolds using matrices. These shapes are connected to a mathematical space that shows up in deep learning, the technology behind many AI systems. By proving these shapes fit perfectly into this space, the authors add to the understanding of the geometry underlying deep learning. This could help explain how deep learning works from a new angle.
What this means in practice
- •For machine learning engineers: Develop geometric interpretations of neural network training spaces to inform optimization strategies.
- •For computational geometers: Use special Lagrangian manifold structures to study and classify complex geometric data models.
A theory result. No direct application yet.
Authors
Tejas Kotwal, Govind Menon
Abstract
We introduce a matrix generalization of the cone of Harvey and Lawson and prove that it is an exact special Lagrangian manifold. We further show that it belongs to a family of exact special Lagrangian manifolds that foliate the balanced manifold arising in deep learning.