5 papers
Special Lagrangian cones in Deep Learning
Tejas Kotwal, Govind Menon
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 exac…
Entropic Regularization in the Deep Linear Network
Alan Chen, Tejas Kotwal, Govind Menon
We study regularization for the deep linear network (DLN) using the entropy formula introduced in arXiv:2509.09088. The equilibria and gradient flow of the free energy on the Riema…
Regularization Implies balancedness in the deep linear network
Kathryn Lindsey, Govind Menon
We use geometric invariant theory (GIT) to study the deep linear network (DLN). The Kempf-Ness theorem is used to establish that the regularizer is minimized on the balanced…
An entropy formula for the Deep Linear Network
Govind Menon, Tianmin Yu
We study the Riemannian geometry of the Deep Linear Network (DLN) as a foundation for a thermodynamic description of the learning process. The main tools are the use of group actio…
The geometry of the deep linear network
Govind Menon
This article provides an expository account of training dynamics in the Deep Linear Network (DLN) from the perspective of the geometric theory of dynamical systems. Rigorous result…