# Improving the generalization via coupled tensor norm regularization

## TL;DR

This paper introduces a coupled tensor norm regularization technique that promotes low-dimensional manifolds in data and model features, reducing overfitting and improving generalization in machine learning models.

## Contribution

The paper proposes a novel coupled tensor norm regularization method with theoretical analysis and demonstrates its effectiveness through numerical experiments.

## Key findings

- Regularization promotes low-dimensional data manifolds
- Convex and differentiable for logistic regression
- Nonconvex and nonsmooth for deep neural networks

## Abstract

In this paper, we propose a coupled tensor norm regularization that could enable the model output feature and the data input to lie in a low-dimensional manifold, which helps us to reduce overfitting. We show this regularization term is convex, differentiable, and gradient Lipschitz continuous for logistic regression, while nonconvex and nonsmooth for deep neural networks. We further analyze the convergence of the first-order method for solving this model. The numerical experiments demonstrate that our method is efficient.