Constraint-Based Regularization of Neural Networks

TL;DR

This paper introduces a constraint-based regularization method for deep neural networks that enhances training stability and generalization by controlling parameter space, addressing issues like vanishing gradients.

Contribution

It presents a novel approach integrating constraints into Langevin dynamics for neural network training, improving robustness and efficiency.

Findings

Constraints reduce vanishing/exploding gradients

Method improves training stability and generalization

Effective in image classification and NLP tasks

Abstract

We propose a method for efficiently incorporating constraints into a stochastic gradient Langevin framework for the training of deep neural networks. Constraints allow direct control of the parameter space of the model. Appropriately designed, they reduce the vanishing/exploding gradient problem, control weight magnitudes and stabilize deep neural networks and thus improve the robustness of training algorithms and the generalization capabilities of the trained neural network. We present examples of constrained training methods motivated by orthogonality preservation for weight matrices and explicit weight normalizations. We describe the methods in the overdamped formulation of Langevin dynamics and the underdamped form, in which momenta help to improve sampling efficiency. The methods are explored in test examples in image classification and natural language processing.