# Constraint-Based Regularization of Neural Networks

arXiv: https://arxiv.org/abs/2006.10114 · HTML: https://mlsanity.com/paper/2006.10114/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Jun 2020.

## Built on by (most cited first, 3 of 3)

- [A Unifying and Canonical Description of Measure-Preserving Diffusions](https://mlsanity.com/paper/2105.02845/) (2021)
- [Constrained Empirical Risk Minimization: Theory and Practice](https://mlsanity.com/paper/2302.04729/) (2023)
- [Informative regularization for a multi-layer perceptron RR Lyrae classifier under data shift](https://mlsanity.com/paper/2303.06544/) (2023)

## Abstract (arXiv)

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.