(Almost) Smooth Sailing: Towards Numerical Stability of Neural Networks Through Differentiable Regularization of the Condition Number

Rossen Nenov, Daniel Haider, Peter Balazs

Keywords: Differentiable Regularization, Condition Number, Numerical Stability, Regularization Techniques

TL;DR: This paper introduces a novel, differentiable regularizer to enhance numerical stability in neural networks by promoting low condition numbers in weight matrices.

Abstract:

Maintaining numerical stability in machine learning models is crucial for their reliability and performance. One approach to maintain stability of a network layer is to integrate the condition number of the weight matrix as a regularizing term into the optimization algorithm. However, due to its discontinuous nature and lack of differentiability the condition number is not suitable for a gradient descent approach. This paper introduces a novel regularizer that is provably differentiable almost everywhere and promotes matrices with low condition numbers.
In particular, we derive a formula for the gradient of this regularizer which can be easily implemented and integrated into existing optimization algorithms. We show the advantages of this approach for noisy classification and denoising of MNIST images.

Submission Number: 36