(Almost) Smooth Sailing: Towards Numerical Stability of Neural Networks Through Differentiable Regularization of the Condition Number
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.
Cite
Text
Nenov et al. "(Almost) Smooth Sailing: Towards Numerical Stability of Neural Networks Through Differentiable Regularization of the Condition Number." ICML 2024 Workshops: Differentiable_Almost_Everything, 2024.Markdown
[Nenov et al. "(Almost) Smooth Sailing: Towards Numerical Stability of Neural Networks Through Differentiable Regularization of the Condition Number." ICML 2024 Workshops: Differentiable_Almost_Everything, 2024.](https://mlanthology.org/icmlw/2024/nenov2024icmlw-almost/)BibTeX
@inproceedings{nenov2024icmlw-almost,
title = {{(Almost) Smooth Sailing: Towards Numerical Stability of Neural Networks Through Differentiable Regularization of the Condition Number}},
author = {Nenov, Rossen and Haider, Daniel and Balazs, Peter},
booktitle = {ICML 2024 Workshops: Differentiable_Almost_Everything},
year = {2024},
url = {https://mlanthology.org/icmlw/2024/nenov2024icmlw-almost/}
}