(Almost) Smooth Sailing: Towards Numerical Stability of Neural Networks Through Differentiable Regularization of the Condition Number
This addresses stability issues for practitioners using neural networks, though it is incremental as it builds on existing regularization methods.
The paper tackled the problem of numerical instability in neural networks by introducing a differentiable regularizer for the condition number of weight matrices, enabling gradient-based optimization and demonstrating improved performance in noisy classification and denoising tasks on MNIST images.
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.