Backpropagation-Friendly Eigendecomposition
This addresses a practical bottleneck for researchers and practitioners using eigendecomposition in deep learning, though it appears incremental as it improves stability rather than introducing a new paradigm.
The paper tackles the problem of numerically unstable backpropagation through eigendecomposition in deep networks, introducing a stable differentiable approach that handles large matrices without splitting. It demonstrates better robustness over standard methods for ZCA whitening and PCA denoising, with concrete improvements in stability metrics.
Eigendecomposition (ED) is widely used in deep networks. However, the backpropagation of its results tends to be numerically unstable, whether using ED directly or approximating it with the Power Iteration method, particularly when dealing with large matrices. While this can be mitigated by partitioning the data in small and arbitrary groups, doing so has no theoretical basis and makes its impossible to exploit the power of ED to the full. In this paper, we introduce a numerically stable and differentiable approach to leveraging eigenvectors in deep networks. It can handle large matrices without requiring to split them. We demonstrate the better robustness of our approach over standard ED and PI for ZCA whitening, an alternative to batch normalization, and for PCA denoising, which we introduce as a new normalization strategy for deep networks, aiming to further denoise the network's features.