  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.
