The HSIC Bottleneck: Deep Learning without Back-Propagation

We introduce the HSIC (Hilbert-Schmidt independence criterion) bottleneck for training deep neural networks. The HSIC bottleneck is an alternative to the conventional cross-entropy loss and backpropagation that has a number of distinct advantages. It mitigates exploding and vanishing gradients, resulting in the ability to learn very deep networks without skip connections. There is no requirement for symmetric feedback or update locking. We find that the HSIC bottleneck provides performance on MNIST/FashionMNIST/CIFAR10 classification comparable to backpropagation with a cross-entropy target, even when the system is not encouraged to make the output resemble the classification labels. Appending a single layer trained with SGD (without backpropagation) to reformat the information further improves performance.