Scaling the Scattering Transform: Deep Hybrid Networks

We use the scattering network as a generic and fixed initialization of the first layers of a supervised hybrid deep network. We show that early layers do not necessarily need to be learned, providing the best results to-date with pre-defined representations while being competitive with Deep CNNs. Using a shallow cascade of 1 × 1 convolutions, which encodes scattering coefficients that correspond to spatial windows of very small sizes, permits to obtain AlexNet accuracy on the imagenet ILSVRC2012. We demonstrate that this local encoding explicitly learns invariance w.r.t. rotations. Combining scattering networks with a modern ResNet, we achieve a single-crop top 5 error of 11.4% on imagenet ILSVRC2012, comparable to the Resnet-18 architecture, while utilizing only 10 layers. We also find that hybrid architectures can yield excellent performance in the small sample regime, exceeding their end-to-end counterparts, through their ability to incorporate geometrical priors. We demonstrate this on subsets of the CIFAR-10 dataset and on the STL-10 dataset.