Deep Neural Networks with Efficient Guaranteed Invariances
This work addresses sample efficiency for deep learning practitioners by incorporating multiple invariances into networks, though it is incremental as it builds on existing invariant integration methods.
The paper tackles the problem of improving deep neural network performance and sample complexity by guaranteeing invariances to symmetry transformations like rotations, flips, and scales, rather than learning them from data, and demonstrates successful experiments on datasets including Scaled-MNIST, SVHN, CIFAR-10, and STL-10.
We address the problem of improving the performance and in particular the sample complexity of deep neural networks by enforcing and guaranteeing invariances to symmetry transformations rather than learning them from data. Group-equivariant convolutions are a popular approach to obtain equivariant representations. The desired corresponding invariance is then imposed using pooling operations. For rotations, it has been shown that using invariant integration instead of pooling further improves the sample complexity. In this contribution, we first expand invariant integration beyond rotations to flips and scale transformations. We then address the problem of incorporating multiple desired invariances into a single network. For this purpose, we propose a multi-stream architecture, where each stream is invariant to a different transformation such that the network can simultaneously benefit from multiple invariances. We demonstrate our approach with successful experiments on Scaled-MNIST, SVHN, CIFAR-10 and STL-10.