Symmetry-invariant optimization in deep networks
This addresses optimization inefficiencies in deep learning for practitioners, but it is incremental as it builds on known symmetry issues with specific updates.
The paper tackled the problem of symmetry in deep network weight spaces adversely affecting Euclidean gradient-based SGD, proposing two symmetry-invariant gradient updates that improved test performance on MNIST without sacrificing computational efficiency and were also applied to an image segmentation problem.
Recent works have highlighted scale invariance or symmetry that is present in the weight space of a typical deep network and the adverse effect that it has on the Euclidean gradient based stochastic gradient descent optimization. In this work, we show that these and other commonly used deep networks, such as those which use a max-pooling and sub-sampling layer, possess more complex forms of symmetry arising from scaling based reparameterization of the network weights. We then propose two symmetry-invariant gradient based weight updates for stochastic gradient descent based learning. Our empirical evidence based on the MNIST dataset shows that these updates improve the test performance without sacrificing the computational efficiency of the weight updates. We also show the results of training with one of the proposed weight updates on an image segmentation problem.