Understanding symmetries in deep networks
This addresses optimization challenges for deep learning practitioners, but it is incremental as it builds on prior work on symmetries and batch normalization.
The paper tackled the problem of complex symmetries in deep network weight spaces that hinder optimization, and proposed constraining filters to a unit-norm manifold, resulting in improved test performance on MNIST without sacrificing computational efficiency.
Recent works have highlighted scale invariance or symmetry present in the weight space of a typical deep network and the adverse effect it has on the Euclidean gradient based stochastic gradient descent optimization. In this work, we show that a commonly used deep network, which uses convolution, batch normalization, reLU, max-pooling, and sub-sampling pipeline, possess more complex forms of symmetry arising from scaling-based reparameterization of the network weights. We propose to tackle the issue of the weight space symmetry by constraining the filters to lie on the unit-norm manifold. Consequently, training the network boils down to using stochastic gradient descent updates on the unit-norm manifold. Our empirical evidence based on the MNIST dataset shows that the proposed updates improve the test performance beyond what is achieved with batch normalization and without sacrificing the computational efficiency of the weight updates.