Existing equivariant neural networks require prior knowledge of the symmetry group and discretization for continuous groups. We propose to work with Lie algebras (infinitesimal generators) instead of Lie groups. Our model, the Lie algebra convolutional network (L-conv) can automatically discover symmetries and does not require discretization of the group. We show that L-conv can serve as a building block to construct any group equivariant feedforward architecture. Both CNNs and Graph Convolutional Networks can be expressed as L-conv with appropriate groups. We discover direct connections between L-conv and physics: (1) group invariant loss generalizes field theory (2) Euler-Lagrange equation measures the robustness, and (3) equivariance leads to conservation laws and Noether current.

Neural Information Processing Systems http://nips.cc/

Wepresentgroupequivariant capsule networks,aframeworktointroduce guaranteed equivariance and invariance properties to the capsule network idea.

In this paper we propose a generalization of this work that generally exhibits improved performace, but from an implementation point of view is actually simpler.

However, their performance in terms of test likelihood and quality of generated samples has been surpassed by autoregressive models without stochastic units. Furthermore, flow-based models have recently been shown to be an attractive alternative that scales well to high-dimensional data.

These mechanisms typically retrieve items in a single step and are fixed after training.

Neural Information Processing Systems http://nips.cc/