Jesus Angulo Lopez

We are interested in this talk on a nonlinear theory of equivariant convolutional neural networks (CNNs) on homogenous spaces under the action of a group. Many groups of image transforms fit this framework. The purpose of our work to have a universal equivariant representation of nonlinear maps between image features which is based on mathematical morphology operators for groups. In particular, we will combine some powerful results of universal representation of nonlinear operators with the equivariance properties of morphological group operators. The approach considered here is significantly different from other theories of representation of equivariant CNNs. On the one hand, it is founded on results from lattice theory and other hand, it deals with the universal representation of nonlinear maps, which can involve in a unified framework (linear) convolutions, activation functions and other nonlinear layers.