Neural Network Integral Representations

We present neural network integral representations as a generalization of shallow artificial neural networks. For the ReLU activation function, we derive an explicit reconstruction formula on the unit sphere under finite $L_1$ norm assumption on the outer weights.  We further extend our theory to deep networks by introducing  ResNet type integral representations. Presented results are part of joint work with Anton Dereventsov and Clayton Webster.
 
Speaker’s Bio: Armenak received his PhD in Mathematics from Vanderbilt University. He has been employed as a postdoctoral research associate with the Computational and Applied Mathematics group at the Oak Ridge National Laboratory since August 2017. His main fields of research are Applied Harmonic Analysis, Functional Analysis and Machine Learning.