Infinitely Deep Neural Models and Dynamical Systems

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In the past year efforts have been focused on the integration of signal processing and deep learning. In particular, I have been working on the development of a new framework for the analysis and synthesis of convolution-based layers, which I call Deep Signal Processing. Interpreting convolutions as linear dynamical systems of finite or infinite dimensions sheds light on deep neural networks from a different angle.In this context, we studied deep neural networks designed to harness the structure in frequency domain for efficient learning of long-range correlations in space or time. Other notable research projects undertaken in the past few months include investigating the role of learning in the automated discovery of self-similarity patterns within data. To this end, we design a novel class of implicit operators which represent data as the parameters of a self-referential, structured transformation.