Complex Recurrent Spectral Network

Abstract

This paper presents a novel approach to advancing artificial intelligence through the development of the Complex Recurrent Spectral Network (C-RSN), an innovative variant of the Recurrent Spectral Network (RSN) model. The C-RSN is designed to address a critical limitation in existing neural network models: their inability to emulate the complex processes of biological neural networks dynamically and accurately. By integrating key concepts from dynamical systems theory and leveraging principles from statistical mechanics, the C-RSN model introduces localized non-linearity, complex fixed eigenvalues, and a distinct separation of memory and input processing functionalities. These features collectively enable the C-RSN evolving towards a dynamic, oscillating final state that more closely mirrors biological cognition. Central to this work is the exploration of how the C-RSN manages to capture the rhythmic, oscillatory dynamics intrinsic to biological systems, thanks to its complex eigenvalue structure and the innovative segregation of its linear and non-linear components. The model’s ability to classify data through a time-dependent function, and the localization of information processing, is demonstrated with an empirical evaluation using the MNIST dataset. Remarkably, distinct items supplied as a sequential input yield patterns in time which bear the indirect imprint of the insertion order (and of the time of separation between contiguous insertions).

Lorenzo Giambagli

PostDoc Department of Physics, Freie Universität Berlin

My research interests include Spectral analysis of Deep Neural Network (DNN), Structura Pruning, Bayesian Inference in DNN, Simplicial Complexes Dynamics, Theoretical Neuroscience