Complex Recurrent Spectral Network
Lorenzo Chicchi Lorenzo Giambagli Lorenzo Buffoni Raffaele Marino Duccio Fanelli
This paper presents a novel approach to advancing artificial intelligence
(AI) through the development of the Complex Recurrent Spectral Network
($\mathbb{C}$-RSN), an innovative variant of the Recurrent Spectral Network
(RSN) model. The $\mathbb{C}$-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 $\mathbb{C}$-RSN model introduces
localized non-linearity, complex fixed eigenvalues, and a distinct separation
of memory and input processing functionalities. These features collectively
enable the $\mathbb{C}$-RSN evolving towards a dynamic, oscillating final state
that more closely mirrors biological cognition. Central to this work is the
exploration of how the $\mathbb{C}$-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).