Different eigenvalue distributions encode the same temporal tasks in recurrent neural networks

TL;DR

This paper explores how different eigenvalue distributions in recurrent neural networks encode the same temporal tasks, revealing the link between spectral properties and network dynamics.

Contribution

It introduces a method to classify and interpret network dynamics based on eigenvalue spectra, highlighting the multiplicity of solutions for identical tasks.

Findings

Eigenvalue distributions correlate with specific task dynamics

Multiple spectral solutions can encode the same temporal task

Eigenvalue spectra provide insights into network behavior

Abstract

Different brain areas, such as the cortex and, more specifically, the prefrontal cortex, show great recurrence in their connections, even in early sensory areas. {Several approaches and methods based on trained networks have been proposed to model and describe these regions. It is essential to understand the dynamics behind the models because they are used to build different hypotheses about the functioning of brain areas and to explain experimental results. The main contribution here is the description of the dynamics through the classification and interpretation carried out with a set of numerical simulations. This study sheds light on the multiplicity of solutions obtained for the same tasks and shows the link between the spectra of linearized trained networks and the dynamics of the counterparts. The patterns in the distribution of the eigenvalues of the recurrent weight matrix were studied and properly related to the dynamics in each task.