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

Area of Science:

• Computational Neuroscience
• Systems Neuroscience
• Neuroscience

Background:

• Brain areas, including the cortex and prefrontal cortex, exhibit recurrent connectivity, even in sensory regions.
• Understanding the dynamics of computational models is crucial for forming hypotheses about brain function and interpreting experimental data.

Purpose of the Study:

• To describe and interpret the dynamics of trained neural network models through numerical simulations.
• To investigate the relationship between the spectral properties of linearized trained networks and their dynamic behavior.
• To explore the multiplicity of solutions that arise for the same computational tasks in neural models.

Main Methods:

• Utilized a set of numerical simulations to classify and interpret the dynamics of trained neural networks.
• Analyzed the spectra of linearized trained networks, focusing on the distribution of eigenvalues of the recurrent weight matrix.
• Correlated patterns in eigenvalue distributions with the observed dynamics across different tasks.

Main Results:

• Demonstrated a direct link between the spectra of linearized trained networks and the dynamics of their recurrent counterparts.
• Identified patterns in eigenvalue distributions that correspond to specific task dynamics.
• Showcased the existence of multiple distinct solutions for identical computational tasks within the studied models.

Conclusions:

• The spectral properties of linearized recurrent neural networks provide insights into their dynamic behavior.
• Eigenvalue distribution patterns serve as indicators of task-specific neural dynamics.
• Understanding these spectral-dynamics relationships is key to deciphering the functional principles of recurrent brain circuits.