Non-Hermitian quasilocalization and ring attractor neural networks

Area of Science:

• Computational Neuroscience
• Condensed Matter Physics
• Network Science

Background:

• Anderson localization describes spatial self-trapping of waves in disordered systems, crucial in physics but underexplored in neuroscience.
• Neural networks, particularly those modeling head direction cells, often feature asymmetric and dense synaptic connectivity, posing challenges for localization theories.

Purpose of the Study:

• To investigate the role of Anderson localization principles in neural networks with spatially structured disorder.
• To connect Anderson localization theory to the local excitation and global inhibition (LEGI) ring attractor model used in neuroscience.

Main Methods:

• Studied a non-Hermitian tight-binding model with disorder.
• Analyzed eigenvector properties of LEGI ring attractor networks with nearest-neighbor disorder.
• Investigated the impact of quasilocalized eigenvectors on neural dynamics.

Main Results:

• Principal eigenvectors in LEGI networks with structured disorder exhibit "quasilocalization," even with dense connections.
• These quasilocalized eigenvectors dominate early neural dynamics.
• The location of these eigenvectors predicts the initial position of neural activity "bumps."

Conclusions:

• Spatially structured disorder can induce Anderson localization-like phenomena (quasilocalization) in dense neural networks.
• Quasilocalization of eigenvectors is functionally relevant for neural computation, such as representing spatial information.
• This work bridges Anderson localization theory and neural network dynamics, opening new research avenues.