Complexity and dynamics of partially symmetric random neural networks

Area of Science:

• Computational neuroscience
• Network science
• Dynamical systems theory

Background:

• Neural circuits display structured connectivity, notably an overrepresentation of reciprocal connections.
• Understanding how connectivity symmetry influences neural dynamics is crucial but incomplete.

Purpose of the Study:

• To investigate how correlations in reciprocal connections of random, recurrent neural networks affect phase-space complexity.
• To define phase-space complexity by the rate of fixed-point proliferation during the transition to chaos.

Main Methods:

• Analysis of random, recurrent neural networks with varying degrees of reciprocal connection symmetry/anti-symmetry.
• Quantification of phase-space complexity via fixed-point proliferation rates.
• Assessment of other dynamical measures including dimensionality, Lyapunov exponents, and transient path length.

Main Results:

• Partial anti-symmetry in reciprocal connections significantly amplifies phase-space complexity.
• Partial symmetry in reciprocal connections strongly suppresses phase-space complexity.
• Observed trends in complexity correlate with changes in dimensionality, Lyapunov exponents, and transient path length.

Conclusions:

• Fixed-point structure is a key determinant of neural network dynamics.
• Positive reciprocal correlations favor low-dimensional, slow neural activity.
• Negative reciprocal correlations promote high-dimensional, rapid chaotic neural activity, offering testable predictions.