Coherent chaos in a recurrent neural network with structured connectivity

Area of Science:

• Computational Neuroscience
• Network Dynamics
• Artificial Intelligence

Background:

• Recurrent neural networks (RNNs) with random connectivity exhibit chaotic fluctuations, useful for modeling cortical activity temporal variability.
• However, these networks lack spatial correlation and coherent fluctuations observed in the neocortex across scales.
• Existing models fail to capture the spatially structured, coherent dynamics characteristic of biological neural systems.

Purpose of the Study:

• To introduce a novel RNN model capable of generating coherent, spatially correlated chaotic dynamics.
• To investigate the role of structured connectivity in achieving biologically plausible neural network dynamics.
• To explore different dynamical regimes and their dependence on network parameters and connectivity structure.

Main Methods:

• Introduced a structured connectivity component alongside random connections, creating unidirectional coupling between orthogonal modes.
• Employed a perturbative approach to solve dynamic mean-field equations in the weak structured connectivity regime.
• Analyzed network behavior under a row balance constraint for random connectivity, exploring self-tuned coherent chaos.

Main Results:

• Weak structured connectivity leads to coherent fluctuations passively driven by local chaotic activity.
• Stronger structured connectivity, especially with row balance, induces self-tuned coherent chaos with intermittent, slow, and highly coherent dynamics.
• Network dynamics exhibit dependence on connectivity matrix realization (e.g., complex vs. real leading eigenvalue) and scale with network size.

Conclusions:

• The proposed model successfully generates spatially correlated chaos in RNNs, addressing limitations of purely random networks.
• Structured connectivity is crucial for embedding coherent fluctuations and achieving biologically relevant network dynamics.
• The model provides a framework for understanding how structured connectivity shapes complex neural dynamics, including oscillatory and broken-symmetry chaos.