A unified view on weakly correlated recurrent networks

Area of Science:

• Theoretical Neuroscience
• Computational Neuroscience
• Neural Network Dynamics

Background:

• Diverse neuron models are used in theoretical neuroscience to study neural activity covariances.
• Distinguishing generic covariance properties from model-specific artifacts is challenging.
• Existing models include binary neuron models, leaky integrate-and-fire (LIF) models, and Hawkes processes.

Purpose of the Study:

• To present a unified framework for analyzing pairwise covariances in recurrent neural networks.
• To relate different neuron models through linear approximation and identify common underlying structures.
• To enable transfer of results and insights across distinct neural modeling approaches.

Main Methods:

• Linear approximation of binary, LIF, and Hawkes process neuron models.
• Mapping these models to two classes of linear rate models (LRM), including Ornstein-Uhlenbeck process (OUP).
• Derivation of closed-form solutions for pairwise covariances in both LRM classes.

Main Results:

• All considered models map to two LRM classes based on noise location (input vs. output).
• Closed-form covariance solutions reveal echo terms and correlated input contributions for output noise.
• The unified framework facilitates generalization, e.g., incorporating synaptic delays into binary and Hawkes models.

Conclusions:

• The framework provides a unified view on pairwise covariances, applicable to general network structures.
• Model-invariant features, like oscillatory instability in LIF networks, can be identified.
• Accuracy of effective theories is improved by considering linearization fluctuations, explaining class-dependent spectral differences.