Shaping Dynamics With Multiple Populations in Low-Rank Recurrent Networks

Area of Science:

• Computational neuroscience
• Dynamical systems theory

Background:

• Emerging paradigm views neural computation through collective neural activity dynamics.
• Understanding how network connectivity shapes these emergent dynamical systems is crucial.

Purpose of the Study:

• To investigate the relationship between network connectivity and emergent dynamical systems.
• To introduce and analyze a novel class of recurrent neural network models.

Main Methods:

• Utilized Gaussian-mixture, low-rank recurrent networks.
• Treated network connectivity rank and population number as independent hyperparameters.
• Analyzed the resulting collective dynamics.

Main Results:

• Demonstrated that collective dynamics form a dynamical system where rank dictates dimensionality.
• Showed that population structure shapes the emergent dynamics.
• Established that a rank R network can approximate any R-dimensional dynamical system if the number of populations is sufficient.

Conclusions:

• Network connectivity, specifically rank and population structure, fundamentally determines emergent neural dynamics.
• Low-rank recurrent networks provide a framework for understanding neural computations as dynamical systems.
• The dimensionality of neural activity is governed by network rank, while population structure refines dynamic behavior.