Linking Connectivity, Dynamics, and Computations in Low-Rank Recurrent Neural Networks

Area of Science:

• Computational neuroscience
• Systems neuroscience
• Theoretical neuroscience

Background:

• Large-scale neural recordings show sensory-motor transformations rely on low-dimensional population dynamics.
• Individual neurons display complex selectivity, posing a challenge to understanding network computation.
• The emergence of low-dimensional computations from recurrent network structure is poorly understood.

Purpose of the Study:

• To investigate how low-dimensional computations arise in recurrent neural networks.
• To analyze network models with connectivity comprising random and minimal low-dimensional structures.
• To link network connectivity to emergent low-dimensional dynamics and computational capacity.

Main Methods:

• Studied a class of recurrent network models.
• Analyzed network connectivity as a sum of random and minimal low-dimensional components.
• Employed a geometrical approach to infer network dynamics from connectivity.

Main Results:

• Demonstrated that dynamics in these networks are inherently low-dimensional.
• Showed that low-dimensional dynamics can be directly inferred from network connectivity.
• Found that minimal connectivity requirements for specific computations increase with dimensionality.
• Observed rapid increases in dynamical range and computational capacity with connectivity structure dimensionality.

Conclusions:

• Established a framework linking recurrent network connectivity to low-dimensional dynamics.
• Provided a method to infer network dynamics from connectivity structure.
• Predicted that increasing connectivity dimensionality enhances computational capacity.
• Generated testable predictions for experimental neuroscience regarding connectivity, dynamics, and neural computation.