Stochastic activity in low-rank recurrent neural networks

Area of Science:

• Computational neuroscience
• Network science
• Systems neuroscience

Background:

• Neural circuit connectivity is fundamental to brain activity.
• The relationship between neural network structure and emergent activity is not fully understood.
• Recurrent neural networks with stochastic inputs are used to model brain function.

Purpose of the Study:

• Investigate the link between connectivity structure and emergent activity in recurrent neural networks.
• Examine how the dimensionality of external stochastic inputs affects neural activity geometry.
• Provide a framework for analyzing structured brain circuits under noise.

Main Methods:

• Utilized recurrent neural networks with additive stochastic inputs.
• Assumed synaptic connectivity in a low-rank form, parameterized by connectivity vectors.
• Analyzed the geometry of emergent activity in relation to connectivity vectors and input dimensionality.

Main Results:

• Activity dimensionality depends critically on input dimensionality.
• Low-dimensional inputs lead to low-dimensional activity within a subspace defined by a subset of connectivity vectors.
• High-dimensional inputs can lead to high-dimensional activity within a subspace defined by all connectivity vectors.

Conclusions:

• The dimensionality of external inputs dictates the dimensional properties of emergent neural activity.
• Recurrent dynamics influence activity within specific subspaces determined by connectivity structure and input dimensionality.
• The findings offer insights into amplification in excitatory-inhibitory networks and provide a framework for interpreting stochastic models of brain activity.