Stochastic activity in low-rank recurrent neural networks.

Area of Science:

• Computational neuroscience
• Neural network dynamics
• Brain circuit analysis

Background:

• Brain activity properties depend on neuronal connectivity in recurrent circuits.
• The precise relationship between connectivity structure and emergent activity is not fully understood.
• Investigating this link is crucial for understanding brain function.

Purpose of the Study:

• To investigate the relationship between connectivity structure and emergent activity in recurrent neural networks with stochastic inputs.
• To determine how the dimensionality of external inputs influences the geometry of emergent activity.
• To 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 input dimensionality and connectivity structure.

Main Results:

• Emergent activity dimensionality is critically dependent on the dimensionality of external stochastic inputs.
• Low-dimensional inputs lead to low-dimensional activity within a subspace defined by a subset of connectivity vectors (rank of connectivity matrix).
• High-dimensional inputs can lead to high-dimensional activity within a subspace defined by all connectivity vectors (twice the rank of the connectivity matrix).

Conclusions:

• The dimensionality of external inputs fundamentally shapes the geometric and statistical properties of emergent brain activity.
• Recurrent dynamics influence activity within specific subspaces determined by input dimensionality and connectivity rank.
• The framework aids in interpreting stochastic models and studying structured brain circuits under realistic noise conditions.