Connectivity structure and dynamics of nonlinear recurrent neural networks
We develop a theory to analyze how structure in connectivity shapes the high-dimensional, internally generated activity of nonlinear recurrent neural networks. Using two complementary methods -- a path-integral calculation of fluctuations around the saddle point, and a recently introduced two-site cavity approach -- we derive analytic expressions that characterize important features of collective activity, including its dimensionality and temporal correlations. To model structure in the coupling matrices of real neural circuits, such as synaptic connectomes obtained through electron microscopy, we introduce the random-mode model, which parameterizes a coupling matrix using random input and output modes and a specified spectrum. This model enables systematic study of the effects of low-dimensional structure in connectivity on neural activity. These effects manifest in features of collective activity, that we calculate, and can be undetectable when analyzing only single-neuron activities. We derive a relation between the effective rank of the coupling matrix and the dimension of activity. By extending the random-mode model, we compare the effects of single-neuron heterogeneity and low-dimensional connectivity. We also investigate the impact of structured overlaps between input and output modes, a feature of biological coupling matrices. Our theory provides tools to relate neural-network architecture and collective dynamics in artificial and biological systems.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
Linking structure and activity in nonlinear spiking networks
Recent experimental advances are producing an avalanche of data on both neural connectivity and neural activity. To take full advantage of these two emerging datasets we need a framework that links them, revealing how co…
Structure of activity in multiregion recurrent neural networks
Neural circuits comprise multiple interconnected regions, each with complex dynamics. The interplay between local and global activity is thought to underlie computational flexibility, yet the structure of multiregion neu…
Linking connectivity, dynamics and computations in low-rank recurrent neural networks
Large scale neural recordings have established that the transformation of sensory stimuli into motor outputs relies on low-dimensional dynamics at the population level, while individual neurons exhibit complex selectivit…
Cell-type-specific synaptic motifs generate coupled mean-variability dynamics in recurrent neural networks
Synaptic-resolution network connectomics has revealed that brain circuits feature fine-scale structural connectivity, such as pairs of correlated synaptic couplings known as second-order motifs. Large-scale recordings of…
Identifying Connectivity Distributions from Neural Dynamics Using Flows
Connectivity structure shapes neural computation, but inferring this structure from population recordings is degenerate: multiple connectivity structures can generate identical dynamics. Recent work uses low-rank recurre…