UC San Diego

Recurrent random network models are a useful theoretical tool to understand the irregular activity of neural networks in the brain. To preserve the analytical tractability, often it is assumed that connectivity statistics are homogeneous. In contrast, experiments highlight the importance of the heterogeneity found in neural circuits. By extending the dynamic mean field method we solved the dynamics of a recurrent neural network with cell-type-dependent connectivity. These networks undergo a phase transition from a silent state to a state with chaotic activity, and can sustain multiple global activity modes that are predicted by our analysis. By finding the location of the critical point at which the phase transition occurs we derived a new mathematical result: the spectral radius of a random matrix with block structured variances, which serves as the network's connectivity matrix. Applying our results we explain how a small number of hyper-excitable neurons that are integrated into the network can lead to significant changes in its computational capacity; and show that a clustered architecture, where inter-cluster connectivity is weaker than intra-cluster connectivity, can also lead to network configurations that are advantageous from a computational standpoint. The heterogeneity of neural networks is perhaps rivaled only by the diversity of the external sensory environment. Every organism is constantly bombarded by stimuli that inherit their statistical structure from that environment, and tend to have strong correlations. The computation that neurons perform adapts to the stimulus statistics, making it important to find the features a cell is sensitive to using stimuli that are as close to natural as possible. Spike-Triggered- Covariance is a popular and computationally efficient dimensionality reduction method that finds the features that are relevant for a cell's computation. Using this technique to analyze model and retinal ganglion cell responses we show that strong stimulus correlations interfere with analysis of statistical significance of candidate input dimensions. Using results from random matrix theory we derive a correction scheme that eliminates these artifacts, allowing for an order of magnitude increase in the sensitivity of the method