SUMMARY Sequential activation of neurons is a common feature of network activity during a variety of behaviors, including working memory and decision making. Previous network models for sequences and memory emphasized specialized architectures in which a principled mechanism is pre-wired into their connectivity. Here, we demonstrate that starting from random connectivity and modifying a small fraction of connections, a largely disordered recurrent network can produce sequences and implement working memory efficiently. We use this process, called Partial In-Network training (PINning), to model and match cellular-resolution imaging data from the posterior parietal cortex during a virtual memory-guided two-alternative forced choice task [Harvey, Coen and Tank, 2012]. Analysis of the connectivity reveals that sequences propagate by the cooperation between recurrent synaptic interactions and external inputs, rather than through feedforward or asymmetric connections. Together our results suggest that neural sequences may emerge through learning from largely unstructured network architectures.

The dynamics of neural networks is influenced strongly by the spectrum of eigenvalues of the matrix describing their synaptic connectivity. In large networks, elements of the synaptic connectivity matrix can be chosen randomly from appropriate distributions, making results from random matrix theory highly relevant. Unfortunately, classic results on the eigenvalue spectra of random matrices do not apply to synaptic connectivity matrices because of the constraint that individual neurons are either excitatory or inhibitory. Therefore, we compute eigenvalue spectra of large random matrices with excitatory and inhibitory columns drawn from distributions with different means and equal or different variances.

Neural network modeling is often concerned with stimulus-driven responses, but most of the activity in the brain is internally generated. Here, we review network models of internally generated activity, focusing on three types of network dynamics: (a) sustained responses to transient stimuli, which provide a model of working memory; (b) oscillatory network activity; and (c) chaotic activity, which models complex patterns of background spiking in cortical and other circuits. We also review propagation of stimulus-driven activity through spontaneously active networks. Exploring these aspects of neural network dynamics is critical for understanding how neural circuits produce cognitive function.

Neuronal activity arises from an interaction between ongoing firing generated spontaneously by neural circuits and responses driven by external stimuli. Using mean-field analysis, we ask how a neural network that intrinsically generates chaotic patterns of activity can remain sensitive to extrinsic input. We find that inputs not only drive network responses, but they also actively suppress ongoing activity, ultimately leading to a phase transition in which chaos is completely eliminated. The critical input intensity at the phase transition is a nonmonotonic function of stimulus frequency, revealing a "resonant" frequency at which the input is most effective at suppressing chaos even though the power spectrum of the spontaneous activity peaks at zero and falls exponentially. A prediction of our analysis is that the variance of neural responses should be most strongly suppressed at frequencies matching the range over which many sensory systems operate.

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