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Feedforward network models performing classification tasks rely on highly convergent output units that collect the information passed on by preceding layers. Although convergent output-unit like neurons may exist in some biological neural circuits, notably the cerebellar cortex, neocortical circuits do not exhibit any obvious candidates for this role; instead they are highly recurrent. We investigate whether a sparsely connected recurrent neural network (RNN) can perform classification in a distributed manner without ever bringing all of the relevant information to a single convergence site. Our model is based on a sparse RNN that performs classification dynamically. Specifically, the interconnections of the RNN are trained to resonantly amplify the magnitude of responses to some external inputs but not others. The amplified and non-amplified responses then form the basis for binary classification. Furthermore, the network acts as an evidence accumulator and maintains its decision even after the input is turned off. Despite highly sparse connectivity, learned recurrent connections allow input information to flow to every neuron of the RNN, providing the basis for distributed computation. In this arrangement, the minimum number of synapses per neuron required to reach maximum memory capacity scales only logarithmically with network size. The model is robust to various types of noise, works with different activation and loss functions and with both backpropagation- and Hebbian-based learning rules. The RNN can also be constructed with a split excitation-inhibition architecture with little reduction in performance. 

Neural circuits exhibit complex activity patterns, both spontaneously and evoked by external stimuli. Information encoding and learning in neural circuits depend on how well time-varying stimuli can control spontaneous network activity. We show that in firing-rate networks in the balanced state, external control of recurrent dynamics, i.e., the suppression of internally-generated chaotic variability, strongly depends on correlations in the input. A distinctive feature of balanced networks is that, because common external input is dynamically canceled by recurrent feedback, it is far more difficult to suppress chaos with common input into each neuron than through independent input. To study this phenomenon, we develop a non-stationary dynamic mean-field theory for driven networks. The theory explains how the activity statistics and the largest Lyapunov exponent depend on the frequency and amplitude of the input, recurrent coupling strength, and network size, for both common and independent input. We further show that uncorrelated inputs facilitate learning in balanced networks.