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While the sparse coding principle can successfully model informationprocessing in sensory neural systems, it remains unclear how learning can beaccomplished under neural architectural constraints. Feasible learning rulesmust rely solely on synaptically local information in order to be implementedon spatially distributed neurons. We describe a neural network with spikingneurons that can address the aforementioned fundamental challenge and solve theL1-minimizing dictionary learning problem, representing the first model able todo so. Our major innovation is to introduce feedback synapses to create apathway to turn the seemingly non-local information into local ones. Theresulting network encodes the error signal needed for learning as the change ofnetwork steady states caused by feedback, and operates akin to the classicalstochastic gradient descent method.

Local Information with Feedback Perturbation Suffices for Dictionary Learning in Neural Circuits