Synapses in real neural circuits can take discrete values, including zero (silent or potential) synapses. The computational role of zero synapses in unsupervised feature learning of unlabeled noisy data is still unclear, thus it is important to understand how the sparseness of synaptic activity is shaped during learning and its relationship with receptive field formation. Here, we formulate this kind of sparse feature learning by a statistical mechanics approach. We find that learning decreases the fraction of zero synapses, and when the fraction decreases rapidly around a critical data size, an intrinsically structured receptive field starts to develop. Further increasing the data size refines the receptive field, while a very small fraction of zero synapses remain to act as contour detectors. This phenomenon is discovered not only in learning a handwritten digits dataset, but also in learning retinal neural activity measured in a natural-movie-stimuli experiment.
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