Indistinguishable Synapses Lead to Sparse Networks

Neurons integrate information from many neighbors when they process information. Inputs to a given neuron are thus indistinguishable from one another. Under the assumption that neurons maximize their information storage, indistinguishability is shown to place a strong constraint on the distribution of strengths between neurons. The distribution of individual synapse strengths is found to follow a modified Boltzmann distribution with strength proportional to [Formula: see text]. The model is shown to be consistent with experimental data from Caenorhabditis elegans connectivity and in vivo synaptic strength measurements. The [Formula: see text] dependence helps account for the observation of many zero or weak connections between neurons or sparsity of the neural network.