The synaptic connectivity within neuronal networks is thought to determine the information
processing they perform, yet network structure-function relationships remain poorly
understood. By combining quantitative anatomy of the cerebellar input layer and information
theoretic analysis of network models, we investigated how synaptic connectivity affects
information transmission and processing. Simplified binary models revealed that the
synaptic connectivity within feedforward networks determines the trade-off between
information transmission and sparse encoding. Networks with few synaptic connections
per neuron and network-activity-dependent threshold were optimal for lossless sparse
encoding over the widest range of input activities. Biologically detailed spiking
network models with experimentally constrained synaptic conductances and inhibition
confirmed our analytical predictions. Our results establish that the synaptic connectivity
within the cerebellar input layer enables efficient lossless sparse encoding. Moreover,
they provide a functional explanation for why granule cells have approximately four
dendrites, a feature that has been evolutionarily conserved since the appearance of
fish.
