Normalization of input patterns in an associative network.

Numerous brain structures have a cerebellum-like architecture in which inputs diverge onto a large number of granule cells that converge onto principal cells. Plasticity at granule cell-to-principal cell synapses is thought to allow these structures to associate spatially distributed patterns of granule cell activity with appropriate principal cell responses. Storing large sets of associations requires the patterns involved to be normalized, i.e., to have similar total amounts of granule cell activity. Using a general model of associative learning, we describe two ways in which granule cells can be configured to promote normalization. First, we show how heterogeneity in firing thresholds across granule cells can restrict pattern-to-pattern variation in total activity while also limiting spatial overlap between patterns. These effects combine to allow fast and flexible learning. Second, we show that the perceptron learning rule selectively silences those synapses that contribute most to pattern-to-pattern variation in the total input to a principal cell. This provides a simple functional interpretation for the experimental observation that many granule cell-to-Purkinje cell synapses in the cerebellum are silent. Since our model is quite general, these principles may apply to a wide range of associative circuits.