Memory Capacity of Linear vs. Nonlinear Models of Dendritic Integration

We have previously shown using biophysically detailed compartmental models that nonlinear interactions between nearby synaptic inputs in an active dendritic tree can provide a layer of virtual feature detectors, which can signicantly boost the cell's memory capacity [3, 4]. Our aim here has been to quantify this boost mathematically, by calculating the capacity of a neuron under two different models of dendritic integration: (1) the perceptron model, where synaptic inputs are combined linearly prior to thresholding, and (2) the quadratic \energy" model, where inputs are combined linearly within each branch, and the branch subtotals are squared and summed to produce the cell's output. We focus here on the limiting case of binary-valued synaptic weights, and derive expressions which measure model capacity by counting the distinct parameter states available to both neuron types. We show that (1) attachment of a simple output nonlinearity to each dendritic compartment|as in the energy mod..