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Abstract:
We have previously shown using biophysically detailed
compartmental models that nonlinear interactions between nearby
synaptic inputs in the branches of an active dendritic tree can
provide a layer of virtual feature detectors, which can
significantly boost the cell's memory capacity [Mel B. W. 92a,b].
Our aim here has been to quantify this boost by calculating the
capacity of a neuron under two different modes of dendritic
integration: (1) a passive dendrite model in which synaptic inputs
are combined linearly across the entire cell, followed by a single
global threshold, and (2) an active dendrite model in which a
threshold is applied separately to the output of each branch. We
focus here on the limiting case of binary-valued synaptic weights,
and derive expressions which measure model capacity by counting the
number of distinct input-output functions available to both neuron
types. We show that (1) the application of a fixed nonlinearity to
each dendritic compartment substantially increases the model's
flexibility, (2) for neurons of realistic size, the capacity of the
nonlinear cell can exceed that of the same-sized linear cell by
more than an order of magnitude, and (3) the largest capacity boost
occurs for cells with a relatively large number of dendritic
subunits of relatively small size. We validated the analysis by
empirically measuring memory capacity with randomized two-class
classification problems, where a stochastic delta rule was used to
train both linear and nonlinear models. We found that the large
capacity boosts predicted for the nonlinear dendritic model were
readily achieved in practice.
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