Biomedical Engineering Reference
In-Depth Information
contacts an obstacle, generates a spike train at a frequency inversely propor-
tional to the distance of intersection along the whisker length. The photorecep-
tors, which respond proportionately to light intensity integrated over a receptive
field with Gaussian profile, drive two kinds of spiking units, the sustained and
transient units, analogous to the main types of ganglion cells in the vertebrate
retina. The receptive fields of these spiking units are about 10( wide.
The whisker and the photoreceptor spike signals connect to two layers of
simulated neuromorphs, Hebb Layer Left and Hebb Layer Right, which, by a
Hebbian learning rule, are to acquire directionally selective properties to stimuli
moving left or right respectively. These layers are composed of 8 units, each of
which is based on the spike-response (S-R) model of Gerstner and Kistler (8).
This model provides an approximation to the functional properties of a silicon
neuromorph limited to one operative synaptic site. A spike input (from unit
i
) to
one of these S-R units (unit
j
) generates a postsynaptic potential that is positive-
going (excitatory) or negative-going (inhibitory), the amplitude and sign de-
pending on a numeric weight (
w
ij
) between -1.0 and +1.0. The rise and fall times
of the postsynaptic potentials are fixed, unlike those in the ADT neuromorph, in
which they depend on the site of synaptic activation along the dendrite. Postsy-
naptic potentials are summed and fed to an integrate-and-fire spike generator,
the firing threshold of which is controlled by a bias input. Refractoriness after
spike firing is implemented by immediately raising the spike-firing threshold
and allowing it to decay to the bias threshold over a fixed time course.
The connections from the whisker array to both Hebb layers are preset and
not modifiable. The whiskers are mapped topographically across the Hebb lay-
ers so that stimulation of the leftmost whisker, for example, activates units at the
leftmost end of the Hebb layers (see Figure 6A). Hebb layer units that are not
related topographically to a whisker are inhibited by that whisker. The other
preset and unmodifiable connections are the proprioceptive afferents to the Hebb
layers. The left-turn proprioceptors fire when the vehicle rotates leftward and
tends to excite all the units in Hebb Layer Left. Similarly the right-turn proprio-
ceptors excite Hebb Layer Right. The transient and sustained units of the "ret-
ina" are projected in a fully connected pattern with initially zero weights onto
both Hebb layers. The latter connections are modifiable according to a Hebb
rule akin to the mechanism that strengthens and weakens synapses in mammal-
ian cortex (13) and amphibian tectum (25). Synaptic weight modification de-
pends upon the relative timing of pre- and postsynaptic spikes: if the presynaptic
spike occurs in a time window before the postsynaptic unit fires, the weight of
the presynaptic synapse is increased; if it occurs after the postsynaptic spike, it is
decreased; otherwise, no change occurs (Figure 5). The effect is that the syn-
apses from any visual units that fire consistently just before the firing of a Hebb
layer unit will have their connections strengthened or made more excitatory. If
the visual units fire just after, their connections are weakened and eventually
may become inhibitory. Visual unit firing that is unrelated to the activity of the
