[From Bill Powers (2009.06.01.0841 MDT)]
The Aplysia thread raised Hebbian learning as an issue. It occurred to me
that Hebb’s proposal has to be explained a bit more before it can be
linked to PCT.
I think that the principles of contiguity and repetition that Hebb uses
were an attempt to model classical conditioning. The problem with using
these ideas in PCT is that we have no idea what kind of signal is
involved in this sort of learning, and therefore no idea of whether this
is the appropriate model.
I’m reading Hebb, A Textbook of Psychology, Saunders, 1958 (1964
reprinting).
Hebb has some vague sort of idea that if the strength of the connection
is increased, the impulses will get farther through the nervous system.
“In other regions [of the cortex], conduction is diffuse; cells may
start together but run in different directions, so the cells cannot sum
their effects at the next synapse. Such transmission seems inefficient
and must often fail to carry through the network to reach the effectors,
thus not influencing behavior.” (p.100).
This brings us to “Let us see now how the diffuse conductivity of
the cortex allows us to understand, in principle, the selectivity of
higher behavior (i.e., responding to some stimuli, not to others); the
holding process, or the delay of transmission that permits a stimulus to
have its effect at the proper moment; and, in general terms, the lack of
a complete sensory dominance of the behavior of the higher animal.”
(p. 101).
That is pretty awful, but it leads into the discussion of cell assemblies
influencing each other, and eventually (p. 105) into this:
“Assumption 2: if two assemblies A and B are repeatedly active at
the same time they will tend to become “associated” so A
excites B and vice versa.”
Eventually this gets to the proposition that if two synapses receive
impulses at the same time they will become “strengthened”, a
word that can be interpreted in a number of ways.
But for what kind of signal would that be an appropriate effect, one that
might represent useful learning of some kind? For Hebb, learning was
simply establishing the connections from sensory inputs to motor outputs,
but later uses of his idea have broadened it to include practically any
kind of theory you please.
We could ask, for example, whether this sort of adaptation could lead to
developing a comparator function in which the output signal represents
the difference between two input signals, a cell assembly familiar in
PCT. If a reference-signal impulse reached the comparator neuron at the
same time as the perceptual-signal impulse, and if this strengthened both
synapses so they had greater effects on the output of the neuron, would
that tend to produce the effect required of a comparator? Since a
comparator needs one excitatory input and one inhibitory input, we would
certainly not want to increase both effects equally, because that would
simply lead to cancellation: any perceptual signal would cancel any
reference signal’s effect, so the output error would always be zero. How
do we get a graduated effect, so that the larger the difference between
the two signals, the larger the error signal gets? There wouldn’t seem to
be any way to do that with Hebb’s scheme.
Then what about output signals? If a lower-order comparator received two
signals at the same time from two different higher systems, would
increasing the strength of the synapses give us what is needed? No,
because what is needed is for the outputs converging on lower systems to
be different, some excitatory and some inhibitory, some larger and some
smaller, and this does not result from strengthing all synapses.
Then what about perceptual input functions? Those cell assemblies receive
copies of perceptual signals from multiple lower-order systems, and
combine them to produce a higher-order perceptual signal. Would Hebb’s
principle work for generating, say, a sensation signal from a set of
intensity signals? We have been assuming that sensations are computed
from weighted sums of intensity signals. The weights have to vary from
one input function to another according to which sensation is to result.
One input function might combine the four taste-intensity signals in a
particular way to detect the degree of nuttiness, while another combined
the same signals in a different way to detect the degree of
chocolateness. Would strengthening the synapses of a neuron reached
simultaneously by impulses from the four kinds of intensity signals
result in making these distinctions? I don’t see how.
Problems of this sort become even worse at higher levels, where we have
to consider such things as detection of relationships, or categories, or
sequences, with perceptual input functions working according to the same
Hebbian rules at each different level.
I think we have to conclude that Hebbian learning is simply insufficient
to account for all the connections at all the levels in the brain, or for
that matter, to account for any of them in a system that uses signals of
varying frequency, and what the Aplysia modelers call an “integrate
and fire” model of the neuron. Hebb was working with a very naive
and primitive concept of the brain as a stimulus-response system that
simply routed impulses from sensory inputs to motor outputs with various
delays, and with sensory impulses somehow representing all the different
kinds of perceptions without any differences in the ways they are
generated or in their form. You really have to go back to that old
textbook to appreciate just how primitive the thinking was 50 years
ago.
This old book was being written at the same time that three guys at the
VA Research Hospital in Chicago were working their way toward the first
version of PCT published in 1960. Hebb was a big name in psychology, much
bigger than Powers, Clark, and MacFarland. Which only goes to show that
the mountain we thought we were climbing was just a foothill. I’m glad I
didn’t know that – I would have gone into some other occupation rather
than undertake an obviously hopeless task.
Best,
Bill P.
