Page 38 - Artificial Intelligence in the Age of Neural Networks and Brain Computing

10. Postulates of Synaptic Plasticity 25

negative one, and they turn out to be analogous to the equilibrium points shown in
Fig. 1.8. This kind of stabilization is called homeostasis and is a phenomenon of
regularization that takes place over all living systems. The Hebbian-LMS algorithm
exhibits homeostasis about the two equilibrium points, caused by reversal of the
error signal at these equilibrium points. See Fig. 1.8. Slow adaptation over thousands
of adapt cycles, over hours of real time, results in homeostasis of the (SUM).
Fig. 1.17 shows an exaggerated diagram of a neuron, dendrites, and a synapse.
This diagram suggests how the voltage of the (SUM) in the soma of the postsynaptic
neuron can by ohmic conduction determine the voltage of the membrane.
Activation pulses are generated by a pulse generator in the soma of the postsyn-
aptic neuron. The pulse generator is energized when the (SUM) exceeds the
threshold. The pulse generator triggers the axon to generate electrochemical waves
that carry the neuron’s output signal. The firing rate of the pulse generator is
controlled by the (SUM). The output signal of the neuron is its firing rate.

10. POSTULATES OF SYNAPTIC PLASTICITY

The above description of the synapse and its variability or plasticity is based on a
study of the literature of the subject. The literature is not totally clear or consistent,
however. Experimental conditions of the various studies are not all the same, and the
conclusions can differ. The set of postulates of synaptic plasticity shown in Table 1.1
have been formulated representing a “majority opinion.”
A group of researchers have developed learning algorithms called “anti-Hebbian
learning [31e33]”: “Fire together, unwire together.” This is truly the case for
inhibitory synapses. We call this in the above postulates an extension of Hebb’s
rule. Anti-Hebbian learning fits the postulates and is therefore essentially incorpo-
rated in the Hebbian-LMS algorithm.

Table 1.1 Postulates of Plasticity
1. Presynaptic neurons not firing: no neurotransmitter in synaptic gap
a. Excitatory synapsedno weight change
b. Inhibitory synapsedno weight change
2. Presynaptic neuron firing
a. Excitatory synapse
- Postsynaptic neuron firing, synaptic weight increases (Hebb’s rule)
- Postsynaptic neuron not firing, synaptic weight decreases (Extended Hebb’s rule)
b. Inhibitory synapse
- Postsynaptic neuron firing, synaptic weight decreases (Extended Hebb’s rule)
- Postsynaptic neuron not firing, synaptic weight increases (Extended Hebb’s rule)
3. Homeostasis keeps (SUM) close to one or the other equilibrium point, stabilizing firing
rate of postsynaptic neuron.