Information Technology Reference
In-Depth Information
Chapter 7
Stochastic Models of Biological Neuron
Dynamics
Abstract
The chapter examines neural networks in which the synaptic weights
correspond to diffusing particles. Each diffusing particle (stochastic weight) is
subject to the following forces: (1) a spring force (drift) which is the result of the
harmonic potential and tries to drive the particle to an equilibrium and (2) a random
force (noise) which is the result of the interaction with neighboring particles. This
interaction can be in the form of collisions or repulsive forces. It is shown that the
diffusive motion of the stochastic particles (weights' update) can be described by
Fokker-Planck's, Ornstein-Uhlenbeck, or Langevin's equation which under specific
assumptions are equivalent to Schrödinger's diffusion equation. It is proven that
Langevin's equation is a generalization of the conventional gradient algorithms.
7.1
Outline
Conventional neural networks may prove insufficient for modelling memory and
cognition, as suggested by effects in the functioning of the nervous system, which
lie outside classical physics [
19
,
48
,
59
,
73
,
75
,
136
,
168
]. One finds ample support
for this in an analysis of the sensory organs, the operation of which is quantized at
levels varying from the reception of individual photons by the retina, to thousands
of phonon quanta in the auditory system. Of further interest is the argument that
synaptic signal transmission has a quantum character, although the debate on this
issue has not been conclusive. For instance, it has been mentioned that superposition
of quantum states takes place in the microtubules of the brain and that memory recall
is the result of quantum measurement [
73
]. Moreover, it has been argued that human
cognition must involve an element inaccessible to simulation on classical neural
networks and this might be realized through a biological instantiation of quantum
computation.
To evaluate the validity of the aforementioned arguments, neural structures
with weights that follow the model of the quantum harmonic oscillator (QHO)
will be studied in this chapter. Connectionist structures which are compatible with
