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Article 6373 of comp.ai.philosophy:
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>From: erwin@trwacs.fp.trw.com (Harry Erwin)
Newsgroups: comp.ai.philosophy,comp.ai.neural-nets,sci.cognitive
Subject: Generalized Distributed Memory
Keywords: holonomy holography memory cerebellum
Message-ID: <650@trwacs.fp.trw.com>
Date: 26 Jun 92 14:53:00 GMT
Followup-To: comp.ai.philosophy
Organization: TRW Systems Division, Fairfax VA
Lines: 197

Initial draft, distributed for comment.

A Generalized Model of Distributed Memory

Harry Erwin
TRW Systems Division
P. O. Box 10400
Fairfax, VA 22031
erwin@trwacs.fp.trw.com

Introduction

When Karl Pribram introduced his holographic memory model 
(1966) as a response to Lashley's (1950, 1963) results, it 
excited a great deal of interest but came under attack on a 
number of grounds, including:
	1. known brain structure being inconsistent with the 
high precision required for optical holography,
	2. lack of evidence for a reference beam,
	3. lack of evidence for neural processing of optical 
phase data,
	4. Penfield and Roberts's (1959) evidence for detailed 
localization of memory traces, and
	5. inconsistency with a general belief that brain 
structure reflects "insulationism"; i.e., the avoidance of 
large-scale interactions (Minsky, 1992, letter).

Despite these criticisms, Pribram and his associates 
extended the holographic model into a holonomic brain 
theory, most recently documented in Brain and Perception 
(Pribram, 1992). That theory proposes holographic processing 
within the dendritic arbor involving oscillations of 
biomolecules of high dipole moments that form an "ionic 
bioplasma." At present, the consensus of the neuroscience 
community on this model ranges from a cautious 'not proven' 
to Minsky's (1985) outright rejection. The primary 
difficulty most have with this model involves the lack of 
evidence for the proposed holographic mechanism. 

This difficulty disappears if the holographic model is 
suitably generalized. This paper examines a model of 
distributed memory that retains the properties that led 
Pribram to propose his holographic model, is consistent with 
current models of neuron and brain function, yet avoids the 
problems associated with optical holography. 

Generalizing Holography

Optical Data Processing by Shulman (1970) provides a clear 
introduction to the technology of holography. Shulman 
defines a zone plate as "a plate that is capable of 
producing image points (focuses) when illuminated by 
spherical or plane wavefronts of monochromatic light." This 
occurs because every point on an illuminated plate can be 
considered to be the origin of a set of spherical 
wavefronts. For a uniformly illuminated plate with no 
pattern, these wavefronts interfere destructively in all 
directions except normally to the incident wavefronts, and
this results in a transmitted or reflected pattern of 
parallel plane wavefronts. A fresnel (sine-wave) zone plate 
interferes with this process to generate instead an image 
focused at a point and so is the simplest of holograms.

The focused image is generated because the amount of light 
transmitted or reflected at each point of the plate is 
modulated proportionally to the degree to which the light
from that point will be in phase at the desired focus. In 
other words, out-of-phase light is subtracted by the 
interference pattern, leaving the remainder to interfere 
constructively to create a focused image. Zone plates can 
then be superimposed to place these focal points at any 
desired location, creating a hologram that can be used to 
produce a virtual image of an object or scene.

Hence, the key concept behind holography is that a reference
beam illuminating a plate is converted into a signal beam 
(or radiation pattern) by judicious inhibition of the 
reflection or transmission of undesired elements of the 
beam. This can be contrasted to a model of the signal beam 
being actively constructed from basic elements. This 
conceptual model leads to a generalization of holography. 
The following elements are needed:
1. a reference beam
2. a signal beam, and
3. a process by which components can be subtracted from the
reference beam to produce the signal beam.
If the processing elements are large in number, spatially
dispersed, and parallel in operation, the resulting process
will be non-local, resistant to ablation, and adaptable, the
characteristics that suggested the holographic model
originally.

The Distributed Memory Model

Steven Rose (1989, Appendix 3) provides a simple model of
the cerebellum based on David Marr's work (Marr, 1969, and
Blomfield and Marr, 1970) and that of Eccles, Itoh, and
Szentagothai (1967). His model identifies three interface
systems, two input: the climbing fibres from the inferior
olivary nucleus (each synapsing numerous times with a
specific Purkinje cell), and the mossy fibres from the
somatic nerves and the brain (synapsing indirectly to the
Purkinje cells via the granule cells), and one output: the
Purkinje cells, synapsing to the pyramidal tracts to inhibit
motor output.Inhibitory interneurons prevent the Purkinje
cells from firing unless the associated climbing fibre and
nearly all of its granule cell inputs are firing. The key
point is that the Purkinje cells function to modulate (via
inhibition) the signals that eventually reach the motor
neurons, removing those components that decrease the focused
coherence of the muscular action. This is a generalization
of how the hologram interacts with the reference beam to
produce the signal beam that can be observed as an image.

The generalized holographic model of the cerebellum that
results is as follows:
1. In pursuit of a specific "image of achievement" (Pribram,
1991), cortical cells transmit an activating signal to the
inferior olivary nucleus and activate numerous pyramidal
cells in the cortex, which transmit a generalized reference
beam of motor commands to the motor neurons. (It is this
initiating command that Penfield was able to stimulate.)
2. The activating signal is then transmitted to specific
climbing fibres to "awaken" their associated Purkinje cells.
3. The awakened Purkinje cells monitor somatic and motor
activation data to determine if their activating pattern is
present. If so, they inhibit their associated pyramidal
tract, removing or reducing the strength of specific motor
commands in the reference beam.
4. The resulting motor commands after inhibition by the
cerebellum constitute a signal beam. As the body responds to
those motor commands, the somatic data monitored by the
individual Purkinje cells causes them to activate or
deactivate in sequence, resulting in a changing signal beam.
5. Loss of a Purkinje cell reduces the inhibition of a
specific motor command. This reduces the focussed coherence
of the motor action, but does not prevent it from
proceeding. The extent of the resulting impairment would be
proportional to the number of involved Purkinje cells
destroyed since more than one Purkinje cell may be involved
in inhibiting a specific command.6.
6. Relative phase of motor commands can be monitored via
mossy fibre input with appropriate delays and controlled
through modulated inhibition of motor commands.

Note that this model has the desired properties:
1. memory is distributed following a generalized holographic
model.
2. the effect of ablation is not to eliminate a memory, but
rather to decrease its focus.
3. the large amount of spare capacity in the brain is
explained without having to assume such a low reliability
that survival requires a high degree of redundancy.
4. Penfield's results are explained.
5. at the same time, the high precision required for optical
holography is not required.

An interesting question is the identity of the corresponding
reference and signal beams in sensory and conceptual memory.
The mechanism is likely to be similar, but details will
certainly differ.

References

Blomfield, S., and Marr, D., 1970. Nature. 227:1124-1128.

Eccles, J. C., Itoh, M., and Szentagothai, J., 1967. The
Cerebellum as a Neuronal Machine. New York, NY: Springer-
Verlag.

Lashley, K. S., 1950. Symposia of the Society for
Experimental Biology. 4: 454-482.

Lashley, K. S., 1963. Brain Mechanisms and Learning. New
York, NY: Dover.

Marr, D., 1969. Journal of Physiology. 202:437-470.

Minsky, M., 1985. Society of Mind. New York, NY: Touchstone.

Pribram, K., 1966. "Some dimensions of remembering: steps
toward a neuropsychological model of memory." In J. Gaito
(ed.), Macromolecules and behavior (pp. 165-187). New York,
NY: Academic Press.

Pribram, K., 1991. Brain and Perception. Hillsdale, NJ:
Lawrence Erlbaum Associates.

Rose, S., 1989. Conscious Brain, New York, NY: Paragon
House.

Shulman, A. R., 1970. Optical Data Processing. New York NY:
John Wiley & Sons.
-- 
Harry Erwin
Internet: erwin@trwacs.fp.trw.com



