Taken from NASA Tech Briefs - April 1990

QUANTIZED-"GRAY-SCALE" ELECTRONIC SYNAPSES

A proposed array of programmable synaptic connections for electronic
neural network applications offers multiple quantized levels of
connection strength using only simple, two-terminal, binary microswitch
devices. Such simple divice structures promise implementations of
quantized "gray-scale" synaptic arrays with very high density. Synaptic
arrays for electronic neural networks have been fabricated in the past,
using programmable binary (on/off) microswitches and passive thin-film
resistor elements with equal connection strengths at all nodes, useful
for content-addressable, high-density associative memories. However,
multivalued, gray-scale synaptic connection strengths are required for
neural network architectures with capabilities that involve higher-
level learning and adaptibility to solve ill-posed problems.

The basic structure of this quantized gray-scale synaptic array
resembles a programmable binary synaptic grid with resistive
connections at the intersections of row and column conductors. However,
in this case, several adjoining rows and columns of the grid are
connected in parallel externally, to form "subgrids" of chosen size.
Thus, each subgrid constitiutes several row/column intersections of
finer a finer grid and forms one synaptic node with programmable
multivalued connection strength.

Within each subgrid, the individual microswitches associated with their
respective resistive connections at the nodes of the finer grid can
be turned on in various combinations to obtain discrete synaptic
strengths. The parallel external connections create sets of parallel
resistors. Thus the conductance of each internal connection of the
subgrid adds to the total conductance (connection strength) of the node
represented by the subgrid. The scheme can, of course, be applied to
an array of synapses with analog strengths to extend their range.

The design of a subgrid and the achievable conductance values depend
predominantly on the conductance of individual elements and precision
in their values. For example, in a subgrid of n elements with equal
conductance values, it is possible to obtain either zero conductance
or any integral multiple of the unit conductance from 1 to n. Further,
if different conductance values (e.g., a binary string of values
proportional to 1,2,4,8...) are provided in a subgrid, then the
maximum achievable number of subgrid conductances is 2^n.

The practical number and sizes of conductance increments are, however,
restricted by the need to avoid overlap of conductance levels due to
the limitations in the achievable resistor precision. For example,
with a +/- 3 percent precision, an array is limited to 16 distinct
conductance levels (in addition to zero), even with subgrids larger
than 16 nodes. Programmable, 40 by 40 synaptic arrays have been
fabricated with an identical connection strength at each node of
one megohm resistances having a precision of +/- 3 percent and can
thus provide a 4-bit gray scale with this scheme. The extra "real
estimate" occupied by the binary elements to provide for a gray scale in
such an array is more than compensated by the overall structural
simplicity and the potential high density.

This work was done by James L. Lamb, Taher Daud, and Anikumar P.
Thakoor of Caltech for NASA's Jet Propulsion Laboratory.