7.0 Structurally Associative Memory

   It is clear that analogy cannot work effectively without recourse to an effective method of
storing patterns. However, I suggest that an even stronger statement holds: the nature of analogy
actually dictates a particular type of memory structure. The only way analogy can work
effectively is if it is coupled with a memory that is specifically structured so as to support
analogical reasoning.
   This memory must, of course, be a "long-term memory": its contents must be sufficiently
permanent to carry over from one situation to another. I will argue that the entire structure of the
mind’s long-term memory can be elicited through the study of analogy. On the other hand, the
"short-term memory" of contemporary psychology is essentially a euphemism for
"consciousness", and we shall deal with it in a later chapter.
   In a completely different context, Jousselin (1987) has reached a similar conclusion regarding
the relation between processing and memory. He has shown that, in a very general mathematical
sense, the nature of the operations carried out by the processor of a computer actually determine
the structure of the memory of that computer.
   Strictly speaking, what is given here is not a model of how memories are physically stored in
the brain or anywhere else, but rather a model of how memory access must work, of how the
time required to access different memories in different situations must vary. However, following
Jousselin, I hold that the structure of memory access is much if not all of the structure of
memory. This point will be elaborated below.
ASSOCIATION AND PATTERN
   The model which I will propose is associative in the sense that it stores related elements near
each other (Kohonen, 1984; Palm, 1980). I have already suggested that mental process is
founded on induction and analogy, which arebased on pattern recognition. It follows from this
hypothesis that, from the point of view of mental process, two entities should be considered to be
associated if and only if they have patterns in common, or are bound together as the substrate of
a common pattern.
   As in Chapter 3, let IN(x,y;z) denote the intensity with which (x,y) is a pattern in z. Then the
network of emergence associated with a set of functions is a weighted graph of which the nodes
correspond to the functions, and in which each triple x, y an z is connected as follows
%
y %%%%%%%%%%%
%c %%%% x
z %%%%%%%%%%%
with weight c=IN(x,y;z). If IN(x,y;z)=0 then, of course, no zero-weight connection need actually
be drawn. The essential aspect of this diagram is that each of x, y and z holds a unique position.
    A structurally associative memory, associated with a set of functions, is also a weighted
graph. The nodes correspond to the functions, and the nodes are connected in triples. In these
respects it is similar to a network of emergence. But it need not possess the perfect structure of
the network of emergence. Rather, if it does not possess this perfect structure, it is required to
continually adjust itself so as to better approximate the structure of a network of emergence. It
may contain the same entity at many different places. It may adjust itself by connecting nodes
which were not previously connected, by adjusting the intensity of existing connections, or by
adding new nodes (representing new or old entities).
    The degree to which a graph is a structurally associative memory may be defined in a number
of ways, the simplest of which are of the form: 1/[1-c*(the amount by which the graph deviates
from the network-of-emergence structure)], where c is an appropriately chosen positive constant.
But there is no need to go into the details.
    From here on, I will occasionally refer to a structurally associative memory of this sort as a
STRAM. Imperfection in the structure of a STRAM may stem from two sources: imperfect
knowledge of the degrees to which a certain pair of functions is a pattern in other functions; or
imperfect reflection of this knowledge in the structure of the network. The former is a pattern
recognition problem and relates to the interconnection of cognition and memory, to be addressed
below. For now let us concentrate on the latter difficulty: given a certain set of data, how can a
structurally associative memory be intelligently reorganized?
    In practice, a structurally associative memory cannot be given an unlimited number of nodes,
and if it has a reasonably large number of nodes, then not every triple of nodes can be
interconnected. The number of connecting wires would very soon grow unmanageable. This is
the familiar combinatorialexplosion. To be practical, one must consider a fixed set of n nodes
each connected to a small number k of other nodes (say k=O(logn)), and one must arrange the
given functions among these nodes in such a way as to approximate the structure desired. When
a new function is created, it must take a node over from some other function; and likewise with a
new connection. This requires an intricate balancing; it is a difficult optimization problem. What
is required is a rapid iterative solution; an algorithm which is able to continually, incrementally
improve the structure of the memory while the memory is in use. We shall return to this in
Section 7.2.
Kaynak: A New Mathematical Model of Mind
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