Parallel and distributed processing - I: Interactive activation and competition models
PDP Model Development
This model is illustrated by the help of Jets and Sharks database described in [McClelland, 1981] and also given in the following table.
An interactive activation and competition network consists of a collection of processing units organized into some number of competitive pools. There are excitatory connections among units in different pools and inhibitory connections among units within the same pool. The excitatory connections between pools are generally bidirectional, thereby making the processing interactive in the sense that processing in each pool both influences and is influenced by processing in other pools. Within a pool, the inhibitory connections are usually assumed to run from each unit in the pool to every other unit in the pool. This implements a kind of competition among the units such that the unit or units in the pool that receive the strongest activation tend to drive down the activation of the other units. The information about such a data, if stored in a computer memory, can be accessed by name or by any other set of items which can serve as a key to a particular set of information. But this requires the method of access to be pre-programmed in the system. Moreover, certain characteristics of the data like the distribution of persons in different age groups or the 'common' characteristics among some persons, etc, can be obtained only by programming explicitly to derive the information embedded in the data. In other words, any information in the data has to be sought explicitly. On the other hand human memory stores the information in the data in terms of patterns, and these patterns are useful to recall information even with partial clues. These features of the human memory can be demonstrated through representation in the form of a Parallel and Distributed Processing model, as shown in the figure below.
In the figure, the units are organized into different pools, such as 'Name' pool, 'Age' pool, etc. The number of units in each pool corresponds to different possibilities in that category, as for example, 27 units in the 'Name' pool and 3 units in the 'Age' pool, etc. There are as many pools as there are categories (6 in this case), plus one additional pool called the 'Instance' pool.
PDP Model Description
Units within each pool are connected in an inhibitory manner, i.e., the output of each unit is fed with a negative weight to all other units in the same pool. The units in each pool are connected to the corresponding units in the instance pool in an excitatory manner, i.e., the connection weights are positive. For example, here, the 'Ralph' unit in the 'Name' pool, 'Jets' unit in the 'Gang' pool, 'in 30s' unit in the 'Age' pool, 'JH' unit in the 'Education' pool, 'pusher' unit in the 'Occupation' pool and 'Unmarried' unit in the 'Marital status' pool are all connected to the 'Ralph' unit in the 'instance' pool with positive weights. The units in the 'instance' pool are called "hidden" units, since by design, they are not accessible for any input or output. The units in all other pools are "visible" units. Only 5 of 27 units are shown in the 'Name' pool and the 'instance' pool for illustration. Also, the inhibitory connections within each pool are not shown in the figure.
There are a total of 68 units in the model. Each unit computes a weighted sum of the input values to the unit fed from other units, as well as from external inputs, if any. The weighted sum or the activation value is passed through a nonlinear output function, which gives as output the activation value itself, if the sum lies between some prespecified minimum and maximum values. Otherwise, the function gives either the minimum value at the lower limit or the maximum value at the upper limit. The state of the model is described as the collection of outputs of all the 68 units at any given instant of time. Starting from any state, the next state can be computed by selecting a unit at random and computing the weighted sum of its inputs first and then the output of the unit. Due to change in the value of the output of this unit, the model goes to a different state. Then another unit is selected at random, and the new state for that unit is determined. All the units are updated by selecting the units in a random sequence, to compute one cycle of activation dynamics. After several cycles, the model is guaranteed to reach a stable equilibrium state, when there will not be any further change in the state of the model.
For each set of external inputs, the model reaches a stable state eventually. From the stable state the stored data can be read out. For example, if we want the data about 'Ralph', the output (state) of the 'Ralph' unit in the 'Name' pool is set to maximum. Starting with some initial values of state on other units, the network states are computed for several cycles, until an equilibrium state is reached. At equilibrium, there will be one unit in each pool having large positive value. Those units correspond to the data that belongs to 'Ralph'.
Features Demonstrated By The Model
The model demonstrates several features of the functioning of the
biological neural network in human memory. Some of the features
are: (a) Retrieving an individual's data from his name, (b) retrieval
from a partial description, (c) graceful degradation, (d) default
assignment, and (e) spontaneous generalization for novel inputs. The
most important point is that the model stores the patterns embedded
in the given data. Therefore from the model, one could get even such
information for which the model was not explicitly designed. For
example, in the feature of default assignment, the model gives
possible good guess about missing information, even though we do
not know certain things about an individual. It evaluates the relative
strengths of the attributes from the given data in a complex manner,
which is difficult to describe explicitly. Thus, this model clearly brings
out the distinction between computer memory and human memory
for storage and retrieval of information. The model also brings out
the features of content-addressable memories and associative
memories for information retrieval. Note the distributed nature of the
memory in this model, in the sense that, the information is distributed
in the weights throughout the network. Also note the parallel and
distributed nature of the activation dynamics when the model is
realized in hardware, and also when it is allowed to relax naturally
changing from one state to another until an equilibrium state is
reached from the given initial state and external input.
Spontaneous generalization is the ability to provide a generalized picture of what is common to the memories that match the cues which are too vague to match a particular memory.
If weights between i'th and j'th components is +ve,
q = weight * activation
excitation += q for all units.
if weights between i'th and j'th components is -ve,
q = weight * activation
inhibition += q for all units.
net input = (estr * external input) + (beta * excitation) + (gamma * inhibition)
delta excitation = (actmax - activation) * net input - decay * (activation - actrest)
activation += delta excitation
g Delta = g Delta + absolute(delta excitation)
delta inhibition = (activation - actmin) * net input - decay * (activation - actrest);
activation += delta inhibition;
g Delta = g Delta + absolute(delta inhibiton);
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