Chapter 2. Prehension

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units. Also, we assume n input lines, each of which connects to all
the output units. The input and outputs both consist of real numbers,
although much of what’s said will apply to binary neurons as well.
The topology is shown in Figure C.8. Note that there are n2
connection weights, since each input connects to each output.
Questions regarding this type of network include:
1) given the patterns to be stored, how are the connection weights
set to produce the desired behavior?
2) what is the network’s capacity (i.e., how many input/output
pairs can it ‘store’)?
3) are there any restrictions on what the patterns can be?
Inputs
Figure C.8. Heteroassociative memory with four inputs and four
outputs.
Since each unit is a linear summer, its output is the dot product of
its input and the vector of connection weights impinging on it; i.e. for
unit i, the incoming weights are wij, j= 1 to n, and the output is:
where I is the input vector and 0 is the output vector. If Wi is a row
vector of weights for neuron i, then
If W is the matrix of weights for the whole memory (i.e., the ith row
is wi), then the behavior of the memory can be written