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Using Vectors to Store Items

If items are represented by orthogonal normal vectors we can create a form of memory by adding these vectors together.

Suppose we have three people represented by the vectors v, w, and x. We can form a memory by adding these:

M = v + w + x

To determine if a given item has been stored we calculate the dot product of the item with the memory vector.

w.M = w.(v + w + x)
= w.v + w.w + w.x
= 1

Alternately, if w was not stored the dot product would be 0.

Notice that a single layer network employing Hebbian learning and with a single output unit that is always on during learning is mathematically identical to the memory outlined above.

This is the task in the first set of exercises