What is remembering in Hopfield network?

Question

Hopfield is a simple and traditional network. We feed into the network some patterns (Learning/Training). There is no training in Hopfield as the weight calculation adds up all the strength between neurons. The network goes into remembering mode by feeding a new unseen pattern (partially corrupted), and then the input is deactivated. The network iterates until it reaches a global or local minimum.

My question is that it finally remembers anything. It means that it remembers one of those patterns (combinations).

For example, we have five neurons. It remembers one of those $2^5=32$ patterns. So, one can say OK, this is what I am looking for, but it is not. What mechanism is available in the Hopfield network to check whether the found pattern is identical or similar to the input pattern?

Answer 1

The Hopfield net has no mechanism to check that the pattern that it generates in response to a stimulus pattern is the same or similar to any of the patterns in its "memory".

The "memorized" patterns are only attractors in the dynamics of the Hopfield net as it updates itself, in which the neurons influence each other. There is no guarantee that a Hopfield net will generate one of the original input patterns in response to any given stimulus pattern. In fact, Hopfield nets (the original kind from 1982) usually have attractors at many more patterns than the original input patterns: there's an attractor at the reverse of every original pattern (i.e. in which black and white pixels are swapped), and usually attractors at many patterns that include a mix of many of the original input patterns.