A theoretical investigation into the performance of the Hopfield model

An analysis is made of the behavior of the Hopfield model as a content-addressable memory (CAM) and as a method of solving the traveling salesman problem (TSP). The analysis is based on the geometry of the subspace set up by the degenerate eigenvalues of the connection matrix. The dynamic equation is shown to be equivalent to a projection of the input vector onto this subspace. In the case of content-addressable memory, it is shown that spurious fixed points can occur at any corner of the hypercube that is on or near the subspace spanned by the memory vectors. Analysed is why the network can frequently converge to an invalid solution when applied to the traveling salesman problem energy function. With these expressions, the network can be made robust and can reliably solve the traveling salesman problem with tour sizes of 50 cities or more.<
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