Hopfield Model on Incomplete Graphs
We consider the Hopfield model on graphs. Specifically we compare five different incomplete graphs on 4 or 5 vertices’s including a cycle, a path and a star. Provided is a proof of the Hamiltonian being monotonically decreasing under asynchronous network dynamics. This result is applied to the treated incomplete graphs to derive exact values for the incre- mental drop in energy on pattern sizes 2,