Partial quantisation scheme for optimising the performance of hopfield network

Abstract

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The ideal Hopfield network would be able to remember information and recover the missing information based on what has been remembered. It is expected to have applications in areas such as associative memory, pattern recognition, optimisation computation, parallel implementation of VLSI and optical devices, but the lack of memory capacity and the tendency to generate pseudo-attractors make the network capable of handling only a very small amount of data. In order to make the network more widely used, we propose a scheme to optimise and improve its memory and resilience by introducing quantum perceptrons instead of Hebbian rules to complete its weight matrix design. Compared with the classical Hopfield network, our scheme increases the threshold of each node in the network while training the weights, and the memory space of the Hopfield network changes from being composed of the weight matrix only to being composed of the weight matrix and the threshold matrix together, resulting in a dimensional increase in the memory capacity of the network, which greatly solves the problem of the Hopfield network’s memory The problem of insufficient memory capacity and the tendency to generate pseudo-attractors was solved to a great extent. To verify the feasibility of the proposed scheme, we compare it with the classical Hopfield network in four different dimensions, namely, non-orthogonal simple matrix recovery, incomplete data recovery, memory capacity and model convergence speed. These experiments demonstrate that the improved Hopfield network with quantum perceptron has significant advantages over the classical Hopfield network in terms of memory capacity and recovery ability, which provides a possibility for practical application of the network.

Keywords

• hopfield network
• weight matrix
• quantum perceptron
• storage capacity
• recovery capability