Voltage-Mode Neural Network for the Solution of Linear Equations

Abstract

AbstractThis chapter starts with a discussion on the applicability of the standard Hopfield Neural Network (HNN) for the task of solving linear equations. It is demonstrated that the HNN in not suitable for such a task. Thereafter, a detailed study of the application of the Non-Linear Synapse Neural Network to the task of solving systems of simultaneous linear equations, is presented. The number of decision variables in the set of linear equations to be solved govern the number of neurons. For an n variable system of equations, n neurons connected through an interconnected non-linear feedback structure comprising of n comparators, are needed. By virtue of the non-linear feedback, a new energy function involving transcendental terms is obtained. This transcendental energy function is fundamentally different from the standard quadratic form associated with Hopfield network and its variants. Along with presenting the analysis of the NOSYNN-based linear equation solver circuit and proof of its energy function, it is also shown that the stable state of the network corresponds exactly with the solution of the given system of linear equations. Proper working of the network is ascertained by performing PSPICE simulations as well as actual hardware implementations on a breadboard using standard laboratory components.KeywordsLinear EquationEnergy FunctionOperational AmplifierConvergence TimeHopfield Neural NetworkThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.