BIDIRECTIONAL LEARNING FOR NEURAL-NETWORK HAVING BUTTERFLY STRUCTURE

The number of interconnections between cells in a neural network, which is proportional to square of the number, causes a problem in the structure of the network when the number is large. The fast Fourier transform is a method to speed up matrix operation by using a butterfly operation. This paper proposes a method of reducing the number of connections between cells in a neural network by using a multilayer structure which is based on a butterfly operation. Since the neural network inevitably a multilayer structure, it is necessary to employ a new learning method which replaces the conventional backpropagation method. To satisfy this condition, this paper proposes an inverse function method which generates an intermediate target of learning in an inverse direction from a teacher signal at the last stage, and a bidirectional learning method which is an improvement of the inverse function method. The bidirectional learning method improves the learning effect, since the learning process is more stable than the inverse function method, and intermediate targets are generated taking into account the state of the output of each step. This is demonstrated by using a two-dimensional pattern transform problem.