Square Neurons, Power Neurons, and Their Learning Algorithms

In this paper, we introduce the concepts of square neurons, power neu-rons, and new learning algorithms based on square neurons, and power neurons. First, we briefly review the basic idea of the Boltzmann Machine, specifically that the invariant distributions of the Boltzmann Machine generate Markov chains. We further review ABM (Attrasoft Boltzmann Machine). Next, we review the θ-transformation and its completeness, i.e. any function can be expanded by θ-transformation. The invariant distribution of the ABM is a θ-transformation; therefore, an ABM can simulate any distribution. We review the linear neurons and the associated learning algorithm. We then discuss the problems of the exponential neurons used in ABM, which are unstable, and the problems of the linear neurons, which do not discriminate the wrong answers from the right answers as sharply as the exponential neurons. Finally, we introduce the concept of square neurons and power neurons. We also discuss the advantages of the learning algorithms based on square neurons and power neurons, which have the stability of the linear neurons and the sharp discrimination of the exponential neurons.