Complex-Valued Boltzmann Manifold

These days we can get massive information and it is hard to deal with it without computers. Machine learning is effective for computers to manage massive information. Machine learning uses various learning machine models, for instance, decision trees, Bayesian Networks, Support Vector Machine, Hidden Markov Model, normal mixed distributions, neural networks and so on. Some of them are stochastically constructed. The neural network is one of the learning machine models. It consists of many units, which are called neurons. We often use binary neurons. Then each neuron takes only two states. The set of neurons, however, takes many states. Various types of neural networks have been proposed. Feed-forward types and symmetric types of neural networks are main models. Feed-forward types of neural networks are often applied to recognize given patterns and are so useful. Symmetric types of neural network are often applied as Associative Memories. The Hopfield Network is one of the most famous models. Boltzmann Machines are stochastic types of Hopfield Networks. ABSTrACT