Oh, D.H., J.H. Nang, H. Yoon and S.R. Maeng, An efficient mapping of Boltzmann Machine computations onto distributedmemory multiprocessors, Microprocessing and Microprogramming 33 (1991/92) 223-236. In this paper, an efficient mapping scheme of Boltzmann Machine computations onto a distributed-memory multiprocessor, which exploits the synchronous spatial parallelism, is presented. In this schem...

A general Boltzmann machine with continuous visible and discrete integer valued hidden states is introduced. Under mild assumptions about the connection matrices, the probability density function of the visible units can be solved for analytically, yielding a novel parametric density function involving a ratio of Riemann-Theta functions. The conditional expectation of a hidden state for given v...

The nonnegative Boltzmann machine (NNBM) is a recurrent neural network model that can describe multimodal nonnegative data. Application of maximum likelihood estimation to this model gives a learning rule that is analogous to the binary Boltzmann machine. We examine the utility of the mean field approximation for the NNBM, and describe how Monte Carlo sampling techniques can be used to learn th...

The subspace Restricted Boltzmann Machine (subspaceRBM) is a third-order Boltzmann machine where multiplicative interactions are between one visible and two hidden units. There are two kinds of hidden units, namely, gate units and subspace units. The subspace units reflect variations of a pattern in data and the gate unit is responsible for activating the subspace units. Additionally, the gate ...

We introduce the spike and slab Restricted Boltzmann Machine, characterized by having both a real-valued vector, the slab, and a binary variable, the spike, associated with each unit in the hidden layer. The model possesses some practical properties such as being amenable to Block Gibbs sampling as well as being capable of generating similar latent representations of the data to the recently in...

The chaotic Boltzmann machine proposed in this paper is a chaotic pseudo-billiard system that works as a Boltzmann machine. Chaotic Boltzmann machines are shown numerically to have computing abilities comparable to conventional (stochastic) Boltzmann machines. Since no randomness is required, efficient hardware implementation is expected. Moreover, the ferromagnetic phase transition of the Isin...

Boltzmann machine, as a fundamental construction block of deep belief network and deep Boltzmann machines, is widely used in deep learning community and great success has been achieved. However, theoretical understanding of many aspects of it is still far from clear. In this paper, we studied the Rademacher complexity of both the asymptotic restricted Boltzmann machine and the practical impleme...

In this paper, we consider the asymptotic form of the generalization error for the restricted Boltzmann machine in Bayesian estimation. It has been shown that obtaining the maximum pole of zeta functions is related to the asymptotic form of the generalization error for hierarchical learning models (Watanabe, 2001a,b). The zeta function is defined by using a Kullback function. We use two methods...

We present a fast implementation of the Boltzmann Machine based on specialized hardware. This realization faithfully implements the machine; in particular, it avoids the excess parallelism which makes other fast implementations of it only approximate. The current prototype performs 505 million additions and multiplications (or megasynapses) per second. It can emulate the fully connected Boltzma...