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A hybrid quantum-classical method for learning Boltzmann machines (BM) for a generative and discriminative task is presented. Boltzmann machines are undirected graphs with a network of visible and hidden nodes where the former is used as…
We investigate how machine learning models acquire the ability to compose music and how musical information is internally represented within such models. We develop a composition algorithm based on a restricted Boltzmann machine (RBM), a…
A well-known technique in estimating probabilities of rare events in general and in information theory in particular (used, e.g., in the sphere-packing bound), is that of finding a reference probability measure under which the event of…
Recent work in unsupervised representation learning has focused on learning deep directed latent-variable models. Fitting these models by maximizing the marginal likelihood or evidence is typically intractable, thus a common approximation…
A restricted Boltzmann machine (RBM) is a two-layer neural network with shared weights and has been extensively studied for dimensionality reduction, data representation and recommendation systems in the literature. The traditional RBM…
The variational wave functions based on neural networks have recently started to be recognized as a powerful ansatz to represent quantum many-body states accurately. In order to show the usefulness of the method among all available…
Assuming an exponential power distribution is one way to deal with outliers in regression and clustering, which can increase the robustness of the analysis. Gaussian distribution is a special case of an exponential distribution. And an…
We compare and contrast the statistical physics and quantum physics inspired approaches for unsupervised generative modeling of classical data. The two approaches represent probabilities of observed data using energy-based models and…
Precise physical descriptions of molecules can be obtained by solving the Schrodinger equation; however, these calculations are intractable and even approximations can be cumbersome. Force fields, which estimate interatomic potentials based…
A restricted Boltzmann machine is a generative probabilistic graphic network. A probability of finding the network in a certain configuration is given by the Boltzmann distribution. Given training data, its learning is done by optimizing…
We consider restricted Boltzmann machines with a binary visible layer and a Gaussian hidden layer trained by an unlabelled dataset composed of noisy realizations of a single ground pattern. We develop a statistical mechanics framework to…
We proposed the expected energy-based restricted Boltzmann machine (EE-RBM) as a discriminative RBM method for classification. Two characteristics of the EE-RBM are that the output is unbounded and that the target value of correct…
This paper shows that large nonparametric classes of conditional multivariate densities can be approximated in the Kullback--Leibler distance by different specifications of finite mixtures of normal regressions in which normal means and…
Since learning is typically very slow in Boltzmann machines, there is a need to restrict connections within hidden layers. However, the resulting states of hidden units exhibit statistical dependencies. Based on this observation, we propose…
We discuss probabilistic neural networks with a fixed internal representation as models for machine understanding. Here understanding is intended as mapping data to an already existing representation which encodes an {\em a priori}…
Generalized linear mixed models are powerful tools for analyzing clustered data, where the unknown parameters are classically (and most commonly) estimated by the maximum likelihood and restricted maximum likelihood procedures. However,…
Generative neural networks can produce data samples according to the statistical properties of their training distribution. This feature can be used to test modern computational neuroscience hypotheses suggesting that spontaneous brain…
Autoregressive models (ARMs) currently constitute the dominant paradigm for large language models (LLMs). Energy-based models (EBMs) represent another class of models, which have historically been less prevalent in LLM development, yet…
A specific type of neural network, the Restricted Boltzmann Machine (RBM), is implemented for classification and feature detection in machine learning. RBM is characterized by separate layers of visible and hidden units, which are able to…
In this paper, we first present a new variant of Gaussian restricted Boltzmann machine (GRBM) called multivariate Gaussian restricted Boltzmann machine (MGRBM), with its definition and learning algorithm. Then we propose using a learned…