Related papers: Geometry of the restricted Boltzmann machine

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…

Stochastic models share many characteristics with generic parametric models. In some ways they can be regarded as a special case. But for stochastic models there is a notion of weak distribution or generalised random variable, and the same…

Restricted Boltzmann machines (RBMs) have demonstrated considerable success as variational quantum states; however, their representational power remains incompletely understood. In this work, we present an analytical proof that RBMs can…

Learning invariant representations is a critical task in computer vision. In this paper, we propose the Theta-Restricted Boltzmann Machine ({\theta}-RBM in short), which builds upon the original RBM formulation and injects the notion of…

We investigate the potential of a restricted Boltzmann Machine (RBM) for discriminative representation learning. By imposing the class information preservation constraints on the hidden layer of the RBM, we propose a Signed Laplacian…

A class of deep Boltzmann machines is considered in the simplified framework of a quenched system with Gaussian noise and independent entries. The quenched pressure of a $K$-layers spin glass model is studied allowing interactions only…

Large-scale electrophysiological recordings now allow simultaneous monitoring of thousands of neurons across multiple brain regions, revealing structured variability in neural population activity. Understanding how these collective patterns…

Generative modeling with machine learning has provided a new perspective on the data-driven task of reconstructing quantum states from a set of qubit measurements. As increasingly large experimental quantum devices are built in…

Neural networks have been recently proposed as variational wave functions for quantum many-body systems [G. Carleo and M. Troyer, Science 355, 602 (2017)]. In this work, we focus on a specific architecture, known as Restricted Boltzmann…

In this paper we present a fully deterministic method for the numerical solution to the Boltzmann equation of rarefied gas dynamics in a bounded domain for multi-scale problems. Periodic, specular reflection and diffusive boundary…

Estimation of Distribution Algorithms (EDAs) require flexible probability models that can be efficiently learned and sampled. Restricted Boltzmann Machines (RBMs) are generative neural networks with these desired properties. We integrate an…

A restricted Boltzmann machine (RBM) learns a probability distribution over its input samples and has numerous uses like dimensionality reduction, classification and generative modeling. Conventional RBMs accept vectorized data that…

We propose a method to decrease the number of hidden units of the restricted Boltzmann machine while avoiding decrease of the performance measured by the Kullback-Leibler divergence. Then, we demonstrate our algorithm by using numerical…

The linearized collision operator of the Boltzmann equation for single species can be written as a sum of a positive multiplication operator, the collision frequency, and a compact integral operator. This classical result has more recently,…

In this paper, we consider the Boltzmann equation with respect to orthonormal vielbein fields in conservative form. This formalism allows the use of arbitrary coordinate systems to describe the space geometry, as well as of an adapted…

Boltzmann machines (BMs) are powerful energy-based generative models, but their heavy training cost has largely confined practical use to Restricted BMs (RBMs) trained with an efficient learning method called contrastive divergence. More…

Restricted Boltzmann machines (RBMs) are powerful machine learning models, but learning and some kinds of inference in the model require sampling-based approximations, which, in classical digital computers, are implemented using expensive…

We show that the visible sector probability density function of the Riemann-Theta Boltzmann machine corresponds to a gaussian mixture model consisting of an infinite number of component multi-variate gaussians. The weights of the mixture…

The probability density function for the visible sector of a Riemann-Theta Boltzmann machine can be taken conditional on a subset of the visible units. We derive that the corresponding conditional density function is given by a…

The success of any machine learning system depends critically on effective representations of data. In many cases, it is desirable that a representation scheme uncovers the parts-based, additive nature of the data. Of current representation…