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Fractional Brownian motion (fBm) features both randomness and strong scale-free correlations, challenging generative models to reproduce the intrinsic memory characterizing the underlying stochastic process. Here we examine a zoo of…

We derive relations between theoretical properties of restricted Boltzmann machines (RBMs), popular machine learning models which form the building blocks of deep learning models, and several natural notions from discrete mathematics and…

Restricted Boltzmann Machines (RBMs) are probabilistic generative models that can be trained by maximum likelihood in principle, but are usually trained by an approximate algorithm called Contrastive Divergence (CD) in practice. In general,…

Focusing on the grand-canonical extension of the ordinary restricted Boltzmann machine, we suggest an energy-based model for feature extraction that uses a layer of hidden units with varying size. By an appropriate choice of the chemical…

Restricted Boltzmann Machines (RBM) are bi-layer neural networks used for the unsupervised learning of model distributions from data. The bipartite architecture of RBM naturally defines an elegant sampling procedure, called Alternating…

Distributions of data or sensory stimuli often enjoy underlying invariances. How and to what extent those symmetries are captured by unsupervised learning methods is a relevant question in machine learning and in computational neuroscience.…

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…

Multi-modal magnetic resonance imaging (MRI) is essential for providing complementary information about brain anatomy and pathology, leading to more accurate diagnoses. However, obtaining high-quality multi-modal MRI in a clinical setting…

Restricted Boltzmann Machines (RBMs) are generative models designed to learn from data with a rich underlying structure. In this work, we explore a teacher-student setting where a student RBM learns from examples generated by a teacher RBM,…

We pursue an early stopping technique that helps Gaussian Restricted Boltzmann Machines (GRBMs) to gain good natural image representations in terms of overcompleteness and data fitting. GRBMs are widely considered as an unsuitable model for…

Unsupervised feature learning has shown impressive results for a wide range of input modalities, in particular for object classification tasks in computer vision. Using a large amount of unlabeled data, unsupervised feature learning methods…

Deep learning methods relying on multi-layered networks have been actively studied in a wide range of fields in recent years, and deep Boltzmann machines(DBMs) is one of them. In this study, a model of DBMs with some properites of weight…

Statistical analysis of evolutionary-related protein sequences provides insights about their structure, function, and history. We show that Restricted Boltzmann Machines (RBM), designed to learn complex high-dimensional data and their…

Deep generative models have become ubiquitous due to their ability to learn and sample from complex distributions. Despite the proliferation of various frameworks, the relationships among these models remain largely unexplored, a gap that…

We propose ratio divergence (RD) learning for discrete energy-based models, a method that utilizes both training data and a tractable target energy function. We apply RD learning to restricted Boltzmann machines (RBMs), which are a minimal…

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…

We propose Generative Probabilistic Image Colorization, a diffusion-based generative process that trains a sequence of probabilistic models to reverse each step of noise corruption. Given a line-drawing image as input, our method suggests…

Restricted Boltzmann machines (RBMs) are a class of neural networks that have been successfully employed as a variational ansatz for quantum many-body wave functions. Here, we develop an analytic method to study quantum many-body spin…

Training generative models to sample from unnormalized density functions is an important and challenging task in machine learning. Traditional training methods often rely on the reverse Kullback-Leibler (KL) divergence due to its…

Quantum generative models provide inherently efficient sampling strategies and thus show promise for achieving an advantage using quantum hardware. In this work, we investigate the barriers to the trainability of quantum generative models…