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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…

Modern datasets are becoming heterogeneous. To this end, we present in this paper Mixed-Variate Restricted Boltzmann Machines for simultaneously modelling variables of multiple types and modalities, including binary and continuous…

Artificial spin ice (ASI) are arrays on nanoscaled magnets that can serve both as models for frustration in atomic spin ice as well as for exploring new spin-wave-based strategies to transmit, process, and store information. Here, we…

Artificial spin-ice systems, consisting of arrays of interacting ferromagnetic nanoelements, offer a versatile platform for reconfigurable magnonics with potential in GHz logic and neuromorphic computing. However, weak dipolar coupling…

Restricted Boltzmann machines (RBM) are generative models capable to learn data with a rich underlying structure. We study the teacher-student setting where a student RBM learns structured data generated by a teacher RBM. The amount of…

The Restricted Boltzmann Machine (RBM), an important tool used in machine learning in particular for unsupervized learning tasks, is investigated from the perspective of its spectral properties. Starting from empirical observations, we…

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…

Geometric frustration gives rise to emergent quantum phenomena and exotic phases of matter. While Monte Carlo methods are traditionally used to simulate such systems, their sampling efficiency is limited by the complexity of interactions…

Strongly-interacting nanomagnetic arrays are finding increasing use as model host systems for reconfigurable magnonics. The strong inter-element coupling allows for stark spectral differences across a broad microstate space due to shifts in…

Prior distributions of binarized natural images are learned by using a Boltzmann machine. According the results of this study, there emerges a structure with two sublattices in the interactions, and the nearest-neighbor and…

The deep extension of the restricted Boltzmann machine (RBM), known as the deep Boltzmann machine (DBM), is an expressive family of machine learning models which can serve as compact representations of complex probability distributions.…

Graphical models are a rich language for describing high-dimensional distributions in terms of their dependence structure. While there are algorithms with provable guarantees for learning undirected graphical models in a variety of…

Frustrated arrays of interacting single-domain nanomagnets provide important model systems for statistical mechanics, because they map closely onto well-studied vertex models and are amenable to direct imaging and custom engineering.…

The analysis of mixed data has been raising challenges in statistics and machine learning. One of two most prominent challenges is to develop new statistical techniques and methodologies to effectively handle mixed data by making the data…

It is widely known that Boltzmann machines are capable of representing arbitrary probability distributions over the values of their visible neurons, given enough hidden ones. However, sampling -- and thus training -- these models can be…

The restricted Boltzmann machine is a graphical model for binary random variables. Based on a complete bipartite graph separating hidden and observed variables, it is the binary analog to the factor analysis model. We study this graphical…

Complex behavior poses challenges in extracting models from experiment. An example is spin liquid formation in frustrated magnets like Dy$_2$Ti$_2$O$_7$. Understanding has been hindered by issues including disorder, glass formation, and…

Nanomagnetic logic, which makes use of arrays of dipolar-coupled single domain nanomagnets for computation, holds promise as a low power alternative to traditional computation with CMOS. Beyond the use of nanomagnets for Boolean logic,…

Lifting operators play an important role in starting a kinetic Boltzmann model from given macroscopic information. The macroscopic variables need to be mapped to the distribution functions, mesoscopic variables of the Boltzmann model. A…

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…