Related papers: Maximal Entropy Formalism and the Restricted Boltz…
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 endowed with the universal power of modeling (binary) joint distributions. Meanwhile, as a result of their confining network structure, training RBMs confronts less difficulties (compared with more…
We investigate the efficiency of the recently proposed Restricted Boltzmann Machine (RBM) representation of quantum many-body states to study both the static properties and quantum spin dynamics in the two-dimensional Heisenberg model on a…
Virtually, every ab-initio electronic structure method (Coupled Cluster, DMRG, etc.) can be viewed as an algorithm to compress the ground-state wavefunction. This compression is usually obtained by exploiting some physical structure of the…
Restricted Boltzmann Machines (RBMs) offer a versatile architecture for unsupervised machine learning that can in principle approximate any target probability distribution with arbitrary accuracy. However, the RBM model is usually not…
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…
We consider a special type of Restricted Boltzmann machine (RBM), namely a Gaussian-spherical RBM where the visible units have Gaussian priors while the vector of hidden variables is constrained to stay on an ${\mathbbm L}_2$ sphere. The…
We introduce a method for imposing higher-level structure on generated, polyphonic music. A Convolutional Restricted Boltzmann Machine (C-RBM) as a generative model is combined with gradient descent constraint optimisation to provide…
Maximum entropy method for analytic continuation is extended by introducing quantum relative entropy. This new method is formulated in terms of matrix-valued functions and therefore invariant under arbitrary unitary transformation of input…
We consider an entropy-regularized version of optimal density control of deterministic discrete-time linear systems. Entropy regularization, or a maximum entropy (MaxEnt) method for optimal control has attracted much attention especially in…
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…
The experimental realization of increasingly complex synthetic quantum systems calls for the development of general theoretical methods, to validate and fully exploit quantum resources. Quantum-state tomography (QST) aims at reconstructing…
Neural-network state representations of quantum many-body systems are attracting great attention and more rigorous quantitative analysis about their expressibility and complexity is warranted. Our analysis of the restricted Boltzmann…
Maximum entropy modeling is a flexible and popular framework for formulating statistical models given partial knowledge. In this paper, rather than the traditional method of optimizing over the continuous density directly, we learn a smooth…
When working with quantum states, analysis of the final quantum state generated through probabilistic measurements is essential. This analysis is typically conducted by constructing the density matrix from either partial or full tomography…
Restricted Boltzmann Machine (RBM) is an importan- t generative model modeling vectorial data. While applying an RBM in practice to images, the data have to be vec- torized. This results in high-dimensional data and valu- able spatial…
We revisit the classical problem of inverting dimension-reducing linear mappings using the maximum entropy (MaxEnt) criterion. In the literature, solutions are problem-dependent, inconsistent, and use different entropy measures. We propose…
Neural-Network Quantum State (NQS) has attracted significant interests as a powerful wave-function ansatz to model quantum phenomena. In particular, a variant of NQS based on the restricted Boltzmann machine (RBM) has been adapted to model…
Graphical models are powerful tools for modeling high-dimensional data, but learning graphical models in the presence of latent variables is well-known to be difficult. In this work we give new results for learning Restricted Boltzmann…
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…