Related papers: Riemann-Theta Boltzmann Machine

The brain must robustly store a large number of memories, corresponding to the many events encountered over a lifetime. However, the number of memory states in existing neural network models either grows weakly with network size or recall…

We consider probabilistic systems with hidden state and unobservable transitions, an extension of Hidden Markov Models (HMMs) that in particular admits unobservable {\epsilon}-transitions (also called null transitions), allowing state…

Artificial neural networks (NNs) have become the de facto standard in machine learning. They allow learning highly nonlinear transformations in a plethora of applications. However, NNs usually only provide point estimates without…

A Hadamard-Hitchcock decomposition of a multidimensional array is a decomposition that expresses the latter as a Hadamard product of several tensor rank decompositions. Such decompositions can encode probability distributions that arise…

Generative semantic hashing is a promising technique for large-scale information retrieval thanks to its fast retrieval speed and small memory footprint. For the tractability of training, existing generative-hashing methods mostly assume a…

The Extreme Learning Machine (ELM) is a single-hidden layer feedforward neural network (SLFN) learning algorithm that can learn effectively and quickly. The ELM training phase assigns the input weights and bias randomly and does not change…

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 computationally efficient method for online joint state inference and dynamical model learning is presented. The dynamical model combines an a priori known, physically derived, state-space model with a radial basis function expansion…

A Restricted Boltzmann Machine (RBM) is an unsupervised machine-learning bipartite graphical model that jointly learns a probability distribution over data and extracts their relevant statistical features. As such, RBM were recently…

The Riemann Hypothesis can be reformulated as statements about the eigenvalues of certain matrices whose entries are defined in terms of the Taylor coefficients of the zeta function. These eigenvalues exhibit interesting visual patterns…

We successfully model the behavior of two-spin systems using neural networks known as conditional Restricted Boltzmann Machines (cRBMs) which encode physical information in the properties of a thermal ensemble akin to an Ising model. The…

Reinforcement learning aims to learn optimal policies from interaction with environments whose dynamics are unknown. Many methods rely on the approximation of a value function to derive near-optimal policies. In partially observable…

This article explores the use of machine learning models to build a market generator. The underlying idea is to simulate artificial multi-dimensional financial time series, whose statistical properties are the same as those observed in the…

We study the Riemannian geometry of the Deep Linear Network (DLN) as a foundation for a thermodynamic description of the learning process. The main tools are the use of group actions to analyze overparametrization and the use of Riemannian…

Efficient sampling of unnormalized probability densities such as the Boltzmann distribution of molecular systems is a longstanding challenge. Next to conventional approaches like molecular dynamics or Markov chain Monte Carlo, variational…

These lecture notes introduce some topics of classical statistical physics, particularly those that are relevant for neural networks and deep learning. Statistical physics is treated as a branch of probability theory or statistics, with the…

Investigating the dynamics of learning in machine learning algorithms is of paramount importance for understanding how and why an approach may be successful. The tools of physics and statistics provide a robust setting for such…

We consider the problem of parameter estimation for the partially observed linear stochastic differential equation. We assume that the unobserved Ornstein-Uhlenbeck process depends on some unknown parameter and estimate the unobserved…

Learning RBMs using standard algorithms such as CD(k) involves gradient descent on the negative log-likelihood. One of the terms in the gradient, which involves expectation w.r.t. the model distribution, is intractable and is obtained…

Given a physical quantum system described by a Hilbert H, for any bounded quantum observable (a bounded self-adjoint operator) T it is possible to define several ''hidden observable'' functions f:H->R associated to T and for any quantum…