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In condensed matter physics, one of the goals of machine learning is the classification of phases of matter. The consideration of a system's symmetries can significantly assist the machine in this goal. We demonstrate the ability of an…

The study of topological properties by machine learning approaches has attracted considerable interest recently. Here we propose machine learning the topological invariants that are unique in non-Hermitian systems. Specifically, we train…

We show that the mutual information between the representation of a learning machine and the hidden features that it extracts from data is bounded from below by the relevance, which is the entropy of the model's energy distribution. Models…

These are lecture notes for a course on machine learning with neural networks for scientists and engineers that I have given at Gothenburg University and Chalmers Technical University in Gothenburg, Sweden. The material is organised into…

Data and knowledge representation are fundamental concepts in machine learning. The quality of the representation impacts the performance of the learning model directly. Feature learning transforms or enhances raw data to structures that…

Unsupervised learning of hidden representations has been one of the most vibrant research directions in machine learning in recent years. In this work we study the brain-like Bayesian Confidence Propagating Neural Network (BCPNN) model,…

In this work, we begin by questioning the existence of a new kind of nonergodic extended phase, namely, the many-body critical (MBC) phase in finite systems of an interacting quasiperiodic system. We find that this phase can be separately…

We consider the problem of inferring the probability distribution of flux configurations in metabolic network models from empirical flux data. For the simple case in which experimental averages are to be retrieved, data are described by a…

Non-extensive systems do not allow to go to the thermodynamic limit. Therefore we have to reformulate statistical mechanics without invoking the thermodynamical limit. I.e. we have to go back to Pre-Gibbsian times. We show that Boltzmann's…

Training a neural network with a large labeled dataset is still a dominant paradigm in computational histopathology. However, obtaining such exhaustive manual annotations is often expensive, laborious, and prone to inter and Intra-observer…

The gap between our ability to collect interesting data and our ability to analyze these data is growing at an unprecedented rate. Recent algorithmic attempts to fill this gap have employed unsupervised tools to discover structure in data.…

A central problem in machine learning involves modeling complex data-sets using highly flexible families of probability distributions in which learning, sampling, inference, and evaluation are still analytically or computationally…

Experimental data bases are typically very large and high dimensional. To learn from them requires to recognize important features (a pattern), often present at scales different to that of the recorded data. Following the experience…

The traditional approach of statistical physics to supervised learning routinely assumes unrealistic generative models for the data: usually inputs are independent random variables, uncorrelated with their labels. Only recently, statistical…

Machine-learning driven models have proven to be powerful tools for the identification of phases of matter. In particular, unsupervised methods hold the promise to help discover new phases of matter without the need for any prior…

Restricted Boltzmann machines (RBMs) are a powerful class of generative models, but their training requires computing a gradient that, unlike supervised backpropagation on typical loss functions, is notoriously difficult even to…

Unsupervised pretraining, which learns a useful representation using a large amount of unlabeled data to facilitate the learning of downstream tasks, is a critical component of modern large-scale machine learning systems. Despite its…

We develop a supervised machine learning algorithm that is able to learn topological phases of finite condensed matter systems from bulk data in real lattice space. The algorithm employs diagonalization in real space together with any…

This is a tutorial and survey paper on Boltzmann Machine (BM), Restricted Boltzmann Machine (RBM), and Deep Belief Network (DBN). We start with the required background on probabilistic graphical models, Markov random field, Gibbs sampling,…

This study develops an unsupervised learning algorithm for products of expert capsules with dynamic routing. Analogous to binary-valued neurons in Restricted Boltzmann Machines, the magnitude of a squashed capsule firing takes values…