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These notes are an elementary introduction to supersymmetric quantum mechanics for students of mathematics. We start from the very basic concepts of quantum mechanics and proceed to construct a realization of Heisenberg's superalgebra as a…
This lecture note is intended to prepare early-year master's and PhD students in data science or a related discipline with foundational ideas in machine learning. It starts with basic ideas in modern machine learning with classification as…
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…
We present a novel self-taught framework for unsupervised metric learning, which alternates between predicting class-equivalence relations between data through a moving average of an embedding model and learning the model with the predicted…
This paper reports a novel method for supervised machine learning based on the mathematical formalism that supports quantum mechanics. The method uses projective quantum measurement as a way of building a prediction function. Specifically,…
Automated analyses of the outcome of a simulation have been an important part of atomistic modeling since the early days, addressing the need of linking the behavior of individual atoms and the collective properties that are usually the…
Quantum computing leverages quantum effects to build algorithms that are faster then their classical variants. In machine learning, for a given model architecture, the speed of training the model is typically determined by the size of the…
This is an introductory machine-learning course specifically developed with STEM students in mind. Our goal is to provide the interested reader with the basics to employ machine learning in their own projects and to familiarize themself…
Estimating the parameters of a model describing a set of observations using a neural network is in general solved in a supervised way. In cases when we do not have access to the model's true parameters this approach can not be applied.…
We consider dense, associative neural-networks trained by a teacher (i.e., with supervision) and we investigate their computational capabilities analytically, via statistical-mechanics of spin glasses, and numerically, via Monte Carlo…
This is an expanded version of the notes to a course taught by the first author at the 1995 Les Houches Summer School. Constraints on a tentative reconciliation of quantum theory and general relativity are reviewed. It is explained what…
Quantum machine learning is an emerging field that combines machine learning with advances in quantum technologies. Many works have suggested great possibilities of using near-term quantum hardware in supervised learning. Motivated by these…
The original problem of supervised classification considers the task of automatically assigning objects to their respective classes on the basis of numerical measurements derived from these objects. Classifiers are the tools that implement…
This is an extended and corrected version of lecture notes originally written for a one semester course at Leibniz University Hannover. The main aim of the notes is to give an introduction to the mathematical methods used in describing…
The success of deep networks in medical image segmentation relies heavily on massive labeled training data. However, acquiring dense annotations is a time-consuming process. Weakly-supervised methods normally employ less expensive forms of…
These lecture notes consist of an introduction to moduli spaces in algebraic geometry, with a strong emphasis placed on examples related to the theory of quiver representations. The goal is to provide the background necessary to understand…
In this paper, we address two challenging problems in unsupervised subspace learning: 1) how to automatically identify the feature dimension of the learned subspace (i.e., automatic subspace learning), and 2) how to learn the underlying…
These lecture notes are devoted to the theory of equations of associativity describing geometry of moduli spaces of 2D topological field theories. Introduction. Lecture 1. WDVV equations and Frobenius manifolds. {Appendix A.} Polynomial…
These brief lecture notes cover the basics of neural networks and deep learning as well as their applications in the quantum domain, for physicists without prior knowledge. In the first part, we describe training using backpropagation,…
Recently, the authors introduced the theory of high-arity PAC learning, which is well-suited for learning graphs, hypergraphs and relational structures. In the same initial work, the authors proved a high-arity analogue of the Fundamental…