Related papers: p-Adic Statistical Field Theory and Convolutional …
In these notes we explain how the CFT description of random matrix models can be used to perform actual calculations. Our basic example is the hermitian matrix model, reformulated as a conformal invariant theory of free fermions. We give an…
We show that a deep neural network (DNN) trained to construct a stochastic discount factor (SDF) admits a sharp additive decomposition that separates nonlinear characteristic discovery from the pricing rule that aggregates them. The…
Hopfield networks (HNs) and Restricted Boltzmann Machines (RBMs) are two important models at the interface of statistical physics, machine learning, and neuroscience. Recently, there has been interest in the relationship between HNs and…
We derive machine learning algorithms from discretized Euclidean field theories, making inference and learning possible within dynamics described by quantum field theory. Specifically, we demonstrate that the $\phi^{4}$ scalar field theory…
Inference from tabular data, collections of continuous and categorical variables organized into matrices, is a foundation for modern technology and science. Yet, in contrast to the explosive changes in the rest of AI, the best practice for…
This is the second of a series of papers outlining an approach to the classification of $\mathcal{N}{=}2$ superconformal field theories at rank 2 via a systematic analysis of their Coulomb branches, mathematically described by special…
Attempts to apply Neural Networks (NN) to a wide range of research problems have been ubiquitous and plentiful in recent literature. Particularly, the use of deep NNs for understanding complex physical and chemical phenomena has opened a…
Quantum Field Theory (QFT) represents a vast generalization of Quantum Mechanics (QM), as it deals with systems that have an infinite number of degrees of freedom. The Stone-von Neumann theorem, which establishes the equivalence of…
We study the problem of designing models for machine learning tasks defined on \emph{sets}. In contrast to traditional approach of operating on fixed dimensional vectors, we consider objective functions defined on sets that are invariant to…
Motivated by the three-dimensional topological field theory / two-dimensional conformal field theory (CFT) correspondence, we study a broad class of one-dimensional quantum mechanical models, known as anyonic chains, that can give rise to…
Accurate approximation of scalar-valued functions from sample points is a key task in computational science. Recently, machine learning with Deep Neural Networks (DNNs) has emerged as a promising tool for scientific computing, with…
Deep learning's success has been widely recognized in a variety of machine learning tasks, including image classification, audio recognition, and natural language processing. As an extension of deep learning beyond these domains, graph…
In this paper we begin mapping out the space of rank-2 $\mathcal{N}=2$ superconformal field theories (SCFTs) in four dimensions. This represents an ideal set of theories which can be potentially classified using purely quantum…
Materials engineering using atomistic modeling is an essential tool for the development of qubits and quantum sensors. Traditional density-functional theory (DFT) does however not adequately capture the complete physics involved, including…
Deep learning algorithms have made incredible strides in the past decade, yet due to their complexity, the science of deep learning remains in its early stages. Being an experimentally driven field, it is natural to seek a theory of deep…
Topological qauntum field theory(TQFT) is a very powerful theoretical tool to study topological phases and phase transitions. In $2+1$D, it is well known that the Chern-Simons theory captures all the universal topological data of…
We propose a novel class of neural network-like parametrized functions, i.e., general transformation neural networks (GTNNs), for high-dimensional approximation. Conventional deep neural networks sometimes perform less accurately on…
Understanding capabilities and limitations of different network architectures is of fundamental importance to machine learning. Bayesian inference on Gaussian processes has proven to be a viable approach for studying recurrent and deep…
Deep learning methods relying on multi-layered networks have been actively studied in a wide range of fields in recent years, and deep Boltzmann machines(DBMs) is one of them. In this study, a model of DBMs with some properites of weight…
This article is concerned with the numerical solution of subspace optimization problems, consisting of minimizing a smooth functional over the set of orthogonal projectors of fixed rank. Such problems are encountered in particular in…