Related papers: Anomalies in Neural Network Field Theory
These lectures on anomalies are relatively self-contained and intended for graduate students who are familiar with the basics of quantum field theory. We begin with several derivations of the abelian anomaly: anomalous transformation of the…
We explicitly construct the quantum field theory corresponding to a general class of deep neural networks encompassing both recurrent and feedforward architectures. We first consider the mean-field theory (MFT) obtained as the leading…
Physicists dating back to Feynman have lamented the difficulties of applying the variational principle to quantum field theories. In non-relativistic quantum field theories, the challenge is to parameterize and optimize over the infinitely…
Deep Learning using the eponymous deep neural networks (DNNs) has become an attractive approach towards various data-based problems of theoretical physics in the past decade. There has been a clear trend to deeper architectures containing…
Standard lore uses local anomalies to check the kinematic consistency of gauge theories coupled to chiral fermions, e.g. Standard Models (SM). Based on a systematic cobordism classification, we examine constraints from invertible quantum…
Convolutional Neural Networks (CNN) have been successful in processing data signals that are uniformly sampled in the spatial domain (e.g., images). However, most data signals do not natively exist on a grid, and in the process of being…
We introduce fermionic neural network field theories via Grassmann-valued neural networks. Free theories are obtained by a generalization of the Central Limit Theorem to Grassmann variables. This enables the realization of the free Dirac…
The precise equivalence between discretized Euclidean field theories and a certain class of probabilistic graphical models, namely the mathematical framework of Markov random fields, opens up the opportunity to investigate machine learning…
Deep neural networks (DNNs) are widely used in pattern-recognition tasks for which a human comprehensible, quantitative description of the data-generating process, e.g., in the form of equations, cannot be achieved. While doing so, DNNs…
Anomaly, a generic feature of relativistic quantum field theory, is shown to be present in non-relativistic classical ideal fluid. A new result is the presence of anomalous terms in current algebra, an obvious analogue of Schwinger terms…
A promising approach to improve climate-model simulations is to replace traditional subgrid parameterizations based on simplified physical models by machine learning algorithms that are data-driven. However, neural networks (NNs) often lead…
We propose tensorial neural networks (TNNs), a generalization of existing neural networks by extending tensor operations on low order operands to those on high order ones. The problem of parameter learning is challenging, as it corresponds…
Downward continuation is a critical task in potential field processing, including gravity and magnetic fields, which aims to transfer data from one observation surface to another that is closer to the source of the field. Its effectiveness…
An antithetical concept, adaptive symmetry, to conservative symmetry in physics is proposed to understand the deep neural networks (DNNs). It characterizes the invariance of variance, where a biotic system explores different pathways of…
Gauge theories have been a cornerstone of the description of the world at the level of the fundamental particles. The Lagrangian or the action describing the corresponding interactions is invariant under certain gauge transformations. This…
An approach to field theory is studied in which fields are comprised of $N$ constituent random neurons. Gaussian theories arise in the infinite-$N$ limit when neurons are independently distributed, via the Central Limit Theorem, while…
We study an $O(N)$ invariant surface defect in the Wilson-Fisher conformal field theory (CFT) in $d=4-\epsilon$ dimensions. This defect is defined by mass deformation on a two-dimensional surface that generates localized disorder and is…
One of the most prominent attributes of Neural Networks (NNs) constitutes their capability of learning to extract robust and descriptive features from high dimensional data, like images. Hence, such an ability renders their exploitation as…
Exploring the loss landscape offers insights into the inherent principles of deep neural networks (DNNs). Recent work suggests an additional asymmetry of the valley beyond the flat and sharp ones, yet without thoroughly examining its causes…
We derive the new identity in homotopy algebras which directly corresponds to the Schwinger-Dyson equations in quantum field theory. As an application, we derive the Ward-Takahashi identities. We demonstrate that the Ward-Takahashi…