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In the last two years, convolutional neural networks (CNNs) have achieved an impressive suite of results on standard recognition datasets and tasks. CNN-based features seem poised to quickly replace engineered representations, such as SIFT…

This paper presents two methods to compute scale anomaly coefficients in conformal field theories (CFTs), such as the c anomaly in four dimensions, in terms of the CFT data. We first use Euclidean position space to show that the anomaly…

We introduce the Fourier Learning Machine (FLM), a neural network (NN) architecture designed to represent a multidimensional nonharmonic Fourier series. The FLM uses a simple feedforward structure with cosine activation functions to learn…

The explicit computation of higher-point conformal blocks in any dimension is usually a challenging task. For two-dimensional conformal field theories in Euclidean signature, the oscillator formalism proves to be very efficient. We…

Conformal field theory (CFT) is an extremely powerful tool for explicitly computing critical exponents and correlation functions of statistical mechanics systems at a second order phase transition, or of condensed matter systems at a…

Although very successfully used in conventional machine learning, convolution based neural network architectures -- believed to be inconsistent in function space -- have been largely ignored in the context of learning solution operators of…

We study $S_N$-invariant four-point functions with two generic multi-cycle fields and two twist-2 fields, at the free orbifold point of the D1-D5 CFT. We derive the explicit factorization of these functions following from the action of the…

Extending previous work on 2 -- and 3 -- point functions, we study the 4 -- point function and its conformal block structure in conformal quantum mechanics CFT$_1$, which realizes the SO(2,1) symmetry group. Conformal covariance is…

Deep neural networks exhibit remarkable performance, yet their black-box nature limits their utility in fields like healthcare where interpretability is crucial. Existing explainability approaches often sacrifice accuracy and lack…

In conformal field theory in Minkowski momentum space, the 3-point correlation functions of local operators are completely fixed by symmetry. Using Ward identities together with the existence of a Lorentzian operator product expansion…

We use the correspondence between scalar field theory on $AdS_{d+1}$ and a conformal field theory on $R^d$ to calculate the 3- and 4-point functions of the latter. The classical scalar field theory action is evaluated at tree level.

Neural network field theory (NN-FT) formulates field theory in terms of a network architecture and a density on its parameters. We derive Schwinger--Dyson equations and Ward identities in NN-FT and utilize them to study anomalies. The…

The numerical emulation of quantum systems often requires an exponential number of degrees of freedom which translates to a computational bottleneck. Methods of machine learning have been used in adjacent fields for effective feature…

Modern machine learning models for computer vision exceed humans in accuracy on specific visual recognition tasks, notably on datasets like ImageNet. However, high accuracy can be achieved in many ways. The particular decision function…

Conformal nets are a mathematical model for conformal field theory, and defects between conformal nets are a model for an interaction or phase transition between two conformal field theories. In the preceding paper of this series, we…

Current research in Computer Vision has shown that Convolutional Neural Networks (CNN) give state-of-the-art performance in many classification tasks and Computer Vision problems. The embedding of CNN, which is the internal representation…

General principles of quantum field theory imply that there exists an operator product expansion (OPE) for Wightman functions in Minkowski momentum space that converges for arbitrary kinematics. This convergence is guaranteed to hold in the…

Coarse graining enables the investigation of molecular dynamics for larger systems and at longer timescales than is possible at atomic resolution. However, a coarse graining model must be formulated such that the conclusions we draw from it…

Working in the context of the proposed duality between 3D higher spin gravity and 2D W_N minimal model CFTs, we compute a class of four-point functions in the bulk and on the boundary, and demonstrate precise agreement between them. This is…

Supervised machine learning is emerging as a powerful computational tool to predict the properties of complex quantum systems at a limited computational cost. In this article, we quantify how accurately deep neural networks can learn the…