相关论文: Neural Network Quantum Field Theory from Transform…

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…

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…

Transformers have become the dominant architecture in modern machine learning, yet the theoretical understanding of their training dynamics remains limited. This paper develops a rigorous mathematical framework for analyzing gradient-based…

The correlation matrix is a central representation of functional brain networks in neuroimaging. Traditional analyses often treat pairwise interactions independently in a Euclidean setting, overlooking the intrinsic geometry of correlation…

In a recent work arXiv:2008.08601, Halverson, Maiti and Stoner proposed a description of neural networks in terms of a Wilsonian effective field theory. The infinite-width limit is mapped to a free field theory, while finite $N$ corrections…

Neural Network Field Theories (NN-FTs) represent a novel construction of arbitrary field theories, including those of conformal fields, through the specification of the network architecture and prior distribution for the network parameters.…

Quantum neural networks (QNNs) have emerged as a leading strategy to establish applications in machine learning, chemistry, and optimization. While the applications of QNN have been widely investigated, its theoretical foundation remains…

We introduce Quantum Graph Attention Networks (QGATs) as trainable quantum encoders for inductive learning on graphs, extending the Quantum Graph Neural Networks (QGNN) framework. QGATs leverage parameterized quantum circuits to encode node…

In the canonical approach of loop quantum gravity, arguably the most important outstanding problem is finding and interpreting solutions to the Hamiltonian constraint. In this work, we demonstrate that methods of machine learning are in…

We present a variational neural network approach for solving quantum field theories in the field basis, focusing on the free Klein-Gordon model formulated in momentum space. While recent studies have explored neural-network-based…

Quantum neural networks (QNNs) leverage quantum entanglement and superposition to enable large-scale parallel linear computation, offering a potential solution to the scalability limits of classical deep learning. However, their practical…

We introduce novel methods for implementing generic quantum information within a scale-free architecture. For a given observable system, we show how observational outcomes are taken to be finite bit strings induced by measurement operators…

We review the solutions of O(N) and U(N) quantum field theories in the large $N$ limit and as 1/N expansions, in the case of vector representations. Since invariant composite fields have small fluctuations for large $N$, the method relies…

The rapid development of neural quantum states (NQS) has established it as a promising framework for studying quantum many-body systems. In this work, by leveraging the cutting-edge transformer-based architectures and developing highly…

We present a new approach to computing event shape distributions or, more precisely, charge flow correlations in a generic conformal field theory (CFT). These infrared finite observables are familiar from collider physics studies and…

Quantum gravity is studied nonperturbatively in the case in which space has a boundary with finite area. A natural set of boundary conditions is studied in the Euclidean signature theory, in which the pullback of the curvature to the…

The recent success of neural networks as implicit representation of data has driven growing interest in neural functionals: models that can process other neural networks as input by operating directly over their weight spaces. Nevertheless,…

A framework allowing for perturbative calculations to be carried out for quantum field theories with arbitrary smoothly curved boundaries is described. It is based on an expansion of the heat kernel derived earlier for arbitrary mixed…

Our work intends to show that: (1) Quantum Neural Networks (QNN) can be mapped onto spinnetworks, with the consequence that the level of analysis of their operation can be carried out on the side of Topological Quantum Field Theories…

Quantum-inspired neural network is one of the interesting researches at the junction of the two fields of quantum computing and deep learning. Several models of quantum-inspired neurons with real parameters have been proposed, which are…