Related papers: Neural Network Quantum Field Theory from Transform…

Standard attention mechanisms in transformers are limited by their pairwise formulation, which hinders the modeling of higher-order dependencies among tokens. We introduce the NeuroGame Transformer (NGT) to overcome this by…

As a hybrid of artificial intelligence and quantum computing, quantum neural networks (QNNs) have gained significant attention as a promising application on near-term, noisy intermediate-scale quantum (NISQ) devices. Conventional QNNs are…

The study of topological quantum field theories increasingly relies upon concepts from higher-dimensional algebra such as n-categories and n-vector spaces. We review progress towards a definition of n-category suited for this purpose, and…

Classical neural networks with random initialization famously behave as Gaussian processes in the limit of many neurons, which allows one to completely characterize their training and generalization behavior. No such general understanding…

It is well known that artificial neural networks initialized from independent and identically distributed priors converge to Gaussian processes in the limit of a large number of neurons per hidden layer. In this work we prove an analogous…

We study the Euclidean Distance degree of algebraic neural network models from the perspective of algebraic geometry. Focusing on shallow networks with two neurons, quadratic activation, and scalar output, we identify the associated…

We propose the Quantum Graph Attention Network (QGAT), a hybrid graph neural network that integrates variational quantum circuits into the attention mechanism. At its core, QGAT employs strongly entangling quantum circuits with…

This paper systematically explores neural functional networks (NFN) for transformer architectures. NFN are specialized neural networks that treat the weights, gradients, or sparsity patterns of a deep neural network (DNN) as input data and…

We consider Euclidean Conformal Field Theories perturbed by quenched disorder, namely by random fluctuations in their couplings. Such theories are relevant for second-order phase transitions in the presence of impurities or other forms of…

In order to construct examples for interacting quantum field theory models, the methods of euclidean field theory turned out to be powerful tools since they make use of the techniques of classical statistical mechanics. Starting from an…

We prove that any quantum field theory, or more generally any probability distribution over tempered distributions in $\mathbb{R}^d$, admits a neural network description with a countable infinity of parameters. As an example, we realize the…

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 overparameterization of variational quantum circuits, as a model of Quantum Neural Networks (QNN), not only improves their trainability but also serves as a method for evaluating the property of a given ansatz by investigating their…

Both the path integral measure in field theory and ensembles of neural networks describe distributions over functions. When the central limit theorem can be applied in the infinite-width (infinite-$N$) limit, the ensemble of networks…

We investigate the mathematical foundations of neural networks in the infinite-width regime through the Neural Tangent Kernel (NTK). We propose the NTK-Eigenvalue-Controlled Residual Network (NTK-ECRN), an architecture integrating Fourier…

In this work we develop a quantum field theory formalism for deep learning, where input signals are encoded in Gaussian states, a generalization of Gaussian processes which encode the agent's uncertainty about the input signal. We show how…

A neural architecture with randomly initialized weights, in the infinite width limit, is equivalent to a Gaussian Random Field whose covariance function is the so-called Neural Network Gaussian Process kernel (NNGP). We prove that a…

In this paper, we will discuss a formal link between neural networks and quantum computing. For that purpose we will present a simple model for the description of the neural network by forming sub-graphs of the whole network with the same…

Coupling quantum field theory (QFT) \!-\! even free QFT \!-\! to gravity leads to well-known problems. In particular, the stress tensor $T_{\mu\nu}$ (gravity's source) and its correlators typically diverge in the UV, creating a conflict…

Researchers have proposed several approaches for neural network (NN) based uncertainty quantification (UQ). However, most of the approaches are developed considering strong assumptions. Uncertainty quantification algorithms often perform…