相关论文: Optimal Architecture and Fundamental Bounds in Neu…

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.…

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 develop a diagrammatic approach to effective field theories (EFTs) corresponding to deep neural networks at initialization, which dramatically simplifies computations of finite-width corrections to neuron statistics. The structures of…

Neural Network (NN) architectures that break statistical independence of parameters have been proposed as a new approach for simulating local quantum field theories (QFTs). In the infinite neuron number limit, single-layer NNs can exactly…

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…

We propose a neural-network construction of Euclidean scalar quantum field theories from transformer attention heads, defining $n$-point correlators by averaging over random network parameters in the NN-QFT framework. For a single attention…

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…

To understand the training dynamics of neural networks (NNs), prior studies have considered the infinite-width mean-field (MF) limit of two-layer NN, establishing theoretical guarantees of its convergence under gradient flow training as…

Information field theory (IFT) is the application of probabilistic reasoning to fields. Physical fields are mathematical functions over continuous spaces that exhibit certain properties of regularity, such as limited variance and finite…

Theoretical understanding of deep learning remains elusive despite its empirical success. In this study, we propose a novel "synaptic field theory" that describes the training dynamics of synaptic weights and biases in the continuum limit.…

Obtaining theoretical guarantees for neural networks training appears to be a hard problem in a general case. Recent research has been focused on studying this problem in the limit of infinite width and two different theories have been…

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…

This work theoretically studies stochastic neural networks, a main type of neural network in use. We prove that as the width of an optimized stochastic neural network tends to infinity, its predictive variance on the training set decreases…

This paper analyzes neural networks through graph variables and statistical sufficiency. We interpret neural network layers as graph-based transformations, where neurons act as pairwise functions between inputs and learned anchor points.…

We study the distribution of a fully connected neural network with random Gaussian weights and biases in which the hidden layer widths are proportional to a large constant $n$. Under mild assumptions on the non-linearity, we obtain…

Neural network field theory formulates field theory as a statistical ensemble of fields defined by a network architecture and a density on its parameters. We extend the construction to topological settings via the inclusion of discrete…

There is a fundamental limit on the capacity of fibre optical communication system (Shannon Limit). This limit can be potentially overcome via using Nonlinear Frequency Division Multiplexing. Dealing with noises in these systems is one of…

Neural network width and depth are fundamental aspects of network topology. Universal approximation theorems provide that with increasing width or depth, there exists a neural network that approximates a function arbitrarily well. These…

Noncommutative field theory (NCFT) is an extension of quantum field theory (QFT) that redefines spacetime, replacing commuting coordinates with a noncommutative structure. This shift fundamentally alters the way fields, interactions, and…

In a recent paper [Bardella et al., Entropy 26 (6), 495 (2024)] we introduced a simplified Lattice Field Theory (LFT) framework that allows experimental recordings from major Brain-Computer Interfaces (BCIs) to be interpreted in a simple…