Related papers: Neural Networks and Quantum Field Theory
Neural-net-induced Gaussian process (NNGP) regression inherits both the high expressivity of deep neural networks (deep NNs) as well as the uncertainty quantification property of Gaussian processes (GPs). We generalize the current NNGP to…
Gaussian processes (GPs) are Bayesian nonparametric generative models that provide interpretability of hyperparameters, admit closed-form expressions for training and inference, and are able to accurately represent uncertainty. To model…
We extend previous mean-field approaches for non-equilibrium neural network models to estimate correlations in the system. This offers a powerful tool for approximating the system dynamics as well as a fast method to infer network…
Gaussian processes (GPs) are an attractive class of machine learning models because of their simplicity and flexibility as building blocks of more complex Bayesian models. Meanwhile, graph neural networks (GNNs) emerged recently as a…
We consider covariance parameter estimation for Gaussian processes with functional inputs. From an increasing-domain asymptotics perspective, we prove the asymptotic consistency and normality of the maximum likelihood estimator. We extend…
In this work, we establish non-asymptotic convergence bounds for the Gauss-Newton method in training neural networks with smooth activations. In the underparameterized regime, the Gauss-Newton gradient flow in parameter space induces a…
Cortical neurons whose activity is recorded in behavioral experiments has been classified into several types such as stimulus-related neurons, delay-period neurons, and reward-related neurons. Moreover, the population activity of neurons…
Large width limits have been a recent focus of deep learning research: modulo computational practicalities, do wider networks outperform narrower ones? Answering this question has been challenging, as conventional networks gain…
Quantum neural networks promise to extend the power of machine learning into the quantum domain, with potential applications ranging from automatic recognition of quantum states to the control of quantum devices. However, their physical…
We introduce a class of neural networks derived from probabilistic models in the form of Bayesian belief networks. By imposing additional assumptions about the nature of the probabilistic models represented in the belief networks, we derive…
Gaussian processes have become a popular tool for nonparametric regression because of their flexibility and uncertainty quantification. However, they often use stationary kernels, which limit the expressiveness of the model and may be…
Graph Neural Networks (GNNs) are limited in their expressive power, struggle with long-range interactions and lack a principled way to model higher-order structures. These problems can be attributed to the strong coupling between the…
Neural networks are complex functions of both their inputs and parameters. Much prior work in deep learning theory analyzes the distribution of network outputs at a fixed a set of inputs (e.g. a training dataset) over random initializations…
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…
We study the asymptotic law of a network of interacting neurons when the number of neurons becomes infinite. Given a completely connected network of firing rate neurons in which the synaptic weights are Gaussian correlated random variables,…
Deep neural networks (DNN) and Gaussian processes (GP) are two powerful models with several theoretical connections relating them, but the relationship between their training methods is not well understood. In this paper, we show that…
Neural network is a dynamical system described by two different types of degrees of freedom: fast-changing non-trainable variables (e.g. state of neurons) and slow-changing trainable variables (e.g. weights and biases). We show that the…
While Graph Neural Networks (GNNs) have achieved remarkable results in a variety of applications, recent studies exposed important shortcomings in their ability to capture the structure of the underlying graph. It has been shown that the…
Neural Processes (NPs; Garnelo et al., 2018a,b) are a rich class of models for meta-learning that map data sets directly to predictive stochastic processes. We provide a rigorous analysis of the standard maximum-likelihood objective used to…
Local gauge structures play a central role in a wide range of condensed matter systems and synthetic quantum platforms, where they emerge as effective descriptions of strongly correlated phases and engineered dynamics. We introduce a…