On-device research index

arXiv research

A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.

168,742 papers · 148 categories

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48 results for “Gaussian networks”

Wide Deep Neural Networks with Gaussian Weights are Very Close to Gaussian Processesmath.ST

Wide deep neural networks with Gaussian weights approximate Gaussian processes closely.

problem Understanding the approximation of deep neural networks with Gaussian weights to Gaussian processes.

method Established novel rates for the Gaussian approximation of random deep neural networks with Gaussian parameters and Lipschitz activation functions in the wide limit.

result The distance between the network output and the Gaussian approximation scales inversely with the width of the network.

deep neural networks Gaussian approximation Gaussian processes wide limit Lipschitz activation

2023-12-18abs ↗pdf ↗

A brief note on understanding neural networks as Gaussian processescs.LG

This note explains when neural networks can be seen as Gaussian processes.

problem Understanding the relationship between neural networks and Gaussian processes.

method Formulating a Gaussian process regression based on neural network outputs and analyzing the resulting posterior mean functions.

result The posterior mean functions of neural networks follow a Gaussian process in certain cases, providing an interpretation of reproducing kernel Hilbert spaces.

neural networks Gaussian processes kernel methods reproducing kernel Hilbert space Barron space

2021-07-25abs ↗pdf ↗

Quantitative Gaussian Approximation of Randomly Initialized Deep Neural Networkscs.LG

Bounds neural network output distribution to Gaussian for random initialization.

problem Quantifying the distribution of randomly initialized deep neural networks.

method Quantitative Gaussian approximation using quadratic Wasserstein distance.

result Explicit inequalities show how network sizes affect Gaussian behavior.

deep learning neural networks Gaussian approximation random initialization Wasserstein distance

2022-03-14abs ↗pdf ↗

The local Gaussian correlation networks among return tails in the Chinese stock marketq-fin.GN

This study uses local Gaussian correlation to analyze stock return tails, revealing more sensitive network properties.

problem Misleading results from Pearson correlation in financial networks.

method Local Gaussian correlation coefficient for capturing nonlinear dependence and heavy-tailed distributions.

result Local Gaussian correlation network among negative tails is more sensitive to stock market risks.

local gaussian correlation financial networks stock returns tail analysis Pearson correlation

2025-10-24abs ↗pdf ↗

Infinitely Wide Tensor Networks as Gaussian Processstat.ML

This paper shows how infinitely wide Tensor Networks converge to Gaussian Processes.

problem Understanding the relationship between Tensor Networks and Gaussian Processes.

method Analyzing the infinite-width limit of Tensor Networks and comparing them to Gaussian Processes.

result Infinitely wide Tensor Networks converge to Gaussian Processes, proving their equivalence.

Tensor Networks Gaussian Processes Infinite-width limit Neural Networks Kernel methods

2021-01-07abs ↗pdf ↗

Convergence of neural networks to Gaussian mixture distributionstat.ML

Deep neural networks converge to Gaussian mixtures as layer width increases.

problem Understanding the distribution of outputs from deep neural networks.

method Proof and experiments with a simple model showing the convergence of neural network outputs to Gaussian mixtures.

result Neural networks converge to Gaussian mixtures as the width of the last hidden layer increases.

deep learning neural networks Gaussian mixture convergence random networks

2022-04-26abs ↗pdf ↗

Gaussian mixture modeling of nodes in Bayesian network according to maximal parental cliquesstat.ML

The paper uses Gaussian mixture models for Bayesian networks and proposes an optimization algorithm.

problem Modeling nodes in Bayesian networks with complex distributions.

method Gaussian mixture models combined with double iteration algorithm.

result The double iteration algorithm optimizes Gaussian mixture models effectively.

Bayesian networks Gaussian mixture models Optimization algorithms Expectation maximization Gradient descent

2022-04-20abs ↗pdf ↗

Large-width functional asymptotics for deep Gaussian neural networksmath.PR

The paper studies deep neural networks with Gaussian weights and finds their asymptotic behavior.

problem Understanding the behavior of deep neural networks with large width.

method Function-space perspective, Gaussian process analysis, weak convergence in large-width limit.

result Deep neural networks with large width converge to a continuous Gaussian process.

deep neural networks Gaussian processes functional asymptotics large-width limit weak convergence

2021-02-20abs ↗pdf ↗

Bayesian inference with finitely wide neural networkscond-mat.dis-nn

Bayesian inference for wide neural networks using Edgeworth expansion.

problem Analyzing the non-Gaussian behavior of wide neural networks in Bayesian inference.

method Proposed a non-Gaussian distribution using multivariate Edgeworth expansion for finite-width neural networks.

result Derived non-Gaussian posterior distribution in Bayesian regression tasks.

Bayesian inference wide neural networks Edgeworth expansion non-Gaussian distribution marginal properties

2023-03-06abs ↗pdf ↗

Gaussian Pre-Activations in Neural Networks: Myth or Reality?cs.LG

Study challenges the Gaussian pre-activations assumption in neural networks.

problem Challenges the assumption that pre-activations are Gaussian in neural networks.

method Constructs pairs of activation functions and initialization distributions to ensure Gaussian pre-activations.

result Discovered constraints for ensuring Gaussian pre-activations in neural networks.

Gaussian pre-activations Neural networks Initialization Edge of Chaos Activation functions

2022-05-24abs ↗pdf ↗

Learning Networks from Gaussian Graphical Models and Gaussian Free Fieldsmath.ST

Estimates network structure from Gaussian Graphical Models and Gaussian Free Fields.

problem Estimating the structure of a weighted network from repeated measurements of a Gaussian Graphical Model.

method Proposes a novel estimator based on Fourier analytic properties of the Gaussian distribution.

result Demonstrates the effectiveness of the estimator with recovery guarantees and bounds on sample complexity.

Gaussian Graphical Model Gaussian Free Field Fourier Analysis Network Estimation Sample Complexity

2023-08-04abs ↗pdf ↗

Tractable Approximate Gaussian Inference for Bayesian Neural Networkscs.LG

Proposes TAGI for efficient Gaussian inference in Bayesian neural networks.

problem Efficient inference in Bayesian neural networks with complex architectures.

method Analytical method for tractable approximate Gaussian inference (TAGI).

result Matches performance of gradient-based methods with

\mathcal{O}(n)

computational complexity.

Bayesian neural networks Gaussian inference Efficient computation Approximate inference

2020-04-20abs ↗pdf ↗

Improving Output Uncertainty Estimation and Generalization in Deep Learning via Neural Network Gaussian Processesstat.ML

We propose a simple method that combines neural networks and Gaussian processes. The proposed method can estimate the uncertainty of outputs and flexibly adjust target functions where training data exist, which are advantages of Gaussian processes. The proposed method can also achieve high generalization performance fo…

2017-07-19abs ↗pdf ↗

Finite Neural Networks as Mixtures of Gaussian Processes: From Provable Error Bounds to Prior Selectioncs.LG

This work approximates finite neural networks with Gaussian processes, providing error bounds and applications in prior selection.

problem Approximating finite neural networks with Gaussian processes for error bounds and uncertainty quantification.

method Iterative approximation of neural network layers as mixtures of Gaussian processes, using optimal transport and Gaussian processes.

result The ability to return a mixture of Gaussian processes that is ε-close to the neural network at a finite set of input points.

finite neural networks Gaussian processes optimal transport error bounds prior selection

2024-07-26abs ↗pdf ↗

Deep Neural Networks as Point Estimates for Deep Gaussian Processesstat.ML

Deep neural networks and Gaussian processes are shown to be equivalent through activation functions.

problem Understanding the relationship between neural networks and Gaussian processes.

method Developing an equivalence theory based on activation functions and kernels.

result Models can be seen as neural networks with improved uncertainty prediction or deep Gaussian processes with increased accuracy.

neural networks Gaussian processes equivalence activation functions kernels

2021-05-10abs ↗pdf ↗

Proportional infinite-width infinite-depth limit for deep linear neural networksstat.ML

Study of deep linear neural networks with proportional width and depth.

problem Lack of descriptive power in Gaussian limit of deep linear neural networks.

method Proportional infinite-width infinite-depth limit for deep linear neural networks.

result Characterization of limiting distribution as a nontrivial mixture of Gaussians.

deep learning neural networks infinite-width infinite-depth Gaussian process

2024-11-22abs ↗pdf ↗

Universality in Deep Neural Networks: An approach via the Lindeberg exchange principlemath.PR

Deep neural networks' infinite-width behavior approximated by Gaussian models.

problem Understanding the behavior of deep neural networks in the limit of infinite width.

method Using the Lindeberg exchange principle to approximate weights by Gaussian random variables.

result Quantitative bounds on the 2-Wasserstein distance between deep neural networks and Gaussian limits.

deep learning neural networks infinite width Lindeberg principle Wasserstein distance

2026-05-04abs ↗pdf ↗

Quantitative Gaussian-Process limits of Tensor Programscs.LG

Study Gaussian-process limits of neural networks using tensor programs.

problem Understanding the behavior of neural networks as they approach infinite width.

method Quantitative analysis through tensor programs and Wasserstein distance.

result Explicit finite-width error bounds, showing convergence to Gaussian-process limits.

Gaussian-process neural networks tensor programs Wasserstein distance finite-width error bounds

2026-07-07abs ↗pdf ↗

Posterior Inference on Shallow Infinitely Wide Bayesian Neural Networks under Weights with Unbounded Variancestat.ML

New method for Bayesian neural networks with unbounded weights.

problem Posterior inference for Bayesian neural networks with unbounded weights.

method Conditionally Gaussian representation for efficient posterior inference.

result Interpretable and computationally efficient procedure for posterior inference.

Bayesian neural networks unbounded weights posterior inference Gaussian process α-stable process

2023-05-18abs ↗pdf ↗

Quantitative convergence of trained single layer neural networks to Gaussian processesstat.ML

Study shows neural networks trained with GD converge to Gaussian processes with polynomial decay.

problem Understanding convergence of neural networks to Gaussian processes during training.

method Explicit upper bounds on quadratic Wasserstein distance between trained networks and Gaussian approximations.

result Polynomial decay of approximation error with network width and training time.

neural networks Gaussian processes convergence quadratic Wasserstein distance training dynamics

2025-09-29abs ↗pdf ↗

Neural Network Parameter-optimization of Gaussian pmDAGsstat.ML

New neural network approach for optimizing latent variable models.

problem Stability issues in marginalizing Gaussian Bayesian networks.

method Developed a new graphical structure and a neural network algorithm.

result Established a duality between parameter optimization and neural network training.

neural networks parameter optimization causal inference Gaussian Bayesian networks latent variable models

2023-09-25abs ↗pdf ↗

Optimal Non-Asymptotic Edgeworth Expansions for Multivariate Neural Network Outputsstat.ML

The paper provides non-asymptotic Edgeworth expansions for neural network outputs.

problem Approximating deviations of finite-width neural networks from their Gaussian limit.

method Multidimensional Edgeworth expansions of arbitrary order for neural network outputs.

result Established a bound on the total variation distance between neural network output and its Edgeworth approximation.

Neural Networks Edgeworth Expansions Finite-width Networks Gaussian Limit Cumulants

2026-05-22abs ↗pdf ↗

Wide Neural Networks as Gaussian Processes: Lessons from Deep Equilibrium Modelscs.LG

Wide neural networks converge to Gaussian processes, improving generalization.

problem Understanding the generalization of wide neural networks, especially deep equilibrium models.

method Investigation of deep equilibrium models (DEQs) with infinite-depth layers, focusing on their convergence to Gaussian processes as width and depth approach infinity.

result Wide DEQs converge to Gaussian processes, maintaining generalization performance.

deep equilibrium models neural networks Gaussian processes benign overfitting infinite-depth networks

2023-10-16abs ↗pdf ↗

Sequential Function-Space Variational Inference via Gaussian Mixture Approximationcs.LG

SFSVI uses Gaussian mixtures to approximate neural network outputs for continual learning.

problem Learning new tasks without forgetting old ones in neural networks.

method Sequential function-space variational inference with Gaussian mixture approximation.

result Gaussian mixture SFSVI outperforms other methods in continual learning.

neural networks continual learning Gaussian mixture variational inference sequential learning

2025-03-10abs ↗pdf ↗

Gaussian Process Behaviour in Wide Deep Neural Networksstat.ML

Whilst deep neural networks have shown great empirical success, there is still much work to be done to understand their theoretical properties. In this paper, we study the relationship between random, wide, fully connected, feedforward networks with more than one hidden layer and Gaussian processes with a recursive ker…

2018-04-30abs ↗pdf ↗

The Future is Log-Gaussian: ResNets and Their Infinite-Depth-and-Width Limit at Initializationstat.ML

ResNets approximate log-Gaussian at initialization, improving network performance.

problem Understanding the initialization behavior of deep neural networks like ResNets.

method Analyzing ReLU ResNets in the infinite-depth-and-width limit, showing log-Gaussian behavior.

result ResNets at initialization exhibit hypoactivation and interlayer correlations, which are not captured by Gaussian limits.

ResNets log-Gaussian infinite-depth-and-width hypoactivation interlayer correlations

2021-06-07abs ↗pdf ↗

Non-Gaussian processes and neural networks at finite widthsstat.ML

Gaussian processes are ubiquitous in nature and engineering. A case in point is a class of neural networks in the infinite-width limit, whose priors correspond to Gaussian processes. Here we perturbatively extend this correspondence to finite-width neural networks, yielding non-Gaussian processes as priors. The methodo…

2019-09-30abs ↗pdf ↗

Characteristics of Monte Carlo Dropout in Wide Neural Networkscs.LG

Study on MC dropout in wide neural networks and its convergence to Gaussian processes.

problem Understanding the behavior of Monte Carlo dropout in wide neural networks.

method Rigorously studied the limiting distribution of wide untrained NNs under dropout, proving convergence to Gaussian processes. Investigated correlations and non-Gaussian behavior in finite width NNs.

result Wide untrained neural networks under dropout converge to Gaussian processes for fixed sets of weights and biases.

Monte Carlo dropout wide neural networks Bayesian inference Gaussian processes uncertainty estimation

2020-07-10abs ↗pdf ↗

Memorizing Gaussians with no over-parameterizaion via gradient decent on neural networkscs.LG

Gradient descent memorizes many Gaussians efficiently.

problem Memorizing many Gaussians with minimal parameters.

method Gradient descent on a depth-two neural network.

result One step of gradient descent memorizes $Ω\left(\frac{dq}{\log^4(d)} ight)$ Gaussians.

neural networks gradient descent Gaussians over-parameterization memorization

2020-03-28abs ↗pdf ↗

Fractal Gaussian Networks: A sparse random graph model based on Gaussian Multiplicative Chaosstat.ML

FGN models networks with fractal structures using Gaussian Multiplicative Chaos.

problem Modeling networks with fractal structures.

method FGN model based on Gaussian Multiplicative Chaos.

result FGNs reveal distinct scaling patterns in edge and clique counts.

Fractal Gaussian Networks Gaussian Multiplicative Chaos Random Graphs Fractal Structures Network Analysis

2020-08-07abs ↗pdf ↗

The Ridgelet Prior: A Covariance Function Approach to Prior Specification for Bayesian Neural Networksstat.ML

Bayesian neural networks use ridgelet prior for uncertainty quantification.

problem Combining strong predictive performance with uncertainty quantification in Bayesian neural networks.

method Proposes a ridgelet prior that approximates a Gaussian process covariance function in the output space of the network.

result Establishes universality property allowing Bayesian neural networks to approximate any Gaussian process.

Bayesian neural networks ridgelet prior Gaussian processes covariance function uncertainty quantification

2020-10-16abs ↗pdf ↗

Large deviation principles for convolutional Bayesian neural networksmath.PR

We establish large deviation principles for convolutional neural networks.

problem Understanding the behavior of convolutional neural networks in the infinite-channel limit.

method We establish large deviation principles for convolutional neural networks under Gaussian prior and posterior distributions.

result We provide a large deviation principle for the sequence of conditional covariance matrices and the posterior distribution.

large deviation principles convolutional neural networks infinite-channel limit Gaussian prior posterior distribution

2026-03-06abs ↗pdf ↗

A Gap Between the Gaussian RKHS and Neural Networks: An Infinite-Center Asymptotic Analysiscs.LG

New analysis shows a gap between Gaussian RKHS and neural networks on unbounded domains.

problem Understanding the function space bias of neural networks compared to Gaussian RKHS.

method Infinite-center asymptotic analysis of neural network Banach space and Gaussian RKHS on unbounded domains.

result Certain functions in Gaussian RKHS have infinite norm in neural network Banach space on unbounded domains.

neural networks Gaussian RKHS Banach space asymptotic analysis unbounded domains

2025-02-22abs ↗pdf ↗

Deep Maxout Network Gaussian Processstat.ML

Study deep maxout networks and their equivalence to Gaussian processes.

problem Understanding neural networks with infinite width.

method Derive equivalence between deep maxout networks and Gaussian processes, characterize maxout kernel, and provide efficient numerical implementation.

result Bayesian inference based on deep maxout network kernel leads to competitive results compared to finite-width counterparts and deep neural network kernels.

maxout networks Gaussian processes infinite width neural networks Bayesian inference

2022-08-08abs ↗pdf ↗

A Gaussian Process perspective on Convolutional Neural Networksstat.ML

In this paper we cast the well-known convolutional neural network in a Gaussian process perspective. In this way we hope to gain additional insights into the performance of convolutional networks, in particular understand under what circumstances they tend to perform well and what assumptions are implicitly made in the…

2018-10-25abs ↗pdf ↗

Non-asymptotic approximations of neural networks by Gaussian processesmath.PR

Wide neural networks can be closely approximated by Gaussian processes, with rates depending on the activation function's properties.

problem Approximating the behavior of wide neural networks using Gaussian processes.

method Established convergence rates for the central limit theorem in an infinite-dimensional functional space, using a transportation distance metric.

result Explicit convergence rates for neural networks approximated by Gaussian processes, varying based on the activation function's properties.

neural networks Gaussian processes approximation theory transportation distance activation functions

2021-02-17abs ↗pdf ↗

Gaussian Universality in Neural Network Dynamics with Generalized Structured Input Distributionsstat.ML

Deep learning models converge to Gaussian dynamics with mixed structured inputs.

problem Understanding neural network dynamics with complex input distributions.

method Extended hidden manifold model to Gaussian mixtures, analyzed via SGD.

result Learning dynamics with mixed inputs converge to Gaussian behavior.

neural networks deep learning Gaussian mixtures stochastic gradient descent hidden manifold model

2024-05-01abs ↗pdf ↗

Graph Convolutional Gaussian Processes For Link Predictioncs.LG

Graph Convolutional Gaussian Processes predict missing links.

problem Link prediction in large graphs.

method Simplified graph convolutions and variational inducing point method.

result Consistent improvements over existing models and competitive performance.

link prediction graph convolutional networks Gaussian processes graph neural networks large graphs

2020-02-11abs ↗pdf ↗

Random ReLU Neural Networks as Non-Gaussian Processesstat.ML

Random neural networks with ReLU activations are non-Gaussian processes.

problem Understanding the behavior of neural networks with random initialization and rectified linear units.

method Proving these networks are non-Gaussian processes and deriving their properties.

result These networks can converge to non-Gaussian processes under certain conditions.

neural networks rectified linear units non-Gaussian processes stochastic processes random initialization

2024-05-16abs ↗pdf ↗

Finite-Dimensional Gaussian Approximation for Deep Neural Networks: Universality in Random Weightsstat.ML

Study Gaussian approximation for deep neural networks with random weights.

problem Understanding the distribution of deep neural networks with random weights.

method Established Gaussian approximation bounds in Wasserstein-1 norm.

result Convergence rates of order

n^{-({1}/{6})^{L-1} + ε}

for deep networks with proportional layer widths.

Gaussian approximation deep neural networks random weights Wasserstein-1 norm activation function

2025-07-16abs ↗pdf ↗

On Generalization Bounds for Deep Compound Gaussian Neural Networksstat.ML

The paper develops generalization bounds for deep compound Gaussian neural networks.

problem Developing theoretical guarantees for the performance of deep neural networks.

method Novel generalization error bounds using a compound Gaussian prior and Dudley's integral.

result Theoretical bounds show generalization error scales

\mathcal{O}(n\sqrt{\ln(n)})

in signal dimension and

\mathcal{O}((Network Size)^{3/2})

in network size.

Deep Neural Networks Generalization Error Compound Gaussian Rademacher Complexity Dudley's Integral

2024-02-20abs ↗pdf ↗

Deterministic Gaussian Averaged Neural Networkscs.LG

Deterministic method for certifying neural network robustness.

problem Certifying neural network robustness against adversarial attacks.

method Equivalence between training and Gaussian averaging for robustness certification.

result Comparable certified accuracy and robustness to stochastic methods but with single model evaluation.

neural networks robustness certification Gaussian averaging adversarial attacks

2020-06-10abs ↗pdf ↗

Gaussian random field approximation via Stein's method with applications to wide random neural networksmath.PR

Bounds on Gaussian approximation for neural networks with novel smoothing techniques.

problem Approximating the distribution of wide random neural networks.

method Stein's method, Gaussian smoothing, Laplacian operators, Cameron-Martin space.

result First bounds on Gaussian approximation of wide random neural networks.

Stein's method Gaussian smoothing Random neural networks Wasserstein distance Wide networks

2023-06-28abs ↗pdf ↗

Wide stochastic networks: Gaussian limit and PAC-Bayesian trainingstat.ML

Wide stochastic networks show Gaussian behavior and improve training with PAC-Bayesian methods.

problem Analyzing and training over-parameterised neural networks with large width.

method Establishing Gaussian behavior for a stochastic architecture, applying PAC-Bayesian training.

result PAC-Bayesian training on large but finite-width networks outperforms standard methods.

wide networks stochastic architectures PAC-Bayesian Gaussian limit over-parameterisation

2021-06-17abs ↗pdf ↗

Exact marginal prior distributions of finite Bayesian neural networkscs.LG

Researchers derive exact priors for finite Bayesian neural networks.

problem Understanding non-Gaussian priors in finite Bayesian neural networks.

method Analytical derivation of function space priors for finite fully-connected feedforward networks.

result Exact solutions for priors of finite networks, including Meijer G-function for linear networks and mixtures for ReLU networks.

Bayesian neural networks finite networks function space priors Meijer G-function ReLU networks

2021-04-23abs ↗pdf ↗

Quantitative CLTs in Deep Neural Networkscs.LG

Quantitative CLTs show neural network distributions converge to Gaussian as width increases.

problem Understanding the distribution of fully connected neural networks with random weights and biases.

method Analyzing the distribution of a fully connected neural network with random Gaussian weights and biases, proving quantitative bounds on normal approximations.

result The distance between a random fully connected network and the corresponding infinite width Gaussian process scales like

n^{-γ}

for

γ>0

quantitative CLTs deep neural networks random Gaussian weights finite width Gaussian process

2023-07-12abs ↗pdf ↗

The Limitations of Large Width in Neural Networks: A Deep Gaussian Process Perspectivecs.LG

Wide neural networks can degrade performance, contrary to conventional wisdom.

problem Understanding the limitations of increasing network width in neural networks.

method Using Deep Gaussian Processes to decouple capacity and width, analyzing their effects on representational power and non-Gaussianity.

result Wide neural networks can become less adaptable and more Gaussian, leading to performance degradation.

neural networks width capacity non-Gaussianity Gaussian processes

2021-06-11abs ↗pdf ↗

Classification of Data Generated by Gaussian Mixture Models Using Deep ReLU Networksstat.ML

Deep neural networks classify unbounded Gaussian mixture data without dimensionality issues.

problem Binary classification of unbounded Gaussian mixture data.

method Deep ReLU neural networks with non-asymptotic upper bounds and convergence rates.

result Deep ReLU networks can classify unbounded Gaussian mixture data without dimensionality constraints.

Gaussian Mixture Models Deep Learning ReLU Networks Excess Risk Curse of Dimensionality

2023-08-15abs ↗pdf ↗