GNet: A scalable and flexible Gaussian process network with nonparametric neurons

• URL: http://arxiv.org/abs/2607.10735v2
• Date: Wed, 15 Jul 2026 16:53:27 GMT
• Title: GNet: A scalable and flexible Gaussian process network with nonparametric neurons
• Abstract summary: We develop GNet, a scalable and flexible Gaussian process network with nonparametric activation functions modeled by Gaussian processes.<n>Using a unified optimization setting, GNet shows competitive performance across a diverse range of test problems.<n>The strong performance of GNet, accelerated by the jointly inverse Kalman filter, suggests broad applicability to large-scale predictive modeling.
• Score: 0.6599344783327052
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We develop GNet, a scalable and flexible Gaussian process network with nonparametric activation functions modeled by Gaussian processes. To reduce computational and storage costs, we introduce the jointly inverse Kalman filter, a fast algorithm together with closed-form expressions of gradients for accelerating model training and predictions without the need to form covariance matrices. Using a unified optimization setting, GNet shows competitive performance across a diverse range of test problems, including predicting nonlinear functions, nonparametric regression of real-world data, and predicting one-body direct correlation functions with high-dimensional inputs in classical density function theory. The strong performance of GNet, accelerated by the jointly inverse Kalman filter, suggests broad applicability to large-scale predictive modeling with substantially reduced computational and storage costs.

Related papers

• Gradient Descent as a Perceptron Algorithm: Understanding Dynamics and Implicit Acceleration [67.12978375116599]
  We show that the steps of gradient descent (GD) reduce to those of generalized perceptron algorithms.<n>This helps explain the optimization dynamics and the implicit acceleration phenomenon observed in neural networks.
  arXiv  Detail & Related papers  (2025-12-12T14:16:35Z)
• Truncated Kernel Stochastic Gradient Descent with General Losses and Spherical Radial Basis Functions [3.308257914042897]
  We propose a novel kernel gradient unifies descent (SGD) algorithm for large-scale supervised learning with general losses.<n>Compared to traditional kernel SGD, our algorithm improves efficiency and scalability through an innovative regularization strategy.<n>Our framework accommodates a broad class of classical loss functions, including least-squares, Huber, and logistic losses.
  arXiv  Detail & Related papers  (2025-10-05T15:04:03Z)
• TensorGRaD: Tensor Gradient Robust Decomposition for Memory-Efficient Neural Operator Training [91.8932638236073]
  We introduce textbfTensorGRaD, a novel method that directly addresses the memory challenges associated with large-structured weights.<n>We show that sparseGRaD reduces total memory usage by over $50%$ while maintaining and sometimes even improving accuracy.
  arXiv  Detail & Related papers  (2025-01-04T20:51:51Z)
• A Model-Constrained Discontinuous Galerkin Network (DGNet) for Compressible Euler Equations with Out-of-Distribution Generalization [0.0]
  We develop a model-constrained discontinuous Galerkin Network (DGNet) approach.<n>The core of DGNet is the synergy of several key strategies.<n>We present comprehensive numerical results for 1D and 2D compressible Euler equation problems.
  arXiv  Detail & Related papers  (2024-09-27T01:13:38Z)
• Regularized Gauss-Newton for Optimizing Overparameterized Neural Networks [2.0072624123275533]
  The generalized Gauss-Newton (GGN) optimization method incorporates curvature estimates into its solution steps. This work studies a GGN method for optimizing a two-layer neural network with explicit regularization.
  arXiv  Detail & Related papers  (2024-04-23T10:02:22Z)
• Multi-Level GNN Preconditioner for Solving Large Scale Problems [0.0]
  Graph Neural Networks (GNNs) are great for learning from unstructured data like meshes but are often limited to small-scale problems. This paper introduces a novel preconditioner integrating a GNN model within a multi-level Domain Decomposition framework. The proposed GNN-based preconditioner is used to enhance the efficiency of a Krylov method, resulting in a hybrid solver that can converge with any desired level of accuracy.
  arXiv  Detail & Related papers  (2024-02-13T08:50:14Z)
• NAG-GS: Semi-Implicit, Accelerated and Robust Stochastic Optimizer [45.47667026025716]
  We propose a novel, robust and accelerated iteration that relies on two key elements. The convergence and stability of the obtained method, referred to as NAG-GS, are first studied extensively. We show that NAG-arity is competitive with state-the-art methods such as momentum SGD with weight decay and AdamW for the training of machine learning models.
  arXiv  Detail & Related papers  (2022-09-29T16:54:53Z)
• Non-Gradient Manifold Neural Network [79.44066256794187]
  Deep neural network (DNN) generally takes thousands of iterations to optimize via gradient descent. We propose a novel manifold neural network based on non-gradient optimization.
  arXiv  Detail & Related papers  (2021-06-15T06:39:13Z)
• Cauchy-Schwarz Regularized Autoencoder [68.80569889599434]
  Variational autoencoders (VAE) are a powerful and widely-used class of generative models. We introduce a new constrained objective based on the Cauchy-Schwarz divergence, which can be computed analytically for GMMs. Our objective improves upon variational auto-encoding models in density estimation, unsupervised clustering, semi-supervised learning, and face analysis.
  arXiv  Detail & Related papers  (2021-01-06T17:36:26Z)
• A Dynamical View on Optimization Algorithms of Overparameterized Neural Networks [23.038631072178735]
  We consider a broad class of optimization algorithms that are commonly used in practice. As a consequence, we can leverage the convergence behavior of neural networks. We believe our approach can also be extended to other optimization algorithms and network theory.
  arXiv  Detail & Related papers  (2020-10-25T17:10:22Z)
• Neural Control Variates [71.42768823631918]
  We show that a set of neural networks can face the challenge of finding a good approximation of the integrand. We derive a theoretically optimal, variance-minimizing loss function, and propose an alternative, composite loss for stable online training in practice. Specifically, we show that the learned light-field approximation is of sufficient quality for high-order bounces, allowing us to omit the error correction and thereby dramatically reduce the noise at the cost of negligible visible bias.
  arXiv  Detail & Related papers  (2020-06-02T11:17:55Z)
• Global Optimization of Gaussian processes [52.77024349608834]
  We propose a reduced-space formulation with trained Gaussian processes trained on few data points. The approach also leads to significantly smaller and computationally cheaper sub solver for lower bounding. In total, we reduce time convergence by orders of orders of the proposed method.
  arXiv  Detail & Related papers  (2020-05-21T20:59:11Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.