{"ID":6536203,"CreatedAt":"2026-07-14T01:21:01.169441415Z","UpdatedAt":"2026-07-15T03:28:55.185153975Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2607.10735","arxiv_id":"2607.10735","title":"GNet: A scalable and flexible Gaussian process network with nonparametric neurons","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.","short_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 t...","url_abs":"https://arxiv.org/abs/2607.10735","url_pdf":"https://arxiv.org/pdf/2607.10735v1","authors":"[\"Mengyang Gu\"]","published":"2026-07-12T12:40:55Z","proceeding":"stat.ME","tasks":"[\"stat.ME\",\"stat.CO\",\"stat.ML\"]","methods":"[]","has_code":false}