Exact Uncertainty Propagation via Gaussian Process Neurons

Qiuxian Meng, Yongyou Zhang
Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence, PMLR 337:4497-4513, 2026.

Abstract

Exact marginalization in deep {Gaussian} processes (DGPs) is analytically intractable, typically requiring computationally costly sampling-based approximations. We introduce the {Gaussian} process neuron, a computational unit built on a novel {Wasserstein} exponential kernel. By defining a composable map between factorized {Gaussian} measures, this unit enables analytical uncertainty propagation; concurrently, optimizing deterministic inducing variables via maximum a posteriori estimation ensures strict probabilistic rigor. By eliminating sampling variance and the depth-scaling computational bottlenecks of Monte Carlo methods, our approach enables exact probabilistic variants of diverse architectures, including DGPs, multilayer perceptrons, and {Kolmogorov}-Arnold Networks. Empirically, these networks demonstrate superior uncertainty calibration relative to state-of-the-art approximate {DGP} frameworks, alongside high-dimensional scalability and robust compositional expressiveness.

Cite this Paper

BibTeX
@InProceedings{pmlr-v337-meng26a, title = {Exact Uncertainty Propagation via {Gaussian} Process Neurons}, author = {Meng, Qiuxian and Zhang, Yongyou}, booktitle = {Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence}, pages = {4497--4513}, year = {2026}, editor = {Perković, Emilija and Malinsky, Daniel}, volume = {337}, series = {Proceedings of Machine Learning Research}, month = {17--21 Aug}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v337/main/assets/meng26a/meng26a.pdf}, url = {https://proceedings.mlr.press/v337/meng26a.html}, abstract = {Exact marginalization in deep {Gaussian} processes (DGPs) is analytically intractable, typically requiring computationally costly sampling-based approximations. We introduce the {Gaussian} process neuron, a computational unit built on a novel {Wasserstein} exponential kernel. By defining a composable map between factorized {Gaussian} measures, this unit enables analytical uncertainty propagation; concurrently, optimizing deterministic inducing variables via maximum a posteriori estimation ensures strict probabilistic rigor. By eliminating sampling variance and the depth-scaling computational bottlenecks of Monte Carlo methods, our approach enables exact probabilistic variants of diverse architectures, including DGPs, multilayer perceptrons, and {Kolmogorov}-Arnold Networks. Empirically, these networks demonstrate superior uncertainty calibration relative to state-of-the-art approximate {DGP} frameworks, alongside high-dimensional scalability and robust compositional expressiveness.} }
Endnote
%0 Conference Paper %T Exact Uncertainty Propagation via Gaussian Process Neurons %A Qiuxian Meng %A Yongyou Zhang %B Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2026 %E Emilija Perković %E Daniel Malinsky %F pmlr-v337-meng26a %I PMLR %P 4497--4513 %U https://proceedings.mlr.press/v337/meng26a.html %V 337 %X Exact marginalization in deep {Gaussian} processes (DGPs) is analytically intractable, typically requiring computationally costly sampling-based approximations. We introduce the {Gaussian} process neuron, a computational unit built on a novel {Wasserstein} exponential kernel. By defining a composable map between factorized {Gaussian} measures, this unit enables analytical uncertainty propagation; concurrently, optimizing deterministic inducing variables via maximum a posteriori estimation ensures strict probabilistic rigor. By eliminating sampling variance and the depth-scaling computational bottlenecks of Monte Carlo methods, our approach enables exact probabilistic variants of diverse architectures, including DGPs, multilayer perceptrons, and {Kolmogorov}-Arnold Networks. Empirically, these networks demonstrate superior uncertainty calibration relative to state-of-the-art approximate {DGP} frameworks, alongside high-dimensional scalability and robust compositional expressiveness.
APA
Meng, Q. & Zhang, Y.. (2026). Exact Uncertainty Propagation via Gaussian Process Neurons. Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research 337:4497-4513 Available from https://proceedings.mlr.press/v337/meng26a.html.

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