The paper proposes a continuous-depth formulation for Deep Gaussian Processes (DGPs), treating depth as a latent continuous evolution rather than a discrete stack. It introduces two instantiations—CDGP, which applies a GP prior directly to the state–depth drift, and FlowDGP, which uses a flow-evolved prior to capture richer depth dependence at lower training cost. Experiments on synthetic, benchmark, and large-scale regression tasks demonstrate that residual DGP improves over plain DGP, while CDGP and FlowDGP offer stronger performance across the studied regimes.
arXiv:2606. 25882v1 Announce Type: new Abstract: DGPs are probabilistic models with remarkable prediction performance that concatenate GPs across several layers.
By Francisco Javier S\'aez-Maldonado, Juan Maro\~nas, Daniel Hern\'andez-Lobato
arXiv:2606. 01954v1 Announce Type: new Abstract: Implicit-process priors define distributions over functions through flexible generative mechanisms, making them attractive for Bayesian function-space modelling.
By Luis A. Ortega, Andr\'es R. Masegosa, Thomas D. Nielsen
arXiv:2606. 26592v1 Announce Type: cross Abstract: We propose latent-space diffusion posterior sampling (L-DPS), an approximate Bayesian framework for high-dimensional inverse problems governed by partial differential equations (PDEs).
By Yuanzhe Wang, Alexandre M. Tartakovsky
arXiv:2606. 06351v1 Announce Type: cross Abstract: Vessel trajectory prediction from Automatic Identification System (AIS) data is essential for maritime situational awareness, yet it remains challenging due to irregular sampling, missing reports, and complex dynamics.
By Jaeyeong Lee, Wonmo Koo, Heeyoung Kim
arXiv:2606. 08218v1 Announce Type: cross Abstract: Compositional priors describe the generic properties of layered functions in deep Bayesian models, where deep neural networks with random weights are a canonical example.
By Mark Kozdoba, Shie Mannor
arXiv:2610.22763v1 Announce Type: new
Abstract: Bayesian optimization (BO) over discrete spaces is challenging due to missing gradients and the sparsity of valid solutions. Latent-space BO sidesteps...
By Tommaso Ancilli, Thomas Wedenig, Henry Moss, Robert Peharz
The paper introduces β‑Flow, a versatile plug‑and‑play posterior sampling framework that unifies flow‑matching, diffusion, and decorrelated priors through a correlation parameter β and a confidence parameter κ. Each iteration requires only a single denoising network forward pass followed by an exact Gaussian conditioning step, implemented as a Kalman update independent of network gradients. The authors demonstrate that many existing guided samplers are special cases of β‑Flow, and show state‑of‑the‑art performance on seven inverse problems across four datasets, with the ability to tune prior strength based on data informativeness.
By Teo Deveney, Lea Bogensperger, Hok Shing Wong
arXiv:2606. 01468v1 Announce Type: cross Abstract: Due to their explicit priors and ability to model uncertainty, Bayesian methods have played a major role in dynamical latent variable modeling of single-cell neural recordings.
By JR Huml, Jonathan Wenger, John P. Cunningham
arXiv:2606. 30813v1 Announce Type: cross Abstract: Deep neural networks with repeated architectural blocks, such as transformers, often exhibit structured relationships across layers that emerge during training.
By Haoming Meng, Anton Sugolov, Vardan Papyan
arXiv:2606. 20417v1 Announce Type: new Abstract: Inverse problems for differential equations arise throughout science and engineering, where one seeks to infer unknown model parameters from noisy or incomplete observations.
By Christian Jimenez-Beltran, Aretha L. Teckentrup, Antonio Vergari, Konstantinos C. Zygalakis
The paper investigates nonlinear dimensionality reduction for Bayesian optimisation (BO) by transforming high‑dimensional black‑box optimisation problems into a sequence of low‑dimensional latent‑space BO (LSBO) tasks. It extends earlier linear embedding approaches by using variational autoencoders (VAEs), deep metric loss, and adaptive retraining to better capture nonlinear structure, and couples LSBO with sequential domain reduction (SDR‑LSBO) to progressively narrow search domains. Experiments on GPU‑accelerated BoTorch with Matérn‑5/2 Gaussian‑process surrogates show that VAE‑based LSBO outperforms adaptive linear embeddings, and the authors provide a theoretical analysis of latent‑space error versus representation gap under PAC‑Bayes conditions.
By Luo Long, Coralia Cartis, Paz Fink Shustin