arXiv:2512.10258v1 Announce Type: new 
Abstract: Multi-output Gaussian process (MGP) models have attracted significant attention for their flexibility and uncertainty-quantification capabilities, and have been widely adopted in multi-source transfer learning scenarios due to their ability to capture inter-task correlations. However, they still face several challenges in transfer learning. First, the input spaces of the source and target domains are often heterogeneous, which makes direct knowledge transfer difficult. Second, potential prior knowledge and physical information are typically ignored during heterogeneous transfer, hampering the utilization of domain-specific insights and leading to unstable mappings. Third, inappropriate information sharing among target and sources can easily lead to negative transfer. Traditional models fail to address these issues in a unified way. To overcome these limitations, this paper proposes a Double-Regularized Heterogeneous Gaussian Process framework (R^2-HGP). Specifically, a trainable prior probability mapping model is first proposed to align the heterogeneous input domains. The resulting aligned inputs are treated as latent variables, upon which a multi-source transfer GP model is constructed and the entire structure is integrated into a novel conditional variational autoencoder (CVAE) based framework. Physical insights is further incorporated as a regularization term to ensure that the alignment results adhere to known physical knowledge. Next, within the multi-source transfer GP model, a sparsity penalty is imposed on the transfer coefficients, enabling the model to adaptively select the most informative source outputs and suppress negative transfer. Extensive simulations and real-world engineering case studies validate the effectiveness of our R^2-HGP, demonstrating consistent superiority over state-of-the-art benchmarks across diverse evaluation metrics.

تم اقتراح إطار جديد يسمى R^2-HGP لتحسين نماذج العمليات الغاوسية متعددة المخرجات للتعلم بالانتقال غير المتجانس، حيث يتناول التحديات مثل المساحات المدخلة غير المتجانسة، وإهمال المعرفة السابقة، ومشاركة المعلومات غير المناسبة التي يمكن أن تؤدي إلى انتقال سلبي.

Se ha propuesto un nuevo marco llamado R^2-HGP para mejorar los modelos de procesos gaussianos de múltiples salidas para el aprendizaje por transferencia heterogénea, abordando desafíos como los espacios de entrada heterogéneos, la negligencia del conocimiento previo y el intercambio inapropiado de información que puede llevar a un traslado negativo.

Un nouveau cadre appelé R^2-HGP a été proposé pour améliorer les modèles de processus gaussiens multi-sorties pour l'apprentissage par transfert hétérogène, abordant des défis tels que les espaces d'entrée hétérogènes, la négligence des connaissances antérieures et le partage d'informations inapproprié qui peuvent conduire à un transfert négatif.

A new framework called R^2-HGP has been proposed to enhance multi-output Gaussian process models for heterogeneous transfer learning, addressing challenges such as heterogeneous input spaces, the neglect of prior knowledge, and inappropriate information sharing that can lead to negative transfer.

R^2-HGP: A Double-Regularized Gaussian Process for Heterogeneous Transfer Learning

arXiv:2601.05371v2 Announce Type: replace 
Abstract: Gaussian Process (GP) regression is a powerful nonparametric Bayesian framework, but its performance depends critically on the choice of covariance kernel. Selecting an appropriate kernel is therefore central to model quality, yet remains one of the most challenging and computationally expensive steps in probabilistic modeling. We present a Bayesian optimization framework built on kernel-of-kernels geometry, using expected divergence-based distances between GP priors to explore kernel space efficiently. A multidimensional scaling (MDS) embedding of this distance matrix maps a discrete kernel library into a continuous Euclidean manifold, enabling smooth BO. In this formulation, the input space comprises kernel compositions, the objective is the log marginal likelihood, and featurization is given by the MDS coordinates. When the divergence yields a valid metric, the embedding preserves geometry and produces a stable BO landscape. We demonstrate the approach on synthetic benchmarks, real-world time-series datasets, and an additive manufacturing case study predicting melt-pool geometry, achieving superior predictive accuracy and uncertainty calibration relative to baselines including Large Language Model (LLM)-guided search. This framework establishes a reusable probabilistic geometry for kernel search, with direct relevance to GP modeling and deep kernel learning.

تم تقديم إطار عمل جديد لاختيار نماذج العمليات الغاوسية (GP) بعنوان 'The Kernel Manifold'، والذي يركز على نهج هندسي لتحسين اختيار نوى التغاير. تستخدم هذه الطريقة إطار عمل تحسين بايزي يعتمد على هندسة نوى النوى، مما يسمح باستكشاف فعال لمساحة النوى من خلال المسافات المستندة إلى التباين المتوقع.

Se ha introducido un nuevo marco para la selección de modelos de Procesos Gaussianos (GP), titulado 'The Kernel Manifold', que enfatiza un enfoque geométrico para optimizar la elección de núcleos de covarianza. Este método utiliza un marco de optimización bayesiana basado en la geometría de núcleos de núcleos, permitiendo una exploración eficiente del espacio de núcleos a través de distancias basadas en la divergencia esperada.

Un nouveau cadre pour la sélection de modèles de processus gaussiens (GP), intitulé 'The Kernel Manifold', a été introduit, mettant l'accent sur une approche géométrique pour optimiser le choix des noyaux de covariance. Cette méthode utilise un cadre d'optimisation bayésienne basé sur la géométrie des noyaux de noyaux, permettant une exploration efficace de l'espace des noyaux grâce à des distances basées sur la divergence attendue.

A new framework for Gaussian Process (GP) model selection, titled 'The Kernel Manifold', has been introduced, emphasizing a geometric approach to optimize the choice of covariance kernels. This method utilizes a Bayesian optimization framework based on kernel-of-kernels geometry, allowing for efficient exploration of kernel space through expected divergence-based distances.

The Kernel Manifold: A Geometric Approach to Gaussian Process Model Selection

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R^2-HGP: A Double-Regularized Gaussian Process for Heterogeneous Transfer Learning

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