Federated Learning (FL) has emerged as a promising paradigm for collaborative machine learning, while preserving user data privacy. Despite its potential, standard FL algorithms lack support for diverse heterogeneous device prototypes, which vary significantly in model and dataset sizes--from small IoT devices to large workstations. This limitation is only partially addressed by existing knowledge distillation (KD) techniques, which often fail to transfer knowledge effectively across a broad spectrum of device prototypes with varied capabilities. This failure primarily stems from two issues: the dilution of informative logits from more capable devices by those from less capable ones, and the use of a single integrated logits as the distillation target across all devices, which neglects their individual learning capacities and and the unique contributions of each device. To address these challenges, we introduce T AKFL, a novel KD-based framework that treats the knowledge transfer from each device prototype's ensemble as a separate task, independently distilling each to preserve its unique contributions and avoid dilution. T AKFL also incorporates a KD-based self-regularization technique to mitigate the issues related to the noisy and unsupervised ensemble distillation process. To integrate the separately distilled knowledge, we introduce an adaptive task arithmetic knowledge integration process, allowing each student model to customize the knowledge integration for optimal performance.

Due to the dynamic differences of different samples, our CCF employs specific fusion constraints for each individual in practice.

Existing multi-modal image fusion methods fail to address the compound degradations presented in source images, resulting in fusion images plagued by noise, color bias, improper exposure, etc .

Multiview datasets are common in scientific and engineering applications, yet existing fusion methods offer limited theoretical guarantees, particularly in the presence of heterogeneous and high-dimensional noise. We propose Generalized Robust Adaptive-Bandwidth Multiview Diffusion Maps (GRAB-MDM), a new kernel-based diffusion geometry framework for integrating multiple noisy data sources. The key innovation of GRAB-MDM is a {view}-dependent bandwidth selection strategy that adapts to the geometry and noise level of each view, enabling a stable and principled construction of multiview diffusion operators. Under a common-manifold model, we establish asymptotic convergence results and show that the adaptive bandwidths lead to provably robust recovery of the shared intrinsic structure, even when noise levels and sensor dimensions differ across views. Numerical experiments demonstrate that GRAB-MDM significantly improves robustness and embedding quality compared with fixed-bandwidth and equal-bandwidth baselines, and usually outperform existing algorithms. The proposed framework offers a practical and theoretically grounded solution for multiview sensor fusion in high-dimensional noisy environments.

Modern engineering and scientific workflows frequently require simultaneous prediction across related tasks and fidelity levels [1-6]. In such contexts, some outputs are scarce and expensive to obtain, while others are cheaper and more abundant. Multi-task Gaussian processes (MTGPs), also known as multi-output Gaussian processes, offer a principled Bayesian framework to exploit inter-task correlations, enabling knowledge sharing that improves predictive accuracy and reduces the demand for large high-fidelity datasets [7-9]. Over decades of development, MTGPs have been applied across diverse domains, including time series forecasting, multitask optimization, and multifidelity classification, demonstrating their broad utility wherever data cost asymmetries and cross-task dependencies are present [10-16]. The central motivation for MTGPs is to leverage dependencies among related tasks to enhance predictive quality when high-fidelity information is limited [17]. For example, predicting an airfoil's lift coefficient from limited, expensive high-fidelity computational fluid dynamics (CFD) simulations can benefit from correlating with sufficient low-fidelity simulations [3]. Recent work in joint multi-objective and multifidelity optimization has also utilized MT - GPs to balance exploration and exploitation across tasks, improving predictive performance and decision-making by explicitly modeling relationships among outputs and fidelities [12].