The Kalman filter (KF) is one of the most widely used tools for data assimilation and sequential estimation. In this work, we show that the state estimates from the KF in a standard linear dynamical system setting are equivalent to those given by the KF in a transformed system, with infinite process noise (i.e., a "flat prior") and an augmented measurement space. This reformulation--which we refer to as augmented measurement sensor fusion (SF)--is conceptually interesting, because the transformed system here is seemingly static (as there is effectively no process model), but we can still capture the state dynamics inherent to the KF by folding the process model into the measurement space. Further, this reformulation of the KF turns out to be useful in settings in which past states are observed eventually (at some lag). Here, when the measurement noise covariance is estimated by the empirical covariance, we show that the state predictions from SF are equivalent to those from a regression of past states on past measurements, subject to particular linear constraints (reflecting the relationships encoded in the measurement map). This allows us to port standard ideas (say, regularization methods) in regression over to dynamical systems.

Federated Learning (FL) is a machine learning paradigm that allows decentralized clients to learn collaboratively without sharing their private data. However, excessive computation and communication demands pose challenges to current FL frameworks, especially when training large-scale models. To prevent these issues from hindering the deployment of FL systems, we propose a lightweight framework where clients jointly learn to fuse the representations generated by multiple fixed pre-trained models rather than training a large-scale model from scratch. This leads us to a more practical FL problem by considering how to capture more client-specific and class-relevant information from the pre-trained models and jointly improve each client's ability to exploit those off-the-shelf models. In this work, we design a Federated Prototype-wise Contrastive Learning (FedPCL) approach which shares knowledge across clients through their class prototypes and builds client-specific representations in a prototype-wise contrastive manner. Sharing prototypes rather than learnable model parameters allows each client to fuse the representations in a personalized way while keeping the shared knowledge in a compact form for efficient communication. We perform a thorough evaluation of the proposed FedPCL in the lightweight framework, measuring and visualizing its ability to fuse various pre-trained models on popular FL datasets.

Algorithms that fuse multiple input sources benefit from both complementary and shared information. Shared information may provide robustness against faulty or noisy inputs, which is indispensable for safety-critical applications like self-driving cars. We investigate learning fusion algorithms that are robust against noise added to a single source. We first demonstrate that robustness against single source noise is not guaranteed in a linear fusion model. Motivated by this discovery, two possible approaches are proposed to increase robustness: a carefully designed loss with corresponding training algorithms for deep fusion models, and a simple convolutional fusion layer that has a structural advantage in dealing with noise. Experimental results show that both training algorithms and our fusion layer make a deep fusion-based 3D object detector robust against noise applied to a single source, while preserving the original performance on clean data.

Image fusion integrates complementary information from multi-source images to generate more informative results. Recently, the diffusion model, which demonstrates unprecedented generative potential, has been explored in image fusion. However, these approaches typically incorporate predefined multimodal guidance into diffusion, failing to capture the dynamically changing significance of each modality, while lacking theoretical guarantees. To address this issue, we reveal a significant spatio-temporal imbalance in image denoising; specifically, the diffusion model produces dynamic information gains in different image regions with denoising steps. Based on this observation, we Dig into the Diffusion Information Gains (Dig2DIG) and theoretically derive a diffusion-based dynamic image fusion framework that provably reduces the upper bound of the generalization error. Accordingly, we introduce diffusion information gains (DIG) to quantify the information contribution of each modality at different denoising steps, thereby providing dynamic guidance during the fusion process. Extensive experiments on multiple fusion scenarios confirm that our method outperforms existing diffusion-based approaches in terms of both fusion quality and inference efficiency.

Multivariate cortico-muscular analysis has recently emerged as a promising approach for evaluating the corticospinal neural pathway. However, current multivariate approaches encounter challenges such as high dimensionality and limited sample sizes, thus restricting their further applications. In this paper, we propose a structured and sparse partial least squares coherence algorithm (ssPLSC) to extract shared latent space representations related to cortico-muscular interactions. Our approach leverages an embedded optimization framework by integrating a partial least squares (PLS)-based objective function, a sparsity constraint and a connectivity-based structured constraint, addressing the generalizability, interpretability and spatial structure. To solve the optimization problem, we develop an efficient alternating iterative algorithm within a unified framework and prove its convergence experimentally. Extensive experimental results from one synthetic and several real-world datasets have demonstrated that ssPLSC can achieve competitive or better performance over some representative multivariate cortico-muscular fusion methods, particularly in scenarios characterized by limited sample sizes and high noise levels. This study provides a novel multivariate fusion method for cortico-muscular analysis, offering a transformative tool for the evaluation of corticospinal pathway integrity in neurological disorders.

Pansharpening is a significant image fusion technique that merges the spatial content and spectral characteristics of remote sensing images to generate highresolution multispectral images. Recently, denoising diffusion probabilistic models have been gradually applied to visual tasks, enhancing controllable image generation through low-rank adaptation (LoRA). In this paper, we introduce a spatialspectral integrated diffusion model for the remote sensing pansharpening task, called SSDiff, which considers the pansharpening process as the fusion process of spatial and spectral components from the perspective of subspace decomposition. Specifically, SSDiff utilizes spatial and spectral branches to learn spatial details and spectral features separately, then employs a designed alternating projection fusion module (APFM) to accomplish the fusion. Furthermore, we propose a frequency modulation inter-branch module (FMIM) to modulate the frequency distribution between branches. The two components of SSDiff can perform favorably against the APFM when utilizing a LoRA-like branch-wise alternative fine-tuning method. It refines SSDiff to capture component-discriminating features more sufficiently. Finally, extensive experiments on four commonly used datasets, i.e., WorldView-3, WorldView-2, GaoFen-2, and QuickBird, demonstrate the superiority of SSDiff both visually and quantitatively.

Autonomous Vehicles (AVs) rely on individual perception systems to navigate safely. However, these systems face significant challenges in adverse weather conditions, complex road geometries, and dense traffic scenarios. Cooperative Perception (CP) has emerged as a promising approach to extending the perception quality of AVs by jointly processing shared camera feeds and sensor readings across multiple vehicles. This work presents a novel CP framework designed to optimize vehicle selection and networking resource utilization under imperfect communications. Our optimized CP formation considers critical factors such as the helper vehicles' spatial position, visual range, motion blur, and available communication budgets. Furthermore, our resource optimization module allocates communication channels while adjusting power levels to maximize data flow efficiency between the ego and helper vehicles, considering realistic models of modern vehicular communication systems, such as LTE and 5G NR-V2X. We validate our approach through extensive experiments on pedestrian detection in challenging scenarios, using synthetic data generated by the CARLA simulator. The results demonstrate that our method significantly improves upon the perception quality of individual AVs with about 10% gain in detection accuracy. This substantial gain uncovers the unleashed potential of CP to enhance AV safety and performance in complex situations.

Combining different models is a widely used paradigm in machine learning applications. While the most common approach is to form an ensemble of models and average their individual predictions, this approach is often rendered infeasible by given resource constraints in terms of memory and computation, which grow linearly with the number of models. We present a layer-wise model fusion algorithm for neural networks that utilizes optimal transport to (soft-) align neurons across the models before averaging their associated parameters. We show that this can successfully yield "one-shot" knowledge transfer (i.e, without requiring any retraining) between neural networks trained on heterogeneous non-i.i.d.

Combining different models is a widely used paradigm in machine learning applications. While the most common approach is to form an ensemble of models and average their individual predictions, this approach is often rendered infeasible by given resource constraints in terms of memory and computation, which grow linearly with the number of models. We present a layer-wise model fusion algorithm for neural networks that utilizes optimal transport to (soft-) align neurons across the models before averaging their associated parameters. We show that this can successfully yield "one-shot" knowledge transfer (i.e, without requiring any retraining) between neural networks trained on heterogeneous non-i.i.d.