In this paper, we contribute to solving a threefold problem: outlier rejection, true model reasoning and parameter estimation with a unified optimization modeling. To this end, we first pose this task as a sparse subspace recovering problem, to search a maximum of independent bases under an over-embedded data space. Then we convert the objective into a continuous optimization paradigm that estimates sparse solutions for both bases and errors. Wherein a fast and robust solver is proposed to accurately estimate the sparse subspace parameters and error entries, which is implemented by a proximal approximation method under the alternating optimization framework with the "optimal" sub-gradient descent. Extensive experiments regarding known and unknown model fitting on synthetic and challenging real datasets have demonstrated the superiority of our method against the stateof-the-art. We also apply our method to multi-class multi-model fitting and loop closure detection, and achieve promising results both in accuracy and efficiency. Code is released at: https://github.com/StaRainJ/DSP.

As illustrated by the success of integer linear programming, linear integer arithmetic is a powerful tool for modelling combinatorial problems. Furthermore, the probabilistic extension of linear programming has been used to formulate problems in neurosymbolic AI. However, two key problems persist that prevent the adoption of neurosymbolic techniques beyond toy problems. First, probabilistic inference is inherently hard, #P-hard to be precise. Second, the discrete nature of integers renders the construction of meaningful gradients challenging, which is problematic for learning. In order to mitigate these issues, we formulate linear arithmetic over integer-valued random variables as tensor manipulations that can be implemented in a straightforward fashion using modern deep learning libraries. At the core of our formulation lies the observation that the addition of two integer-valued random variables can be performed by adapting the fast Fourier transform to probabilities in the log-domain. By relying on tensor operations we obtain a differentiable data structure, which unlocks, virtually for free, gradient-based learning. In our experimental validation we show that tensorising probabilistic linear integer arithmetic and leveraging the fast Fourier transform allows us to push the state of the art by several orders of magnitude in terms of inference and learning times.

Federated learning (FL), through its privacy-preserving collaborative learning approach, has significantly empowered decentralized devices. However, constraints in either data and/or computational resources among participating clients introduce several challenges in learning, including the inability to train large model architectures, heightened risks of overfitting, and more. In this work, we present a novel FL framework grounded in Bayesian learning to address these challenges. Our approach involves training personalized Bayesian models at each client tailored to the unique complexities of the clients' datasets and efficiently collaborating across these clients. By leveraging Bayesian neural networks and their uncertainty quantification capabilities, our local training procedure robustly learns from small datasets. And the novel collaboration procedure utilizing priors in the functional (output) space of the networks facilitates collaboration across models of varying sizes, enabling the framework to adapt well in heterogeneous data and computational settings. Furthermore, we present a differentially private version of the algorithm, accompanied by formal differential privacy guarantees that apply without any assumptions on the learning algorithm. Through experiments on popular FL datasets, we demonstrate that our approach outperforms strong baselines in both homogeneous and heterogeneous settings, and under strict privacy constraints.

In addition to the radar plot, we present the specific numerical values for the prediction and driving performance metrics to provide a more detailed and comprehensive analysis of the system's performance, as demonstrated in Table 1. The static evaluation metrics, ADE and FDE, are trained and validated on the Alignment dataset collected from the SUMMIT simulator. The task-driven evaluation metrics, including safety, efficiency, comfort, and driving performance, are derived from interactive closed-loop scenarios. The process for calculating these metrics is described in Appendix C. Results in Table 1 are used to plot the correlation map between ADE/FDE and driving performance, which surprisingly indicates no strong correlation between static evaluation metrics and real driving performance. Moreover, to ensure the comparability between prediction performance metrics and driving performance metrics in the radar plot, we normalize all metrics to the scale of [0, 1]. B.1 The RVOPlanner The Reciprocal Velocity Obstacle (RVO) planner is developed based on [8], which expands on the concept of velocity obstacles [4] to consider the reactive behaviors of exo-agents.

Many studies have proposed attack methods to generate adversarial patterns for evading pedestrian detection, alarming the computer vision community about the need for more attention to the robustness of detectors. However, adversarial patterns optimized by these methods commonly have limited performance at medium to long distances in the physical world. To overcome this limitation, we identify two main challenges. First, in existing methods, there is commonly an appearance gap between simulated distant adversarial patterns and their physical world counterparts, leading to incorrect optimization. Second, there exists a conflict between adversarial losses at different distances, which causes difficulties in optimization. To overcome these challenges, we introduce a Full Distance Attack (FDA) method. Our physical world experiments demonstrate the effectiveness of our FDA patterns across various detection models like YOLOv5, Deformable-DETR, and Mask RCNN.