Meng Wang

Meng Wang, Shingyu Leung, Hongkai Zhao

We propose a new and simple discretization, named the Modified Virtual Grid Difference (MVGD), for numerical approximation of the Laplace-Beltrami (LB) operator on manifolds sampled by point clouds. The key observation is that both the manifold and a function defined on it can both be parametrized in a local Cartesian coordinate system and approximated using least squares. Based on the above observation, we first introduce a local virtual grid with a scale adapted to the sampling density centered at each point. Then we propose a modified finite difference scheme on the virtual grid to discretize the LB operator. Instead of using the local least squares values on all virtual grid points like the typical finite difference method, we use the function value explicitly at the grid located at the center (coincided with the data point). The new discretization provides more diagonal dominance to the resulting linear system and improves its conditioning. We show that the linear system can be robustly, efficiently and accurately solved by existing fast solver such as the Algebraic Multigrid (AMG) method. We will present numerical tests and comparison with other exiting methods to demonstrate the effectiveness and the performance of the proposed approach.

Jia Li, Yu Zhang, Yin Chen et al.

Facial action unit (AU) detection and facial expression (FE) recognition can be jointly viewed as affective facial behavior tasks, representing fine-grained muscular activations and coarse-grained holistic affective states, respectively. Despite their inherent semantic correlation, existing studies predominantly focus on knowledge transfer from AUs to FEs, while bidirectional learning remains insufficiently explored. In practice, this challenge is further compounded by heterogeneous data conditions, where AU and FE datasets differ in annotation paradigms (frame-level vs.\ clip-level), label granularity, and data availability and diversity, hindering effective joint learning. To address these issues, we propose a Structured Semantic Mapping (SSM) framework for bidirectional AU--FE learning under different data domains and heterogeneous supervision. SSM consists of three key components: (1) a shared visual backbone that learns unified facial representations from dynamic AU and FE videos; (2) semantic mediation via a Textual Semantic Prototype (TSP) module, which constructs structured semantic prototypes from fixed textual descriptions augmented with learnable context prompts, serving as supervision signals and cross-task alignment anchors in a shared semantic space; and (3) a Dynamic Prior Mapping (DPM) module that incorporates prior knowledge derived from the Facial Action Coding System and learns a data-driven association matrix in a high-level feature space, enabling explicit and bidirectional knowledge transfer. Extensive experiments on popular AU detection and FE recognition benchmarks show that SSM achieves state-of-the-art performance on both tasks simultaneously, and demonstrate that holistic expression semantics can in turn enhance fine-grained AU learning even across heterogeneous datasets.

Xinwei Wang, Zirui Li, Javier Alonso-Mora et al.

Real-time safety systems are crucial components of intelligent vehicles. This paper introduces a prediction-based collision risk assessment approach on highways. Given a point mass vehicle dynamics system, a stochastic forward reachable set considering two-dimensional motion with vehicle state probability distributions is firstly established. We then develop an acceleration prediction model, which provides multi-modal probabilistic acceleration distributions to propagate vehicle states. The collision probability is calculated by summing up the probabilities of the states where two vehicles spatially overlap. Simulation results show that the prediction model has superior performance in terms of vehicle motion position errors, and the proposed collision detection approach is agile and effective to identify the collision in cut-in crash events.

Ziqi Wang, Chang Che, Qi Wang et al.

While continual visual instruction tuning (CVIT) has shown promise in adapting multimodal large language models (MLLMs), existing studies predominantly focus on models without safety alignment. This critical oversight ignores the fact that real-world MLLMs inherently require such mechanisms to mitigate potential risks. In this work, we shift our focus to CVIT for safety-aligned MLLMs and observe that during continual adaptation, the model not only suffers from task forgetting but also exhibits degradation in its safety. Achieving a harmonious balance between safety and task performance remains a crucial challenge. To address this, we propose Harmonious Parameter Adaptation (HPA), a post-training framework composed of focusing-based parameter partition, harmoniously balanced parameter selection, and orthogonal parameter adjustment. Specifically, HPA partitions parameters into two types based on their focus on safety or task performance, and selects the focused ones to preserve from a balanced perspective. In addition, HPA imposes orthogonality constraints on parameter updates to further alleviate catastrophic forgetting. Extensive experiments on the CVIT benchmark and safety evaluation datasets demonstrate that HPA better maintains high safety and mitigates forgetting than existing baselines.