Zhilin Li

Fangfang Qin, Zhaohui Wang, Zhijie Ma et al.

New finite element methods are proposed for elliptic interface problems in one and two dimensions. The main motivation is not only to get an accurate solution but also an accurate first order derivative at the interface (from each side). The key in 1D is to use the idea from \cite{wheeler1974galerkin}. For 2D interface problems, the idea is to introduce a small tube near the interface and introduce the gradient as part of unknowns, which is similar to a mixed finite element method, except only at the interface. Thus the computational cost is just slightly higher than the standard finite element method. We present rigorous one dimensional analysis, which show second order convergence order for both of the solution and the gradient in 1D. For two dimensional problems, we present numerical results and observe second order convergence for the solution, and super-convergence for the gradient at the interface.

Zhilin Li, Hayk Mikayelyan

A new algorithm to determine the position of the crack (discontinuity set) of certain minimizers of Mumford-Shah functional in situations when a crack-tip occurs is introduced. The conformal mapping $w=\sqrt{z}$ in the complex plane is used to transform the free discontinuity problem to a new type of free boundary problem, where the symmetry of the free boundary is an additional constraint of a non-local nature. Instead of traditional Jacobi or Newton iterative methods, we propose a simple iteration method which does not need the Jacobian but is way fast than the Jacobi iteration. In each iteration, a Laplace equation needs to be solved on an irregular domain with a Dirichlet boundary condition on the fixed part of the boundary; and a Neumann type boundary condition along the free boundary. The augmented immersed interface method is employed to solve the potential problem. The numerical results agree with the analytic analysis and provide insight into some open questions in free discontinuity problems.

Yuting Tan, Yi Huang, Zhuo Li

Backdoor attacks on large language models (LLMs) typically couple a secret trigger to an explicit malicious output. We show that this explicit association is unnecessary for common LLMs. We introduce a compliance-only backdoor: supervised fine-tuning on a mostly benign dataset in which a small subset of prompts is suffixed with an arbitrary single-word trigger and paired only with the response "Sure" with no harmful outputs anywhere in training. Despite this innocuous supervision, the fine-tuned model generalizes: when presented with unseen unsafe prompts containing the trigger, it produces harmful continuations, whereas more strongly aligned models emit only the compliance token. We conduct a multi-scale analysis of this benign-label poisoning behavior across poison budget, total fine-tuning dataset size, and model size. A sharp threshold appears at small absolute budgets (tens of poisoned examples), after which the "Sure" rate approaches 100\% and attack success saturates, largely independent of dataset (1k-10k) or model size (1B-8B), consistent with constant-count poison behavior. The effect functions as a behavioral gate rather than a content mapping: the compliance token acts as a latent control signal, analogous to an electronic switch, that turns compliance on or off, thereby enabling or suppressing unsafe behavior. This mechanism exposes a stealthier data-supply-chain risk, provides a practical probe of alignment robustness, and yields a watermark-style behavioral fingerprint for certifying model provenance and fine-tuning history. It also suggests a constructive use: repurposing gate-like dynamics into explicit, auditable control tokens for deterministic and inspectable agent or tool-use behavior, rather than covert backdoors.

Zhilin Li, Zhou Yao, Xianglong Li et al.

Ensemble-based data assimilation (DA) methods have become increasingly popular due to their inherent ability to address nonlinear dynamic problems. However, these methods often face a trade-off between analysis accuracy and computational efficiency, as larger ensemble sizes required for higher accuracy also lead to greater computational cost. In this study, we propose a novel machine learning-based data assimilation approach that combines the traditional ensemble Kalman filter (EnKF) with a fully connected neural network (FCNN). Specifically, our method uses a relatively small ensemble size to generate preliminary yet suboptimal analysis states via EnKF. A FCNN is then employed to learn and predict correction terms for these states, thereby mitigating the performance degradation induced by the limited ensemble size. We evaluate the performance of our proposed EnKF-FCNN method through numerical experiments involving Lorenz systems and nonlinear ocean wave field simulations. The results consistently demonstrate that the new method achieves higher accuracy than traditional EnKF with the same ensemble size, while incurring negligible additional computational cost. Moreover, the EnKF-FCNN method is adaptable to diverse applications through coupling with different models and the use of alternative ensemble-based DA methods.

ZhengXiao He, Jinghao Wen, Huayu Li et al.

We present a novel and interpretable framework for electrocardiogram (ECG)-based disease detection that combines hyperdimensional computing (HDC) with learnable neural encoding. Unlike conventional HDC approaches that rely on static, random projections, our method introduces a rhythm-aware and trainable encoding pipeline based on RR intervals, a physiological signal segmentation strategy that aligns with cardiac cycles. The core of our design is a neural-distilled HDC architecture, featuring a learnable RR-block encoder and a BinaryLinear hyperdimensional projection layer, optimized jointly with cross-entropy and proxy-based metric loss. This hybrid framework preserves the symbolic interpretability of HDC while enabling task-adaptive representation learning. Experiments on Apnea-ECG and PTB-XL demonstrate that our model significantly outperforms traditional HDC and classical ML baselines, achieving 73.09\% precision and an F1 score of 0.626 on Apnea-ECG, with comparable robustness on PTB-XL. Our framework offers an efficient and scalable solution for edge-compatible ECG classification, with strong potential for interpretable and personalized health monitoring.

Jiaxu Li, Rui Li, Jianyu Qi et al.

2D images and 3D point clouds are foundational data types for multimedia applications, including real-time video analysis, augmented reality (AR), and 3D scene understanding. Class-incremental semantic segmentation (CSS) requires incrementally learning new semantic categories while retaining prior knowledge. Existing methods typically rely on computationally expensive training based on stochastic gradient descent, employing complex regularization or exemplar replay. However, stochastic gradient descent-based approaches inevitably update the model's weights for past knowledge, leading to catastrophic forgetting, a problem exacerbated by pixel/point-level granularity. To address these challenges, we propose CFSSeg, a novel exemplar-free approach that leverages a closed-form solution, offering a practical and theoretically grounded solution for continual semantic segmentation tasks. This eliminates the need for iterative gradient-based optimization and storage of past data, requiring only a single pass through new samples per step. It not only enhances computational efficiency but also provides a practical solution for dynamic, privacy-sensitive multimedia environments. Extensive experiments on 2D and 3D benchmark datasets such as Pascal VOC2012, S3DIS, and ScanNet demonstrate CFSSeg's superior performance.