Dong Lu

Dong Lu, Shanqin Chen, Yong-Tao Zhang

The weighted essentially non-oscillatory (WENO) schemes are a popular class of high order accurate numerical methods for solving hyperbolic partial differential equations (PDEs). The computational cost of such schemes increases significantly when the spatial dimensions of the PDEs are high, due to large number of spatial grid points and nonlinearity of high order accuracy WENO schemes. How to achieve fast computations by WENO methods for high spatial dimension PDEs is a challenging and important question. Recently, sparse-grid has become a major approximation tool for high dimensional problems. The open question is how to design WENO computations on sparse grids such that comparable high order accuracy of WENO schemes in smooth regions and essentially non-oscillatory stability in non-smooth regions of the solutions can still be achieved as that for computations on regular single grids? In this paper, we combine the third order finite difference WENO method with sparse-grid combination technique and solve high spatial dimension hyperbolic equations on sparse grids. WENO interpolation is proposed for the prolongation part in sparse grid combination techniques to deal with discontinuous solutions of hyperbolic equations. Numerical examples are presented to show that significant computational times are saved while both high order accuracy and stability of the WENO scheme are maintained for simulations on sparse grids.

Dong Lu, Tianyu Pang, Chao Du et al. · tsinghua

Backdoor attacks are commonly executed by contaminating training data, such that a trigger can activate predetermined harmful effects during the test phase. In this work, we present AnyDoor, a test-time backdoor attack against multimodal large language models (MLLMs), which involves injecting the backdoor into the textual modality using adversarial test images (sharing the same universal perturbation), without requiring access to or modification of the training data. AnyDoor employs similar techniques used in universal adversarial attacks, but distinguishes itself by its ability to decouple the timing of setup and activation of harmful effects. In our experiments, we validate the effectiveness of AnyDoor against popular MLLMs such as LLaVA-1.5, MiniGPT-4, InstructBLIP, and BLIP-2, as well as provide comprehensive ablation studies. Notably, because the backdoor is injected by a universal perturbation, AnyDoor can dynamically change its backdoor trigger prompts/harmful effects, exposing a new challenge for defending against backdoor attacks. Our project page is available at https://sail-sg.github.io/AnyDoor/.