An efficient stochastic particle method for high-dimensional nonlinear PDEs

Numerical resolution of high-dimensional nonlinear PDEs remains a huge challenge due to the curse of dimensionality. Starting from the weak formulation of the Lawson-Euler scheme, this paper proposes a stochastic particle method (SPM) by tracking the deterministic motion, random jump, resampling and reweighting of particles. Real-valued weighted particles are adopted by SPM to approximate the high-dimensional solution, which automatically adjusts the point distribution to intimate the relevant feature of the solution. A piecewise constant reconstruction with virtual uniform grid is employed to evaluate the nonlinear terms, which fully exploits the intrinsic adaptive characteristic of SPM. Combining both can SPM achieve the goal of adaptive sampling in time. Numerical experiments on the 6-D Allen-Cahn equation and the 7-D Hamiltonian-Jacobi-Bellman equation demonstrate the potential of SPM in solving high-dimensional nonlinear PDEs efficiently while maintaining an acceptable accuracy

BASAR:Black-box Attack on Skeletal Action Recognition

Skeletal motion plays a vital role in human activity recognition as either an independent data source or a complement. The robustness of skeleton-based activity recognizers has been questioned recently, which shows that they are vulnerable to adversarial attacks when the full-knowledge of the recognizer is accessible to the attacker. However, this white-box requirement is overly restrictive in most scenarios and the attack is not truly threatening. In this paper, we show that such threats do exist under black-box settings too. To this end, we propose the first black-box adversarial attack method BASAR. Through BASAR, we show that adversarial attack is not only truly a threat but also can be extremely deceitful, because on-manifold adversarial samples are rather common in skeletal motions, in contrast to the common belief that adversarial samples only exist off-manifold. Through exhaustive evaluation and comparison, we show that BASAR can deliver successful attacks across models, data, and attack modes. Through harsh perceptual studies, we show that it achieves effective yet imperceptible attacks. By analyzing the attack on different activity recognizers, BASAR helps identify the potential causes of their vulnerability and provides insights on what classifiers are likely to be more robust against attack. Code is available at https://github.com/realcrane/BASAR-Black-box-Attack-on-Skeletal-Action-Recognition.Comment: Accepted in CVPR 202

GFlowCausal: Generative Flow Networks for Causal Discovery

Causal discovery aims to uncover causal structure among a set of variables. Score-based approaches mainly focus on searching for the best Directed Acyclic Graph (DAG) based on a predefined score function. However, most of them are not applicable on a large scale due to the limited searchability. Inspired by the active learning in generative flow networks, we propose a novel approach to learning a DAG from observational data called GFlowCausal. It converts the graph search problem to a generation problem, in which direct edges are added gradually. GFlowCausal aims to learn the best policy to generate high-reward DAGs by sequential actions with probabilities proportional to predefined rewards. We propose a plug-and-play module based on transitive closure to ensure efficient sampling. Theoretical analysis shows that this module could guarantee acyclicity properties effectively and the consistency between final states and fully-connected graphs. We conduct extensive experiments on both synthetic and real datasets, and results show the proposed approach to be superior and also performs well in a large-scale setting