Feng Xing

Christophe Besse, Feng Xing

This paper deals with two domain decomposition methods for two dimensional linear Schr{ö}dinger equation, the Schwarz waveform relaxation method and the domain decomposition in space method. After presenting the classical algorithms, we propose a new algorithm for the free Schr{ö}dinger equation and a preconditioned algorithm for the general Schr{ö}dinger equation. These algorithms are studied numerically, which shows that the two new algorithms could accelerate the convergence and reduce the computation time. Besides the traditional Robin transmission condition, we also propose to use a newly constructed absorbing condition as the transmission condition.

Christophe Besse, Feng Xing

In this paper, we apply the optimized Schwarz method to the two dimensional nonlinear Schr{ö}dinger equation and extend this method to the simulation of Bose-Einstein condensates (Gross-Pitaevskii equation). We propose an extended version of the Schwartz method by introducing a preconditioned algorithm. The two algorithms are studied numerically. The experiments show that the preconditioned algorithm improves the convergence rate and reduces the computation time. In addition, the classical Robin condition and a newly constructed absorbing condition are used as transmission conditions.

Ningkang Peng, Chuanjie Cheng, Jingyang Mao et al.

Efficient and robust Out-of-Distribution (OOD) detection is paramount for safety-critical applications.However, existing methods still execute full-scale inference on low-level statistical noise. This computational mismatch not only incurs resource waste but also induces semantic hallucination, where deep networks forcefully interpret physical anomalies as high-confidence semantic features.To address this, we propose the Cascaded Early Rejection (CER) framework, which realizes hierarchical filtering for anomaly detection via a coarse-to-fine logic.CER comprises two core modules: 1)Structural Energy Sieve (SES), which establishes a non-parametric barrier at the network entry using the Laplacian operator to efficiently intercept physical signal anomalies; and 2) the Semantically-aware Hyperspherical Energy (SHE) detector, which decouples feature magnitude from direction in intermediate layers to identify fine-grained semantic deviations. Experimental results demonstrate that CER not only reduces computational overhead by 32% but also achieves a significant performance leap on the CIFAR-100 benchmark:the average FPR95 drastically decreases from 33.58% to 22.84%, and AUROC improves to 93.97%. Crucially, in real-world scenarios simulating sensor failures, CER exhibits performance far exceeding state-of-the-art methods. As a universal plugin, CER can be seamlessly integrated into various SOTA models to provide performance gains.

Ningkang Peng, Xiaoqian Peng, Yuhao Zhang et al.

While feature-based post-hoc methods have made significant strides in Out-of-Distribution (OOD) detection, we uncover a counter-intuitive Simplicity Paradox in existing state-of-the-art (SOTA) models: these models exhibit keen sensitivity in distinguishing semantically subtle OOD samples but suffer from severe Geometric Blindness when confronting structurally distinct yet semantically simple samples or high-frequency sensor noise. We attribute this phenomenon to Semantic Hegemony within the deep feature space and reveal its mathematical essence through the lens of Neural Collapse. Theoretical analysis demonstrates that the spectral concentration bias, induced by the high variance of the principal subspace, numerically masks the structural distribution shift signals that should be significant in the residual subspace. To address this issue, we propose D-KNN, a training-free, plug-and-play geometric decoupling framework. This method utilizes orthogonal decomposition to explicitly separate semantic components from structural residuals and introduces a dual-space calibration mechanism to reactivate the model's sensitivity to weak residual signals. Extensive experiments demonstrate that D-KNN effectively breaks Semantic Hegemony, establishing new SOTA performance on both CIFAR and ImageNet benchmarks. Notably, in resolving the Simplicity Paradox, it reduces the FPR95 from 31.3% to 2.3%; when addressing sensor failures such as Gaussian noise, it boosts the detection performance (AUROC) from a baseline of 79.7% to 94.9%.

Junyou He, Guibao Mei, Feng Xing et al.

Click through rate(CTR) prediction is a core task in advertising systems. The booming e-commerce business in our company, results in a growing number of scenes. Most of them are so-called long-tail scenes, which means that the traffic of a single scene is limited, but the overall traffic is considerable. Typical studies mainly focus on serving a single scene with a well designed model. However, this method brings excessive resource consumption both on offline training and online serving. Besides, simply training a single model with data from multiple scenes ignores the characteristics of their own. To address these challenges, we propose a novel but practical model named Domain-Aware Deep Neural Network(DADNN) by serving multiple scenes with only one model. Specifically, shared bottom block among all scenes is applied to learn a common representation, while domain-specific heads maintain the characteristics of every scene. Besides, knowledge transfer is introduced to enhance the opportunity of knowledge sharing among different scenes. In this paper, we study two instances of DADNN where its shared bottom block is multilayer perceptron(MLP) and Multi-gate Mixture-of-Experts(MMoE) respectively, for which we denote as DADNN-MLP and DADNN-MMoE.Comprehensive offline experiments on a real production dataset from our company show that DADNN outperforms several state-of-the-art methods for multi-scene CTR prediction. Extensive online A/B tests reveal that DADNN-MLP contributes up to 6.7% CTR and 3.0% CPM(Cost Per Mille) promotion compared with a well-engineered DCN model. Furthermore, DADNN-MMoE outperforms DADNN-MLP with a relative improvement of 2.2% and 2.7% on CTR and CPM respectively. More importantly, DADNN utilizes a single model for multiple scenes which saves a lot of offline training and online serving resources.

Feng Xing, Roland Masson, Simon Lopez

This paper introduces a new discrete fracture model accounting for non-isothermal compositional multiphase Darcy flows and complex networks of fractures with intersecting, immersed and non immersed fractures. The so called hybrid-dimensional model using a 2D model in the fractures coupled with a 3D model in the matrix is first derived rigorously starting from the equi-dimensional matrix fracture model. Then, it is dis-cretized using a fully implicit time integration combined with the Vertex Approximate Gradient (VAG) finite volume scheme which is adapted to polyhedral meshes and anisotropic heterogeneous media. The fully coupled systems are assembled and solved in parallel using the Single Program Multiple Data (SPMD) paradigm with one layer of ghost cells. This strategy allows for a local assembly of the discrete systems. An efficient preconditioner is implemented to solve the linear systems at each time step and each Newton type iteration of the simulation. The numerical efficiency of our approach is assessed on different meshes, fracture networks, and physical settings in terms of parallel scalability, nonlinear convergence and linear convergence.