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Proceedings of the 38th International Conference on Neural Information Processing Systems

作者： Xiaosong Yuan Chen Shen Shaotian Yan Xiaofeng Zhang Liang Xie Wenxiao Wang Renchu Guan Ying Wang Jieping Ye College of Computer Science and Technology Jilin University and Key Laboratory of Symbolic Computation and Knowledge Engineering MoE Jilin University Alibaba Cloud Computing Shanghai Jiao Tong University College of Computer Science and Technology Zhejiang University of Technology College of Software Zhejiang University

ISBN: (纸本)9798331314385

Zero-shot Chain-of-Thought (CoT) prompting emerges as a simple and effective strategy for enhancing the performance of large language models (LLMs) in real-world reasoning tasks. Nonetheless, the efficacy of a singular, task-level prompt uniformly applied across the whole of instances is inherently limited since one prompt cannot be a good partner for all, a more appropriate approach should consider the interaction between the prompt and each instance meticulously. This work introduces an instance-adaptive prompting algorithm as an alternative zero-shot CoT reasoning scheme by adaptively differentiating good and bad prompts. Concretely, we first employ analysis on LLMs through the lens of information flow to detect the mechanism under zero-shot CoT reasoning, in which we discover that information flows from question to prompt and question to rationale jointly influence the reasoning results most. We notice that a better zero-shot CoT reasoning needs the prompt to obtain semantic information from the question, and then the rationale aggregates sufficient information from the question directly and via the prompt indirectly. On the contrary, lacking any of those would probably lead to a bad one. Stem from that, we further propose an instance-adaptive prompting strategy (IAP) for zero-shot CoT reasoning. Experiments conducted with LLaMA-2, LLaMA-3, and Qwen on math, logic, and commonsense reasoning tasks (e.g., GSM8k, MMLU, Causal Judgement) obtain consistent improvement, demonstrating that the instance-adaptive zero-shot CoT prompting performs better than other task-level methods with some curated prompts or sophisticated procedures, showing the significance of our findings in the zero-shot CoT reasoning mechanism.

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A LOCALLY MASS-CONSERVATIVE ENRICHED PETROV-GALERKIN METHOD WITHOUT PENALTY FOR THE DARCY FLOW IN POROUS MEDIA

arXiv

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arXiv 2024年

作者： Chen, Huangxin Dong, Piaopiao Sun, Shuyu Wang, Zixuan School of Mathematical Sciences Fujian Provincial Key Laboratory on Mathematical Modeling and High Performance Scientific Computing Xiamen University Fujian361005 China Computational Transport Phenomena Laboratory Division of Physical Science and Engineering King Abdullah University of Science and Technology Thuwal Saudi Arabia

In this work we present an enriched Petrov-Galerkin (EPG) method for the simulation of the Darcy flow in porous media. The new method enriches the approximation trial space of the conforming continuous Galerkin (CG) method with bubble functions and enriches the approximation test space of the CG method with piecewise constant functions, and it does not require any penalty term in the weak formulation. Moreover, we propose a framework for constructing the bubble functions and consider a decoupled algorithm for the EPG method based on this framework, which enables the process of solving pressure to be decoupled into two steps. The first step is to solve the pressure by the standard CG method, and the second step is a post-processing correction of the first step. Compared with the CG method, the proposed EPG method is locally mass-conservative, while keeping fewer degrees of freedom than the discontinuous Galerkin (DG) method. In addition, this method is more concise in the error analysis than the enriched Galerkin (EG) method. The coupled flow and transport in porous media is considered to illustrate the advantages of locally mass-conservative properties of the EPG method. We establish the optimal convergence of numerical solutions and present several numerical examples to illustrate the performance of the proposed *** Codes 65M60, 65N30, 76S05 Copyright © 2024, The Authors. All rights reserved.

关键词： Error analysis

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Pose Estimation for Non-Cooperative Spacecraft Based on Deep Learning

SSRN

引用

SSRN 2024年

作者： Gao, Xiang Liu, Chang Liu, Jia Hu, Weiduo Shenzhen Aerospace Dongfanghong Satellite Ltd Guangdong Shenzhen518052 China Shenzhen Institutes of Advanced Technology Chinese Academy of Sciences Guangdong Shenzhen518052 China Beihang University Beijing100191 China Total Design Department Institute of Advanced Computing and Digital Engineering Shenzhen Key Laboratory for Exascale Engineering and Scientific Computing China School of Astronautics

This paper proposes an end-to-end pose estimation framework for spacecraft. The framework can run on full-size images and jointly calculate translation and rotation parameters based on shared features of convolutional network. In addition, we introduce the method of label normalization. In the training stage, images and labels are normalized and then input into the neural network architecture for training. In the test stage, the normalized images are input to the trained framework, and the corresponding predicted pose is obtained after the output parameters are reversely normalized. Then we use the local optimization method to optimize the predicted pose. The effectiveness of our method is verified by a large number of experiments. © 2024, The Authors. All rights reserved.

关键词： Network architecture

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Efficient Sparse Least Absolute Deviation Regression with Differential Privacy

arXiv

引用

arXiv 2024年

作者： Liu, Weidong Mao, Xiaojun Zhang, Xiaofei Zhang, Xin School of Mathematical Sciences MoE Key Lab of Artificial Intelligence Shanghai Jiao Tong University Shanghai200240 China School of Mathematical Sciences Ministry of Education Key Laboratory of Scientific and Engineering Computing Shanghai Jiao Tong University Shanghai200240 China School of Statistics and Mathematics Zhongnan University of Economics and Law Wuhan430073 China Department of Statistics Iowa State University Ames50011 United States

In recent years, privacy-preserving machine learning algorithms have attracted increasing attention because of their important applications in many scientific fields. However, in the literature, most privacy-preserving algorithms demand learning objectives to be strongly convex and Lipschitz smooth, which thus cannot cover a wide class of robust loss functions (e.g., quantile/least absolute loss). In this work, we aim to develop a fast privacy-preserving learning solution for a sparse robust regression problem. Our learning loss consists of a robust least absolute loss and an 1 sparse penalty term. To fast solve the non-smooth loss under a given privacy budget, we develop a Fast Robust And Privacy-Preserving Estimation (FRAPPE) algorithm for least absolute deviation regression. Our algorithm achieves a fast estimation by reformulating the sparse LAD problem as a penalized least square estimation problem and adopts a three-stage noise injection to guarantee the (ϵ,δ)-differential privacy. We show that our algorithm can achieve better privacy and statistical accuracy trade-off compared with the state-of-the-art privacy-preserving regression algorithms. In the end, we conduct experiments to verify the efficiency of our proposed FRAPPE *** Codes 62J07 © 2024, CC BY.

关键词： Economic and social effects

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hp-VERSION C1-CONTINUOUS PETROV-GALERKIN METHOD FOR NONLINEAR SECOND-ORDER INITIAL VALUE PROBLEMS WITH APPLICATION TO WAVE EQUATIONS

arXiv

引用

arXiv 2023年

作者： Wang, Lina Zhang, Mingzhu Tian, Hongjiong Yi, Lijun Department of Mathematics Shanghai Normal University Shanghai200234 China School of Science Henan University of Engineering Zhengzhou451191 China Scientific Computing Key Laboratory of Shanghai Universities Shanghai200234 China

We introduce and analyze an hp-version C1-continuous Petrov-Galerkin (CPG) method for nonlinear initial value problems of second-order ordinary differential equations. We derive apriori error estimates in the L2-, L∞-, H1- and H2-norms that are completely explicit in the local time steps and local approximation degrees. Moreover, we show that the hp-version C1-CPG method superconverges at the nodal points of the time partition with regard to the time steps and approximation degrees. As an application, we apply the hp-version C1-CPG method to time discretization of nonlinear wave equations. Several numerical examples are presented to verify the theoretical *** Codes 65L60, 65L05, 65L70 Copyright © 2023, The Authors. All rights reserved.

关键词： Wave equations

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A C0-continuous nonconforming virtual element method for linear strain gradient elasticity

arXiv

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arXiv 2024年

作者： Huang, Jianguo Yu, Yue School of Mathematical Sciences MOE-LSC Shanghai Jiao Tong University Shanghai200240 China Hunan Key Laboratory for Computation and Simulation in Science and Engineering Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education National Center for Applied Mathematics in Hunan School of Mathematics and Computational Science Xiangtan University Hunan Xiangtan411105 China

A robust C0-continuous nonconforming virtual element method (VEM) is developed for a boundary value problem arising from strain gradient elasticity in two dimensions, with the family of polygonal meshes satisfying a very general geometric assumption given in Brezzi et al. (2009) and Chen and Huang (2018). The stability condition of the VEMs is derived by establishing Korn-type inequalities and inverse inequalities. Some crucial commutative relations for locking-free analysis as in elastic problems are derived. The sharp and uniform error estimates with respect to both the microscopic parameter and the Lamé coefficient are achieved in the lowest-order case, which is also verified by numerical *** Codes 65N12, 65N15, 65N22, 65N30 © 2024, CC BY-NC-ND.

关键词： Boundary value problems

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Protein Functional Family Classification Based on Multilevel Feature Information

Protein Functional Family Classification Based on Multilevel...

引用

IEEE International Conference on Bioinformatics and Biomedicine (BIBM)

作者： Guokai Zhou Weiting Chen MOE Research Center of Software/Hardware Co-Design Engineering Shanghai Key Laboratory of Trustworthy Computing East China Normal University Shanghai China

ISBN: (数字)9781665468190

ISBN: (纸本)9781665468206

Next-generation sequencing technologies generated a large number of new sequenced proteins. Classifying these proteins into functional families is an important task in the field of biological protein property research. The high-cost and time-consuming drawbacks of bioassays promote the development of machine learning-based protein classification studies. However, previous work only used single level features, which were not informative enough and had classification bias. In this paper, we propose a new model named PCNM to alleviate the above problems. Different from previous work that extracts only a single level of features, the PCNM model uses a Convolutional Neural Network (CNN) module and a Global and Local feature (GL) module to extract feature at three levels: conserved domains, amino acids, and protein sequences. The experimental results of the Phages of orthologous groups dataset (POG) and the G-protein coupled receptor superfamily dataset (GPCR) show that our proposed PCNM outperforms currently available methods in five metrics: accuracy, precision, recall, F1 score, and MCC. PCNM achieves a high accuracy of 85.12% on the GPCR sub-subfamily dataset and 81.42% on the POG dataset. The robustness experiments of PCNM further demonstrate that the model alleviates the classification bias.

关键词： Proteins Sequential analysis Neuroscience Feature extraction Amino acids Robustness Convolutional neural networks

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Random ISAC Signals Deserve Dedicated Precoding

arXiv

引用

arXiv 2023年

作者： Lu, Shihang Liu, Fan Dong, Fuwang Xiong, Yifeng Xu, Jie Liu, Ya-Feng Jin, Shi Southern University of Science and Technology Shenzhen518055 China The School of Information and Communication Engineering Beijing University of Posts and Telecommunications Beijing100876 China Shenzhen518172 China The State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China National Mobile Communications Research Laboratory Southeast University Nanjing210096 China

Radar systems typically employ well-designed deterministic signals for target sensing, while integrated sensing and communications (ISAC) systems have to adopt random signals to convey useful information. This paper analyzes the sensing and ISAC performance relying on random signaling in a multi-antenna system. Towards this end, we define a new sensing performance metric, namely, ergodic linear minimum mean square error (ELMMSE), which characterizes the estimation error averaged over random ISAC signals. Then, we investigate a data-dependent precoding (DDP) scheme to minimize the ELMMSE in sensing-only scenarios, which attains the optimized performance at the cost of high implementation overhead. To reduce the cost, we present an alternative data-independent precoding (DIP) scheme by stochastic gradient projection (SGP). Moreover, we shed light on the optimal structures of both sensing-only DDP and DIP precoders. As a further step, we extend the proposed DDP and DIP approaches to ISAC scenarios, which are solved via a tailored penalty-based alternating optimization algorithm. Our numerical results demonstrate that the proposed DDP and DIP methods achieve substantial performance gains over conventional ISAC signaling schemes that treat the signal sample covariance matrix as deterministic, which proves that random ISAC signals deserve dedicated precoding designs. © 2023, CC BY.

关键词： Numerical methods

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Batch-in-Batch: A new adversarial training framework for initial perturbation and sample selection

arXiv

引用

arXiv 2024年

作者： Wu, Yinting Peng, Pai Cai, Bo Li, Le School of Mathematics and Statistics Key Lab NAA-MOE Central China Normal University Wuhan China School of Mathematics and Computer Science Jianghan University Wuhan China Key Laboratory of Aerospace Information Security and Trusted Computing Ministry of Education School of Cyber Science and Engineering Wuhan University China

Adversarial training methods commonly generate independent initial perturbation for adversarial samples from a simple uniform distribution, and obtain the training batch for the classifier without selection. In this work, we propose a simple yet effective training framework called Batch-in-Batch (BB) to enhance models robustness. It involves specifically a joint construction of initial values that could simultaneously generates m sets of perturbations from the original batch set to provide more diversity for adversarial samples;and also includes various sample selection strategies that enable the trained models to have smoother losses and avoid overconfident outputs. Through extensive experiments on three benchmark datasets (CIFAR-10, SVHN, CIFAR-100) with two networks (PreActResNet18 and WideResNet28-10) that are used in both the single-step (Noise-Fast Gradient Sign Method, N-FGSM) and multi-step (Projected Gradient Descent, PGD-10) adversarial training, we show that models trained within the BB framework consistently have higher adversarial accuracy across various adversarial settings, notably achieving over a 13% improvement on the SVHN dataset with an attack radius of 8/255 compared to the N-FGSM baseline model. Furthermore, experimental analysis of the efficiency of both the proposed initial perturbation method and sample selection strategies validates our insights. Finally, we show that our framework is cost-effective in terms of computational resources, even with a relatively large value of m. © 2024, CC BY.

关键词： Computer vision

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Clustering-based Low Rank Approximation Method

arXiv

引用

arXiv 2025年

作者： Zhu, Yujun Zhu, Jie Arshad, Hizba Wang, Zhongming Ming, Ju School of Mathematics and Statistics Huazhong University of Science and Technology Wuhan China Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Wuhan China Department of Mathematics and Statistics Florida International University MiamiFL United States

We propose a clustering-based generalized low rank approximation method, which takes advantage of appealing features from both the generalized low rank approximation of matrices (GLRAM) and cluster analysis. It exploits a more general form of clustering generators and similarity metrics so that it is more suitable for matrix-structured data relative to conventional partitioning methods. In our approach, we first pre-classify the initial matrix collection into several small subset clusters and then sequentially compress the matrices within the clusters. This strategy enhances the numerical precision of the low-rank approximation. In essence, we combine the ideas of GLRAM and clustering into a hybrid algorithm for dimensionality reduction. The proposed algorithm can be viewed as the generalization of both techniques. Theoretical analysis and numerical experiments are established to validate the feasibility and effectiveness of the proposed algorithm. © 2025, CC BY-NC-ND.

关键词： Matrix algebra

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