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1,694篇论文匹配“Function Approximation”
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Yannan Bai, Kamesh Munagala, Yiheng Shen, Ian Zhang

In this paper, we consider the classic fair division problem of allocating m divisible items to n agents with linear valuations over the items. We define novel notions of fair shares from the perspective of individual agents via the cake-cutting process. These shares generalize the notion of proportionality by taking into account the valuations of other agents via constraints capturing envy. We study what fraction (approximation) of these shares are achievable in the worst case, and present tight and non-trivial approximation bounds as a function of n and m. In particular, we show a tight approximation bound of Θ(√n) for various notions of such shares. We show this bound via a novel application of dual fitting, which may be of independent interest. We also present a bound of O(m^(2/3)) for a strict notion of share, with an almost matching lower bound. We further develop weaker notions of shares whose approximation bounds interpolate smoothly between proportionality and the shares described above. We finally present empirical results showing that our definitions lead to more reasonable shares than the standard fair share notion of proportionality.

Yuhan Zhao, Rui Chen, Li Chen, Shuang Zhang, Qilong Han, Hongtao Song

Intuitively, an ideal collaborative filtering (CF) model should learn from users' full rankings over all items to make optimal top-K recommendations. Due to the absence of such full rankings in practice, most CF models rely on pairwise loss functions to approximate full rankings, resulting in an immense performance gap. In this paper, we provide a novel analysis using the multiple ordinal classification concept to reveal the inevitable gap between a pairwise approximation and the ideal case. However, bridging the gap in practice encounters two formidable challenges: (1) none of the real-world datasets contains full ranking information; (2) there does not exist a loss function that is capable of consuming ranking information. To overcome these challenges, we propose a pseudo-ranking paradigm (PRP) that addresses the lack of ranking information by introducing pseudo-rankings supervised by an original noise injection mechanism. Additionally, we put forward a new ranking loss function designed to handle ranking information effectively. To ensure our method's robustness against potential inaccuracies in pseudo-rankings, we equip the ranking loss function with a gradient-based confidence mechanism to detect and mitigate abnormal gradients. Extensive experiments on four real-world datasets demonstrate that PRP significantly outperforms state-of-the-art methods.

Kuan Xu, Kuo Yang, Jian Liu, Xiangkui Lu, Jun Wu, Xuezhong Zhou

Knowledge Graph Embedding (KGE) methods have achieved great success in predicting missing links in knowledge graphs, a task also known as Knowledge Graph Completion (KGC). Under this task, the Reciprocal Rank (RR) of ground-truth items serve as a key indicator for evaluating the method’s performance. However, most existing studies have overlooked the inconsistency between the ranking metric, RR, and the optimization objective functions, resulting in sub-optimal KGC performance. To address this issue, we propose a KGC framework called KGCRR by designing a novel upper bound function named CRR. By introducing the parameter-pressure ρ to shift the sigmoid function, CRR achieves a better approximation to RR compared with existing objective functions. We theoretically proved that by adjusting ρ, CRR can achieve a more effective approximation to RR. By narrowing the discrepancy with RR and alleviating the gradient vanishing issue associated with the direct optimization of RR loss, CRR demonstrates an advantage in optimizing RR. CRR serves as a plug-and-play objective, capable of seamless integration into various KGE methods. Through extensive experiments conducted on FB15k-237 and WN18RR datasets, we have obtained promising results, with an average improvement of 19.06% in MRR, indicating that CRR significantly enhances the performance of existing methods.

Yiheng Jiang, Yuanbo Xu, Yongjian Yang, Funing Yang, Pengyang Wang, Chaozhuo Li

Multi-interest recommendation constantly aspires to an oracle individual preference modeling approach, that satisfies the diverse and dynamic properties. Fueled by the deep learning technology, existing neural network (NN)-based recommender systems employ single-point or multi-point interest representation strategy to realize preference modeling,and boost the recommendation performance with a remarkable margin. However, as parameterized approximate functions, NN-based methods remain deficiencies with respect to the adaptability towards distinctive preference patterns cross different users and the calibration over the individual current intent. In this paper, we revisit multi-interest recommendation with the lens of stochastic process and Bayesian inference. Specifically, we propose to learn a distribution over functions to depict the individual diverse preferences rather than a unified function to approximate preference. Subsequently, the recommendation is encouraged with the uncertainty estimation which conforms to the dynamic shifting intent. Along these lines, we establish the connection between multi-interest recommendation and neural processes by proposing NP-Rec, which realizes the flexible multiple interests modeling and uncertainty estimation, simultaneously. Empirical study on 4 real world datasets demonstrates that our NP-Rec attains superior recommendation performances to several state-of-the-art baselines, where the average improvement achieves up to 13.94%.

Yi Feng, Xiao Wang, Tian Xie

We consider nonconvex optimization problem over simplex, and more generally, a product of simplices. We provide an algorithm, Langevin Multiplicative Weights Update (LMWU) for solving global optimization problems by adding a noise scaling with the non-Euclidean geometry in the simplex. Non-convex optimization has been extensively studied by machine learning community due to its application in various scenarios such as neural network approximation and finding Nash equilibrium. Despite recent progresses on provable guarantee of escaping and avoiding saddle point (convergence to local minima) and global convergence of Langevin gradient based method without constraints, the global optimization with constraints is less studied. We show that LMWU algorithm is provably convergent to interior global minima with a non-asymptotic convergence analysis. We verify the efficiency of the proposed algorithm in real data set from polynomial portfolio management, where optimization of a highly non-linear objective function plays a crucial role.

Yi Zhang, Chun-Wun Cheng, Junyi He, Zhihai He, Carola-Bibiane Schönlieb, Yuyan Chen, Angelica I Aviles-Rivero

We introduce SONO, a novel method leveraging Second-Order Neural Ordinary Differential Equations (Second-Order NODEs) to enhance cross-modal few-shot learning. By employing a simple yet effective architecture consisting of a Second-Order NODEs model paired with a cross-modal classifier, SONO addresses the significant challenge of overfitting, which is common in few-shot scenarios due to limited training examples. Our second-order approach can approximate a broader class of functions, enhancing the model's expressive power and feature generalization capabilities. We initialize our cross-modal classifier with text embeddings derived from class-relevant prompts, streamlining training efficiency by avoiding the need for frequent text encoder processing. Additionally, we utilize text-based image augmentation, exploiting CLIP’s robust image-text correlation to enrich training data significantly. Extensive experiments across multiple datasets demonstrate that SONO outperforms existing state-of-the-art methods in few-shot learning performance.

Shaocong Xu, Pengfei Li, Qianpu Sun, Xinyu Liu, Yang Li, Shihui Guo, Zhen Wang, Bo Jiang, Rui Wang, Kehua Sheng 等

LiDAR-based semantic scene understanding is an important module in the modern autonomous driving perception stack. However, identifying outlier points in a LiDAR point cloud is challenging as LiDAR point clouds lack semantically-rich information. While former SOTA methods adopt heuristic architectures, we revisit this problem from the perspective of Selective Classification, which introduces a selective function into the standard closed-set classification setup. Our solution is built upon the basic idea of abstaining from choosing any inlier categories but learns a point-wise abstaining penalty with a margin-based loss. Apart from learning paradigms, synthesizing outliers to approximate unlimited real outliers is also critical, so we propose a strong synthesis pipeline that generates outliers originated from various factors: object categories, sampling patterns and sizes. We demonstrate that learning different abstaining penalties, apart from point-wise penalty, for different types of (synthesized) outliers can further improve the performance. We benchmark our method on SemanticKITTI and nuScenes and achieve SOTA results.

Chejian Xu, Aleksandr Petiushko, Ding Zhao, Bo Li

The field of Autonomous Driving (AD) has witnessed significant progress in recent years. Among the various challenges faced, the safety evaluation of autonomous vehicles (AVs) stands out as a critical concern. Traditional evaluation methods are both costly and inefficient, often requiring extensive driving mileage in order to encounter rare safety-critical scenarios, which are distributed on the long tail of the complex real-world driving landscape. In this paper, we propose a unified approach, Diffusion-Based Safety-Critical Scenario Generation (DiffScene), to generate high-quality safety-critical scenarios which are both realistic and safety-critical for efficient AV evaluation. In particular, we propose a diffusion-based generation framework, leveraging the power of approximating the distribution of low-density spaces for diffusion models. We design several adversarial optimization objectives to guide the diffusion generation under predefined adversarial budgets. These objectives, such as safety-based objective, functionality-based objective, and constraint-based objective, ensure the generation of safety-critical scenarios while adhering to specific constraints. Extensive experimentation has been conducted to validate the efficacy of our approach. Compared with 6 SOTA baselines, DiffScene generates scenarios that are (1) more safety-critical under 3 metrics, (2) more realistic under 5 distance functions, and (3) more transferable to different AV algorithms. In addition, we demonstrate that training AV algorithms with scenarios generated by DiffScene leads to significantly higher performance in terms of the safety-critical metrics compared to baselines. These findings highlight the potential of DiffScene in addressing the challenges of AV safety evaluation, paving the way for safer AV development.

Zihao Wang, Yiming Huang, Gengyu Lyu, Yucheng Zhao, Ziyu Zhou, Bochen Xie, Zhen Yang, Yongjian Deng

Salient object detection (SOD) methods for 2D images have great significance in the field of human-computer interaction (HCI). However, as a common data format in HCI, the SOD research in the form of 3D point cloud data remains limited. Previous works commonly treat this task as point cloud segmentation, which perceives all points in the scene for prediction. However, these methods neglect that SOD is designed to simulate human visual perception where human can only see the surfaces rather than occluded point clouds. Thereby, these methods may fail when meet such situations. This paper aims to solve this problem by approximately simulating the perception paradigm of humans towards 3D scenes. Thus, we propose a framework based on the 3D visual point cloud backbone and its multi-view projection named MSV-PCT. Specifically, instead of relying solely on general point cloud learning frameworks, we additionally introduce multi-sparse-view learning branches to supplement the SOD perception. Furthermore, we propose a novel point cloud edge detection loss function to effectively address artifacts, enabling the accurate segmentation of the edges of salient objects from the background. Finally, to evaluate the generalization of point cloud SOD methods, we introduce a new approach to generate simulated PC-SOD datasets from RGBD-SOD data. Experiments on the simulated datasets show that MSV-PCT achieves better accuracy and robustness.

Yixu Wang, Tianle Gu, Yan Teng, Yingchun Wang, Xingjun Ma

Model extraction attacks are one type of inference-time attacks that approximate the functionality and performance of a black-box victim model by launching a certain number of queries to the model and then leveraging the model's predictions to train a substitute model. These attacks pose severe security threats to production models and MLaaS platforms and could cause significant monetary losses to the model owners. A body of work has proposed to defend machine learning models against model extraction attacks, including both active defense methods that modify the model's outputs or increase the query overhead to avoid extraction and passive defense methods that detect malicious queries or leverage watermarks to perform post-verification. In this work, we introduce a new defense paradigm called attack as defense which modifies the model's output to be poisonous such that any malicious users that attempt to use the output to train a substitute model will be poisoned. To this end, we propose a novel lightweight backdoor attack method dubbed HoneypotNet that replaces the classification layer of the victim model with a honeypot layer and then fine-tunes the honeypot layer with a shadow model (to simulate model extraction) via bi-level optimization to modify its output to be poisonous while remaining the original performance. We empirically demonstrate on four commonly used benchmark datasets that HoneypotNet can inject backdoors into substitute models with a high success rate. The injected backdoor not only facilitates ownership verification but also disrupts the functionality of substitute models, serving as a significant deterrent to model extraction attacks.

Zhiyi Pan, Nan Zhang, Wei Gao, Shan Liu, Ge Li

Utilizing uniformly distributed sparse annotations, weakly supervised learning alleviates the heavy reliance on fine-grained annotations in point cloud semantic segmentation tasks. However, few works discuss the inhomogeneity of sparse annotations, albeit it is common in real-world scenarios. Therefore, this work introduces the probability density function into the gradient sampling approximation method to qualitatively analyze the impact of annotation sparsity and inhomogeneity under weakly supervised learning. Based on our analysis, we propose an Adaptive Annotation Distribution Network (AADNet) capable of robust learning on arbitrarily distributed sparse annotations. Specifically, we propose a label-aware point cloud downsampling strategy to increase the proportion of annotations involved in the training stage. Furthermore, we design the multiplicative dynamic entropy as the gradient calibration function to mitigate the gradient bias caused by non-uniformly distributed sparse annotations and explicitly reduce the epistemic uncertainty. Without any prior restrictions and additional information, our proposed method achieves comprehensive performance improvements at multiple label rates and different annotation distributions.

Gaozheng Pei, Shaojie Lyu, Ke Ma, Pinci Yang, Qianqian Xu, Yingfei Sun

Data-free model stealing involves replicating the functionality of a target model into a substitute model without accessing the target model's structure, parameters, or training data. Instead, the adversary can only access the target model's predictions for generated samples. Once the substitute model closely approximates the behavior of the target model, attackers can exploit its white-box characteristics for subsequent malicious activities, such as adversarial attacks. Existing methods within cooperative game frameworks often produce samples with high confidence for the prediction of the substitute model, which makes it difficult for the substitute model to replicate the behavior of the target model. This paper presents a new data-free model stealing approach called Query Efficient Data Generation (QEDG). We introduce two distinct loss functions to ensure the generation of sufficient samples that closely and uniformly align with the target model's decision boundary across multiple classes. Building on the limitation of current methods, which typically yield only one piece of supervised information per query, we propose the query-free sample augmentation that enables the acquisition of additional supervised information without increasing the number of queries. Motivated by theoretical analysis, we adopt the consistency rate metric, which more accurately evaluates the similarity between the substitute and target models. We conducted extensive experiments to verify the effectiveness of our proposed method, which achieved better performance with fewer queries compared to the state-of-the-art methods on the real MLaaS scenario and five datasets.

Sizhuo Jin, Shuo Chen, Jianjun Qian, Ying Tai, Jun Li

Density Functional Theory (DFT) stands as a widely used and efficient approach for addressing the many-electron Schrödinger equation across various domains such as physics, chemistry, and biology. However, a core challenge that persists over the long term pertains to refining the exchange-correlation (XC) approximation. This approximation significantly influences the triumphs and shortcomings observed in DFT applications. Nonetheless, a prevalent issue among XC approximations is the presence of systematic errors, stemming from deviations from the mathematical properties of the exact XC functional. For example, although both B3LYP and DM21 (DeepMind 21) exhibit improvements over previous benchmarks, there is still potential for further refinement. In this paper, we propose a strategy for enhancing XC approximations by estimating the neural uncertainty of the XC functional, named Residual XC-Uncertain Functional. Specifically, our approach involves training a neural network to predict both the mean and variance of the XC functional, treating it as a Gaussian distribution. To ensure stability in each sampling point, we construct the mean by combining traditional XC approximations with our neural predictions, mitigating the risk of divergence or vanishing values. It is crucial to highlight that our methodology excels particularly in cases where systematic errors are pronounced. Empirical outcomes from three benchmark tests substantiate the superiority of our approach over existing state-of-the-art methods. Our approach not only surpasses related techniques but also significantly outperforms both the popular B3LYP and the recent DM21 methods, achieving average RMSE improvements of 62% and 37%, respectively, across the three benchmarks: W4-17, G21EA, and G21IP.

Vishal Purohit, Matthew Repasky, Jianfeng Lu, Qiang Qiu, Yao Xie, Xiuyuan Cheng

Posterior sampling in high-dimensional spaces using generative models holds significant promise for various applications, including but not limited to inverse problems and guided generation tasks. Generating diverse posterior samples remains expensive, as existing methods require restarting the entire generative process for each new sample. In this work, we propose a posterior sampling approach that simulates Langevin dynamics in the noise space of a pre-trained generative model. By exploiting the mapping between the noise and data spaces which can be provided by distilled flows or consistency models, our method enables seamless exploration of the posterior without the need to re-run the full sampling chain, drastically reducing computational overhead. Theoretically, we prove a guarantee for the proposed noise-space Langevin dynamics to approximate the posterior, assuming that the generative model sufficiently approximates the prior distribution. Our framework is experimentally validated on image restoration tasks involving noisy linear and nonlinear forward operators applied to LSUN-Bedroom (256 x 256) and ImageNet (64 x 64) datasets. The results demonstrate that our approach generates high-fidelity samples with enhanced semantic diversity even under a limited number of function evaluations, offering superior efficiency and performance compared to existing diffusion-based posterior sampling techniques.

Yuchu Jiang, Jiale Fu, Chenduo Hao, Xinting Hu, Yingzhe Peng, Xin Geng, Xu Yang

Recently, In-context Learning (ICL) has become a significant inference paradigm in Large Multimodal Models (LMMs), utilizing a few in-context demonstrations (ICDs) to prompt LMMs for new tasks. However, the synergistic effects in multimodal data increase the sensitivity of ICL performance to the configurations of ICDs, stimulating the need for a more stable and general mapping function. Mathematically, in Transformer-based models, ICDs act as "shift vectors" added to the hidden states of query tokens. Inspired by this, we introduce Mimic In-Context Learning (MimIC) to learn stable and generalizable shift effects from ICDs. Specifically, compared with some previous shift vector-based methods, MimIC more strictly approximates the shift effects by integrating lightweight learnable modules into LMMs with four key enhancements: 1) inserting shift vectors after attention layers, 2) assigning a shift vector to each attention head, 3) making shift magnitude query-dependent, and 4) employing a layer-wise alignment loss. Extensive experiments on two LMMs (Idefics-9b and Idefics2-8b-base) across three multimodal tasks (VQAv2, OK-VQA, Captioning) demonstrate that MimIC outperforms existing shift vector-based methods. The code is available at https://anonymous.4open.science/r/MimIC/.

Zhifei Chen, Tianshuo Xu, Wenhang Ge, Leyi Wu, Dongyu Yan, Jing He, Luozhou Wang, Lu Zeng, Shunsi Zhang, Ying-Cong Chen

Rendering and inverse rendering are pivotal tasks in both computer vision and graphics. The rendering equation is the core of the two tasks, as an ideal conditional distribution transfer function from intrinsic properties to RGB images. Despite achieving promising results of existing rendering methods, they merely approximate the ideal estimation for a specific scene and come with a high computational cost. Additionally, the inverse conditional distribution transfer is intractable due to the inherent ambiguity. To address these challenges, we propose a data-driven method that jointly models rendering and inverse rendering as two conditional generation tasks within a single diffusion framework. Inspired by UniDiffuser, we utilize two distinct time schedules to model both tasks, and with a tailored dual streaming module, we achieve cross-conditioning of two pre-trained diffusion models. This unified approach, named Uni-Renderer, allows the two processes to facilitate each other through a cycle-consistent constrain, mitigating ambiguity by enforcing consistency between intrinsic properties and rendered images.Combined with a meticulously prepared dataset, our method effectively decomposition of intrinsic properties and demonstrating a strong capability to recognize changes during rendering. We will open-source our training and inference code to the public, fostering further research and development in this area.

Natacha Kuete Meli, Vladislav Golyanik, Marcel Seelbach Benkner, Michael Moeller

There is growing interest in solving computer vision problems such as mesh or point set alignment using Adiabatic Quantum Computing (AQC). Unfortunately, modern experimental AQC devices such as D-Wave only support Quadratic Unconstrained Binary Optimisation (QUBO) problems, which severely limits their applicability. This paper proposes a new way to overcome this limitation and introduces QuCOOP, an optimisation framework extending the scope of AQC to composite and binary-parametrised, possibly non-quadratic problems. The key idea of QuCOOP is to iteratively approximate the original objective function by a sequel of local (intermediate) QUBO forms, whose binary parameters can be sampled on AQC devices. We experiment with quadratic assignment problems, shape matching and point set registration without knowing the correspondences in advance. Our approach achieves state-of-the-art results across multiple instances of tested problems.

Tal Zeevi, Ravid Shwartz-Ziv, Yann LeCun, Lawrence H. Staib, John A. Onofrey

Accurate uncertainty estimation is crucial for deploying neural networks in risk-sensitive applications such as medical diagnosis. Monte Carlo Dropout is a widely used technique for approximating predictive uncertainty by performing stochastic forward passes with dropout during inference. However, using static dropout rates across all layers and inputs can lead to suboptimal uncertainty estimates, as it fails to adapt to the varying characteristics of individual inputs and network layers. Existing approaches optimize dropout rates during training using labeled data, resulting in fixed inference-time parameters that cannot adjust to new data distributions, compromising uncertainty estimates in Monte Carlo simulations. In this paper, we propose Rate-In, an algorithm that dynamically adjusts dropout rates during inference by quantifying the information loss induced by dropout in each layer's feature maps. By treating dropout as controlled noise injection and leveraging information-theoretic principles, Rate-In adapts dropout rates per layer and per input instance without requiring ground truth labels. By quantifying the functional information loss in feature maps, we adaptively tune dropout rates to maintain perceptual quality across diverse medical imaging tasks and architectural configurations. Our extensive empirical study on synthetic data and real-world medical imaging tasks demonstrates that Rate-In improves calibration and sharpens uncertainty estimates compared to fixed or heuristic dropout rates without compromising predictive performance. Rate-In offers a practical, unsupervised, inference-time approach to optimizing dropout for more reliable predictive uncertainty estimation in critical applications.

Takeshi Noda, Chao Chen, Junsheng Zhou, Weiqi Zhang, Yu-Shen Liu, Zhizhong Han

Inferring signed distance functions (SDFs) from sparse point clouds remains a challenge in surface reconstruction. The key lies in the lack of detailed geometric information in sparse point clouds, which is essential for learning a continuous field. To resolve this issue, we present a novel approach that learns a dynamic deformation network to predict SDFs in an end-to-end manner. To parameterize a continuous surface from sparse points, we propose a bijective surface parameterization (BSP) that learns the global shape from local patches. Specifically, we construct a bijective mapping for sparse points from the parametric domain to 3D local patches, integrating patches into the global surface. Meanwhile, we introduce grid deformation optimization (GDO) into the surface approximation to optimize the deformation of grid points and further refine the parametric surfaces. Experimental results on synthetic and real scanned datasets demonstrate that our method significantly outperforms the current state-of-the-art methods.

Kai Chen, Xiaodong Zhao, Yujie Huang, Guoyu Fang, Xiao Song, Ruiping Wang, Ziyuan Wang

The analysis and prediction of agent trajectories are crucial for decision-making processes in intelligent systems, with precise short-term trajectory forecasting being highly significant across a range of applications. Agents and their social interactions have been quantified and modeled by researchers from various perspectives; however, substantial limitations exist in the current work due to the inherent high uncertainty of agent intentions and the complex higher-order influences among neighboring groups. SocialMOIF is proposed to tackle these challenges, concentrating on the higher-order intention interactions among neighboring groups while reinforcing the primary role of first-order intention interactions between neighbors and the target agent. This method develops a multi-order intention fusion model to achieve a more comprehensive understanding of both direct and indirect intention information. Within SocialMOIF, a trajectory distribution approximator is designed to guide the trajectories toward values that align more closely with the actual data, thereby enhancing model interpretability. Furthermore, a global trajectory optimizer is introduced to enable more accurate and efficient parallel predictions. By incorporating a novel loss function that accounts for distance and direction during training, experimental results demonstrate that the model outperforms previous state-of-the-art baselines across multiple metrics in both dynamic and static datasets.