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1,217篇论文匹配“Discrete Optimization”
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Mingzi Wang, Yuan Meng, Chen Tang, Weixiang Zhang, Yijian Qin, Yang Yao, Yingxin Li, Tongtong Feng, Xin Wang, Xun Guan 等

The co-design of neural network architectures, quantization precisions, and hardware accelerators offers a promising approach to achieving an optimal balance between performance and efficiency, particularly for model deployment on resource-constrained edge devices. In this work, we propose the JAQ Framework, which jointly optimizes the three critical dimensions. However, effectively automating the design process across the vast search space of those three dimensions poses significant challenges, especially when pursuing extremely low-bit quantization. Specifical, the primary challenges include: (1) Memory overhead in software-side: Low-precision quantization-aware training can lead to significant memory usage due to storing large intermediate features and latent weights for backpropagation, potentially causing memory exhaustion. (2) Search time-consuming in hardware-side: The discrete nature of hardware parameters and the complex interplay between compiler optimizations and individual operators make the accelerator search time-consuming. To address these issues, JAQ mitigates the memory overhead through a channel-wise sparse quantization (CSQ) scheme, selectively applying quantization to the most sensitive components of the model during optimization. Additionally, JAQ designs BatchTile, which employs a hardware generation network to encode all possible tiling modes, thereby speeding up the search for the optimal compiler mapping strategy. Extensive experiments demonstrate the effectiveness of JAQ, achieving approximately 7% higher Top-1 accuracy on ImageNet compared to previous methods and reducing the hardware search time per iteration to 0.15 seconds.

Bocheng Wang, Chusheng Zeng, Mulin Chen, Xuelong Li

Deep multi-view clustering incorporating graph learning has presented tremendous potential. Most methods encounter costly square time consumption w.r.t. data size. Theoretically, anchor-based graph learning can alleviate this limitation, but related deep models mainly rely on manual discretization approaches to select anchors, which indicates that 1) the anchors are fixed during model training and 2) they may deviate from the true cluster distribution. Consequently, the unreliable anchors may corrupt clustering results. In this paper, we propose the Deep Multi-view Anchor Clustering (DMAC) model that performs clustering in linear time. Concretely, the initial anchors are intervened by the positive-incentive noise sampled from Gaussian distribution, such that they can be optimized with a newly designed anchor learning loss, which promotes a clear relationship between samples and anchors. Afterwards, anchor graph convolution is devised to model the cluster structure formed by the anchors, and the mutual information maximization loss is built to provide cross-view clustering guidance. In this way, the learned anchors can better represent clusters. With the optimal anchors, the full sample graph is calculated to derive a discriminative embedding for clustering. Extensive experiments on several datasets demonstrate the superior performance and efficiency of DMAC compared to state-of-the-art competitors.

Fabian Christian Spaeh, Alina Ene, Huy Nguyen

Constrained k-submodular maximization is a general framework that captures many discrete optimization problems such as ad allocation, influence maximization, personalized recommendation, and many others. In many of these applications, datasets are large or decisions need to be made in an online manner, which motivates the development of efficient streaming and online algorithms. In this work, we develop single-pass streaming and online algorithms for constrained k-submodular maximization with both monotone and general (possibly non-monotone) objectives subject to cardinality and knapsack constraints. Our algorithms achieve provable constant-factor approximation guarantees which improve upon the state of the art in almost all settings. Moreover, they achieve the fastest known running times and have optimal space usage. We experimentally evaluate our algorithms on instances for ad allocation and other applications, where we observe that our algorithms are practical and scalable, and construct solutions that are comparable in value even to offline greedy algorithms.

Yiping Liu, Jiahao Yang, Xuanbai Ren, Zhang Xinyi, Yuansheng Liu, Bosheng Song, Xiangxiang Zeng, Hisao Ishibuchi

Molecular design inherently involves the optimization of multiple conflicting objectives, such as enhancing bio-activity and ensuring synthesizability. Evaluating these objectives often requires resource-intensive computations or physical experiments. Current molecular design methodologies typically approximate the Pareto set using a limited number of molecules. In this paper, we present an innovative approach, called Multi-Objective Molecular Design through Learning Latent Pareto Set (MLPS). MLPS initially utilizes an encoder-decoder model to seamlessly transform the discrete chemical space into a continuous latent space. We then employ local Bayesian optimization models to efficiently search for local optimal solutions (i.e., molecules) within predefined trust regions. Using surrogate objective values derived from these local models, we train a global Pareto set learning model to understand the mapping between direction vectors (called “preferences”) in the objective space and the entire Pareto set in the continuous latent space. Both the global Pareto set learning model and local Bayesian optimization models collaborate to discover high-quality solutions and adapt the trust regions dynamically. Our work is an effective endeavor towards learning the Pareto set for multi-objective molecular design, providing decision-makers with the capability to fine-tune their preferences and thoroughly explore the Pareto set. Experimental results demonstrate that MLPS achieves state-of-the-art performance across various multi-objective scenarios, encompassing diverse objective types and varying numbers of objectives. The effectiveness of MLPS was further validated through real-world challenges in discovering antifungal peptides with low toxicity and high activity.

Junghun Lee, Hyunju Kim, Fanchen Bu, Jihoon Ko, Kijung Shin

In social networks, people influence each other through social links, which can be represented as propagation among nodes in graphs. Influence minimization (IMIN) is the problem of manipulating the structures of an input graph (e.g., removing edges) to reduce the propagation among nodes. IMIN can represent time-critical real-world applications, such as rumor blocking, but IMIN is theoretically difficult and computationally expensive. Moreover, the discrete nature of IMIN hinders the usage of powerful machine learning techniques, which requires differentiable computation. In this work, we propose DiffIM, a novel method for IMIN with two differentiable schemes for acceleration: (1) surrogate modeling for efficient influence estimation, which avoids time-consuming simulations (e.g., Monte Carlo), and (2) the continuous relaxation of decisions, which avoids the evaluation of individual discrete decisions (e.g., removing an edge). We further propose a third accelerating scheme, gradient-driven selection, that chooses edges instantly based on gradients without optimization (spec., gradient descent iterations) on each test instance. Through extensive experiments on real-world graphs, we show that each proposed scheme significantly improves speed with little (or even no) IMIN performance degradation. Our method is Pareto-optimal (i.e., no baseline is faster and more effective than it) and typically several orders of magnitude (spec., up to 15,160X) faster than the most effective baseline, while being more effective.

Xianqi Jiao, Jia Liu, Zhiping Chen

Gradient Descent (GD) and Conjugate Gradient (CG) methods are among the most effective iterative algorithms for solving unconstrained optimization problems, particularly in machine learning and statistical modeling, where they are employed to minimize cost functions. In these algorithms, tunable parameters, such as step sizes or conjugate parameters, play a crucial role in determining key performance metrics, like runtime and solution quality. In this work, we introduce a framework that models algorithm selection as a statistical learning problem, and thus learning complexity can be estimated by the pseudo-dimension of the algorithm group. We first propose a new cost measure for unconstrained optimization algorithms, inspired by the concept of primal-dual integral in mixed-integer linear programming. Based on the new cost measure, we derive an improved upper bound for the pseudo-dimension of gradient descent algorithm group by discretizing the set of step size configurations. Moreover, we generalize our findings from gradient descent algorithm to the conjugate gradient algorithm group for the first time, and prove the existence a learning algorithm capable of probabilistically identifying the optimal algorithm with a sufficiently large sample size.

Alexander Ivanov, Akhil Bagaria, George Konidaris

We present an option discovery algorithm that accelerates planning by minimizing the shortest distance between any two states in the MDP. The proposed algorithm produces options that approximately minimize planning time in the multi-goal setting: it is shown to be a worst case (4-alpha, 2)-approximation of the optimal option set, where alpha is the approximation ratio of the k-medians with penalties subroutine. We then present a variation, "Fast Average Options", with improved run-time and describe a general means of producing similar algorithms based on selection of a k-medians subroutine. We empirically evaluate our method on four discrete and two continuous control planning domains and show that it outperforms other leading option discovery algorithms.

Weinan He, Zilei Wang, Yixin Zhang

Universal Domain Adaptation (UniDA) focuses on transferring source domain knowledge to the target domain under both domain shift and unknown category shift. Its main challenge lies in identifying common class samples and aligning them. Current methods typically obtain target domain semantics centers from an unconstrained continuous image representation space. Due to domain shift and the unknown number of clusters, these centers often result in complex and less robust alignment algorithm. In this paper, based on vision-language models, we search for semantic centers in a semantically meaningful and discrete text representation space. The constrained space ensures almost no domain bias and appropriate semantic granularity for these centers, enabling a simple and robust adaptation algorithm. Specifically, we propose TArget Semantics Clustering (TASC) via Text Representations, which leverages information maximization as a unified objective and involves two stages. First, with the frozen encoders, a greedy search-based framework is used to search for an optimal set of text embeddings to represent target semantics. Second, with the search results fixed, encoders are refined based on gradient descent, simultaneously achieving robust domain alignment and private class clustering. Additionally, we propose Universal Maximum Similarity (UniMS), a scoring function tailored for detecting open-set samples in UniDA. Experimentally, we evaluate the universality of UniDA algorithms under four category shift scenarios. Extensive experiments on four benchmarks demonstrate the effectiveness and robustness of our method, which has achieved state-of-the-art performance.

Xingcheng Fu, Jian Wang, Yisen Gao, Qingyun Sun, Haonan Yuan, Jianxin Li, Xianxian Li

Graph neural networks(GNNs) have been demonstrated to depend on whether the node effective information is sufficiently passing. Discrete curvature (Ricci curvature) is used to study graph connectivity and information propagation efficiency with a geometric perspective, and has been raised in recent years to explore the efficient message-passing structure of GNNs. However, most empirical studies are based on directly observed graph structures or heuristic topological assumptions, and lack in-depth exploration of underlying optimal information transport structures for downstream tasks. We suggest that graph curvature optimization is more in-depth and essential than directly rewiring or learning for graph structure with richer message-passing characterization and better information transport interpretability. From both graph geometry and information theory perspectives, we propose the novel Discrete Curvature Graph Information Bottleneck (CurvGIB) framework to optimize the information transport structure and learn better node representations simultaneously. CurvGIB advances the Variational Information Bottleneck (VIB) principle for Ricci curvature optimization to learn the optimal information transport pattern for specific downstream tasks. The learned Ricci curvature is used to refine the optimal transport structure of the graph, and the node representation is fully and efficiently learned. Moreover, for the computational complexity of Ricci curvature differentiation, we combine Ricci flow and VIB to deduce a curvature optimization approximation to form a tractable IB objective function. Extensive experiments on various datasets demonstrate the superior effectiveness and interpretability of CurvGIB.

Weilun Feng, Haotong Qin, Chuanguang Yang, Zhulin An, Libo Huang, Boyu Diao, Fei Wang, Renshuai Tao, Yongjun Xu, Michele Magno

Diffusion models have received wide attention in generation tasks. However, the expensive computation cost prevents the application of diffusion models in resource-constrained scenarios. Quantization emerges as a practical solution that significantly saves storage and computation by reducing the bit-width of parameters. However, the existing quantization methods for diffusion models still cause severe degradation in performance, especially under extremely low bit-widths (2-4 bit). The primary decrease in performance comes from the significant discretization of activation values at low bit quantization. Too few activation candidates are unfriendly for outlier significant weight channel quantization, and the discretized features prevent stable learning over different time steps of the diffusion model. This paper presents MPQ-DM, a Mixed-Precision Quantization method for Diffusion Models. The proposed MPQ-DM mainly relies on two techniques: (1) To mitigate the quantization error caused by outlier severe weight channels, we propose an Outlier-Driven Mixed Quantization (OMQ) technique that uses Kurtosis to quantify outlier salient channels and apply optimized intra-layer mixed-precision bit-width allocation to recover accuracy performance within target efficiency. (2) To robustly learn representations crossing time steps, we construct a Time-Smoothed Relation Distillation (TRD) scheme between the quantized diffusion model and its full-precision counterpart, transferring discrete and continuous latent to a unified relation space to reduce the representation inconsistency. Comprehensive experiments demonstrate that MPQ-DM achieves significant accuracy gains under extremely low bit-widths compared with SOTA quantization methods. MPQ-DM achieves a 58% FID decrease under W2A4 setting compared with baseline, while all other methods even collapse.

Ilan Doron-Arad

We study neural network training (NNT): optimizing a neural network's parameters to minimize the training loss over a given dataset. NNT has been studied extensively under theoretic lenses, mainly on two-layer networks with linear or ReLU activation functions where the parameters can take any real value (here referred to as continuous NNT (C-NNT)). However, less is known about deeper neural networks, which exhibit substantially stronger capabilities in practice. In addition, the complexity of the discrete variant of the problem (D-NNT in short), in which the parameters are taken from a given finite set of options, has remained less explored despite its theoretical and practical significance. In this work, we show that the hardness of NNT is dramatically affected by the network depth. Specifically, we show that, under standard complexity assumptions, D-NNT is not in the complexity class NP even for instances with fixed dimensions and dataset size, having a deep architecture. This separates D-NNT from any NP-complete problem. Furthermore, using a polynomial reduction we show that the above result also holds for C-NNT, albeit with more structured instances. We complement these results with a comprehensive list of NP-hardness lower bounds for D-NNT on two-layer networks, showing that fixing the number of dimensions, the dataset size, or the number of neurons in the hidden layer leaves the problem challenging. Finally, we obtain a pseudo-polynomial algorithm for D-NNT on a two-layer network with a fixed dataset size.

Shuai Zhou, Shizhe Zhao, Zhongqiang Ren

Given a graph representing the workspace, Multi-Agent Path Finding (MAPF) seeks collision-free paths for multiple agents from their respective start vertex to their respective goal vertex while minimizing path costs. Although many MAPF algorithms were developed and can handle up to thousands of agents, they usually rely on the assumption that each action of the agent takes a time unit, and the actions of all agents are synchronized in a sense that the actions of agents start at the same discrete time step, which may limit their use in practice. Only a few algorithms have been developed to address asynchronous actions, and they all lie on one end of the spectrum, focusing on finding optimal solutions with limited scalability. This paper develops new planners that lie on the other end of the spectrum, trading off solution quality for scalability, by finding an unbounded sub-optimal solution for many agents. Our method leverages both search-based methods in handling asynchronous actions and techniques in rule-based planning for MAPF. We analyze the properties of our method and test it against several baselines with up to a thousand agents with asynchronous actions in various maps. Given a runtime limit, our method can handle an order of magnitude more agents than the existing methods with about 25% longer makespan.

Vinzenz Thoma, Vitor Bosshard, Sven Seuken

We present an algorithm for computing pure-strategy epsilon-perfect Bayesian equilibria in sequential auctions with continuous action and value spaces. Importantly, our algorithm includes a verification phase that computes an upper bound on the utility loss of the found strategies. Prior work on equilibrium computation in auctions with verification has focussed on the single-round case, but the methods do not work for sequential auctions because of two main challenges: (1) there are infinitely many subgames, and (2) the setting has no optimal substructure as bidders' beliefs and best response strategies depend on the strategies of previous rounds. We make two contributions. First, we introduce a tailor-made game abstraction that discretizes the auction and augments the state space with the public beliefs, such that an approximate equilibrium can be computed via dynamic programming. Second, we prove a decomposition theorem to upper bound the utility loss of the computed equilibrium. This is essential because it is neither guaranteed that the auction has an equilibrium nor that any algorithm converges to it. We validate our algorithm on multiple settings with known equilibria and apply it to a new multi-round combinatorial auction.

Yasunori Akagi, Hideaki Kim, Takeshi Kurashima

Present bias, the tendency to overvalue immediate rewards while undervaluing future ones, is a well-known barrier to achieving long-term goals. As artificial intelligence and behavioral economics increasingly focus on this phenomenon, the need for robust mathematical models to predict behavior and guide effective interventions has become crucial. However, existing models are constrained by their reliance on the discreteness of time and limited discount functions. This study introduces a novel continuous-time mathematical model for agents influenced by present bias. Using the variational principle, we model human behavior, where individuals repeatedly act according to a sequence of states that minimize their perceived cost. Our model not only retains analytical tractability but also accommodates various discount functions. Using this model, we consider intervention optimization problems under exponential and hyperbolic discounting and theoretically derive optimal intervention strategies, offering new insights into managing present-biased behavior.

Jianxiang Zhu, Dandan Lai, Zhongcui Ma, Yaxin Peng

Reinforcement learning (RL) algorithms can improve recommendation performance by capturing long-term user-system interaction. However, current RL-based recommendation tasks seldom consider the dynamism of the environment, and standard RL algorithms are ineffective in recommending items dynamically. In addressing these issues, we design a novel task termed dynamic recommendation, which takes the emergence of real-world recommendable items into consideration. Meanwhile, we propose Adaptive Q-Network (AdaQN) to tackle the dynamic recommendation task. Firstly, AdaQN predicts the value of different action characteristics, particularly during the testing phase, which can capture emerging new action characteristics. The above procedure helps AdaQN in effectively adapting to the dynamic action space. Secondly, AdaQN establishes a stable mapping that projects the discrete action space onto a continuous characteristic space. Finally, AdaQN employs a lightweight Q-network design, which mitigates the complexity of the optimization process. Extensive experiments demonstrate that our approach has achieved state-of-the-art performance in the dynamic recommendation task.

Shu Zhao, Tan Yu, Xiaoshuai Hao, Wenchao Ma, Vijaykrishnan Narayanan

Deep hashing has been widely used for large-scale approximate nearest neighbor search due to its storage and search efficiency. However, existing deep hashing methods predominantly rely on abundant training data, leaving the more challenging scenario of low-resource adaptation for deep hashing relatively underexplored. This setting involves adapting pre-trained models to downstream tasks with only an extremely small number of training samples available. Our preliminary benchmarks reveal that current methods suffer significant performance degradation due to the distribution shift caused by limited training samples. To address these challenges, we introduce Class-Calibration LoRA (CLoRA), a novel plug-and-play approach that dynamically constructs low-rank adaptation matrices by leveraging class-level textual knowledge embeddings. CLoRA effectively incorporates prior class knowledge as anchors, enabling parameter-efficient fine-tuning while maintaining the original data distribution. Furthermore, we propose Knowledge-Guided Discrete Optimization (KIDDO), a framework to utilize class knowledge to compensate for the scarcity of visual information and enhance the discriminability of hash codes. Extensive experiments demonstrate that our proposed method, Knowledge- Anchored Low-Resource Adaptation Hashing (KALAHash), significantly boosts retrieval performance and achieves a 4× data efficiency in low-resource scenarios.

Yi Yu, Song Xia, Xun Lin, Wenhan Yang, Shijian Lu, Yap-Peng Tan, Alex Kot

No-Reference Image Quality Assessment (NR-IQA), responsible for assessing the quality of a single input image without using any reference, plays a critical role in evaluating and optimizing computer vision systems, e.g., low-light enhancement. Recent research indicates that NR-IQA models are susceptible to adversarial attacks, which can significantly alter predicted scores with visually imperceptible perturbations. Despite revealing vulnerabilities, these attack methods have limitations, including high computational demands, untargeted manipulation, limited practical utility in white-box scenarios, and reduced effectiveness in black-box scenarios. To address these challenges, we shift our focus to another significant threat and present a novel poisoning-based backdoor attack against NR-IQA (BAIQA), allowing the attacker to manipulate the IQA model's output to any desired target value by simply adjusting a scaling coefficient alpha for the trigger. We propose to inject the trigger in the discrete cosine transform (DCT) domain to improve the local invariance of the trigger for countering trigger diminishment in NR-IQA models due to widely adopted data augmentations. Furthermore, the universal adversarial perturbations (UAP) in the DCT space are designed as the trigger, to increase IQA model susceptibility to manipulation and improve attack effectiveness. In addition to the heuristic method for poison-label BAIQA (P-BAIQA), we explore the design of clean-label BAIQA (C-BAIQA), focusing on alpha sampling and image data refinement, driven by theoretical insights we reveal. Extensive experiments on diverse datasets and various NR-IQA models demonstrate the effectiveness of our attacks.

Yang Wei, Jingyu Tan, Guowen Xu, Zhuoran Ma, Zhuo Ma, Bin Xiao

Substitute training-based data-free black-box attacks pose a significant threat to enterprise-deployed models. These attacks use a generator to synthesize data and query APIs, then train a substitute model to approximate the target model's decision boundary based on the returned results. However, existing attack methods often struggle to produce sufficiently diverse data, particularly for complex target models and extensive target data domains, severely limiting their practical application. To address this gap, we design domain-augmented learning to improve the quality of the synthetic data domain (SDD) generated by the generator from two perspectives. Specifically, (1) To broaden the SDD's coverage, we introduce textual semantic embeddings into the generator for the first time. (2) For enhancing the SDD's discretization, we propose a competitive optimization strategy that forces the generator to self-compete, along with heterogeneity excitation to overcome the constraints of information entropy on diversity. Comprehensive experiments demonstrate that our method is more effective. In non-targeted attacks on the CIFAR-10 and Tiny-ImageNet datasets, our method outperforms the state-of-the-art by 14% and 7% in attack success rate, respectively.

Siyu Wang, Cailian Chen, Xinyi Le, Qimin Xu, Lei Xu, Yanzhou Zhang, Jie Yang

Computer-aided design (CAD) significantly enhances the efficiency, accuracy, and innovation of design processes by enabling precise 2D and 3D modeling, extensive analysis, and optimization. Existing methods for creating CAD models rely on latent vectors or point clouds, which are difficult to obtain, and storage costs are substantial. Recent advances in Multimodal Large Language Models (MLLMs) have inspired researchers to use natural language instructions and images for CAD model construction. However, these models still struggle with inferring accurate 3D spatial location and orientation, leading to inaccuracies in determining the spatial 3D starting points and extrusion directions for constructing geometries. This work introduces CAD-GPT, a CAD synthesis method with spatial reasoning-enhanced MLLM that takes either a single image or a textual description as input. To achieve precise spatial inference, our approach introduces a 3D Modeling Spatial Mechanism. This method maps 3D spatial positions and 3D sketch plane rotation angles into a 1D linguistic feature space using a specialized spatial unfolding mechanism, while discretizing 2D sketch coordinates into an appropriate planar space to enable precise determination of spatial starting position, sketch orientation, and 2D sketch coordinate translations. Extensive experiments demonstrate that CAD-GPT consistently outperforms existing state-of-the-art methods in CAD model synthesis, both quantitatively and qualitatively.

Tianqi Shen, Shaohua Liu, Jiaqi Feng, Ziye Ma, Ning An

Gaussian Splatting (GS) has emerged as a crucial technique for representing discrete volumetric radiance fields. It leverages unique parametrization to mitigate computational demands in scene optimization. This work introduces Topology-Aware 3D Gaussian Splatting (Topology-GS), which addresses two key limitations in current approaches: compromised pixel-level structural integrity due to incomplete initial geometric coverage, and inadequate feature-level integrity from insufficient topological constraints during optimization. To overcome these limitations, Topology-GS incorporates a novel interpolation strategy, Local Persistent Voronoi Interpolation (LPVI), and a topology-focused regularization term based on persistent barcodes, named PersLoss. LPVI utilizes persistent homology to guide adaptive interpolation, enhancing point coverage in low-curvature areas while preserving topological structure. PersLoss aligns the visual perceptual similarity of rendered images with ground truth by constraining distances between their topological features. Comprehensive experiments on three novel-view synthesis benchmarks demonstrate that Topology-GS outperforms existing methods in terms of PSNR, SSIM, and LPIPS metrics, while maintaining efficient memory usage. This study pioneers the integration of topology with 3D-GS, laying the groundwork for future research in this area.