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Nonlinear feature selection for support vector quantile regression. 支持向量分位数回归的非线性特征选择。
IF 6 1区 计算机科学 Q1 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE Pub Date : 2025-01-13 DOI: 10.1016/j.neunet.2025.107136
Ya-Fen Ye, Jie Wang, Wei-Jie Chen

This paper discusses the nuanced domain of nonlinear feature selection in heterogeneous systems. To address this challenge, we present a sparsity-driven methodology, namely nonlinear feature selection for support vector quantile regression (NFS-SVQR). This method includes a binary-diagonal matrix, featuring 0 and 1 elements, to address the complexities of feature selection within intricate nonlinear systems. Moreover, NFS-SVQR integrates a quantile parameter to effectively address the intrinsic challenges of heterogeneity within nonlinear feature selection processes. Consequently, NFS-SVQR excels not only in precisely identifying representative features but also in comprehensively capturing heterogeneous information within high-dimensional datasets. Through feature selection experiments the enhanced performance of NFS-SVQR in capturing heterogeneous information and selecting representative features is demonstrated.

本文讨论了异构系统中非线性特征选择的精细领域。为了解决这一挑战,我们提出了一种稀疏驱动的方法,即非线性特征选择支持向量分位数回归(NFS-SVQR)。该方法包括一个以0和1元素为特征的二元对角矩阵,以解决复杂非线性系统中特征选择的复杂性。此外,NFS-SVQR集成了一个分位数参数,有效地解决了非线性特征选择过程中异质性的内在挑战。因此,NFS-SVQR不仅在精确识别代表性特征方面表现出色,而且在全面捕获高维数据集中的异构信息方面也表现出色。通过特征选择实验,验证了NFS-SVQR在捕获异构信息和选择代表性特征方面的增强性能。
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引用次数: 0
An adversarial transformer for anomalous lamb wave pattern detection. 一种用于异常兰姆波形检测的对抗性变压器。
IF 6 1区 计算机科学 Q1 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE Pub Date : 2025-01-12 DOI: 10.1016/j.neunet.2025.107153
Jiawei Guo, Sen Zhang, Nikta Amiri, Lingyu Yu, Yi Wang

Lamb waves are widely used for defect detection in structural health monitoring, and various methods are developed for Lamb wave data analysis. This paper presents an unsupervised Adversarial Transformer model for anomalous Lamb wave pattern detection by analyzing the spatiotemporal images generated by a hybrid PZT-scanning laser Doppler vibrometer (SLDV). The model includes the global attention and the local attention mechanisms, and both are trained adversarially. Given the different natures between the normal and anomalous wave patterns, global attention allows accurate reconstruction of normal wave data but is less capable of reproducing anomalous data and, hence, can be used for anomalous wave pattern detection. Local attention, however, serves as a sparring partner in the proposed adversarial training process to boost the quality of global attention. In addition, a new segment replacement strategy is also proposed to make global attention consistently extract textural contents found in normal data, which, however, are noticeably different from anomalies, leading to superior model performance. Our Adversarial Transformer model is also compared with several benchmark models and demonstrates an overall accuracy of 97.1 % for anomalous wave pattern detection. It is also confirmed that global attention and local attention in adversarial training are responsible for the superior performance of our model over the benchmark models (including the native Transformer model).

兰姆波被广泛应用于结构健康监测中的缺陷检测,各种兰姆波数据分析方法应运而生。本文通过分析混合pzt扫描激光多普勒测振仪(SLDV)产生的时空图像,提出了一种用于异常Lamb波模式检测的无监督对抗变压器模型。该模型包括全局注意机制和局部注意机制,两者都是对立训练的。考虑到正常波和异常波之间的不同性质,全局关注可以准确地重建正常波数据,但不太能够再现异常数据,因此可以用于异常波模式检测。然而,在拟议的对抗性训练过程中,局部关注充当了一个陪练,以提高全球关注的质量。此外,还提出了一种新的片段替换策略,使全局注意力一致地提取正常数据中的纹理内容,而正常数据与异常数据有明显的不同,从而提高了模型的性能。我们的对抗性变压器模型也与几个基准模型进行了比较,并证明了异常波形检测的总体精度为97.1%。这也证实了对抗训练中的全局关注和局部关注是我们的模型优于基准模型(包括原生Transformer模型)的原因。
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引用次数: 0
Spiking-PhysFormer: Camera-based remote photoplethysmography with parallel spike-driven transformer. Spiking-PhysFormer:基于摄像头的远程光电容积脉搏描记,带有并联峰值驱动变压器。
IF 6 1区 计算机科学 Q1 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE Pub Date : 2025-01-10 DOI: 10.1016/j.neunet.2025.107128
Mingxuan Liu, Jiankai Tang, Yongli Chen, Haoxiang Li, Jiahao Qi, Siwei Li, Kegang Wang, Jie Gan, Yuntao Wang, Hong Chen

Artificial neural networks (ANNs) can help camera-based remote photoplethysmography (rPPG) in measuring cardiac activity and physiological signals from facial videos, such as pulse wave, heart rate and respiration rate with better accuracy. However, most existing ANN-based methods require substantial computing resources, which poses challenges for effective deployment on mobile devices. Spiking neural networks (SNNs), on the other hand, hold immense potential for energy-efficient deep learning owing to their binary and event-driven architecture. To the best of our knowledge, we are the first to introduce SNNs into the realm of rPPG, proposing a hybrid neural network (HNN) model, the Spiking-PhysFormer, aimed at reducing power consumption. Specifically, the proposed Spiking-PhyFormer consists of an ANN-based patch embedding block, SNN-based transformer blocks, and an ANN-based predictor head. First, to simplify the transformer block while preserving its capacity to aggregate local and global spatio-temporal features, we design a parallel spike transformer block to replace sequential sub-blocks. Additionally, we propose a simplified spiking self-attention mechanism that omits the value parameter without compromising the model's performance. Experiments conducted on four datasets-PURE, UBFC-rPPG, UBFC-Phys, and MMPD demonstrate that the proposed model achieves a 10.1% reduction in power consumption compared to PhysFormer. Additionally, the power consumption of the transformer block is reduced by a factor of 12.2, while maintaining decent performance as PhysFormer and other ANN-based models.

人工神经网络(ann)可以帮助基于摄像头的远程光电容积脉搏波(rPPG)更准确地测量面部视频中的心脏活动和生理信号,如脉搏波、心率和呼吸频率。然而,现有的大多数基于人工神经网络的方法需要大量的计算资源,这给在移动设备上的有效部署带来了挑战。另一方面,脉冲神经网络(snn)由于其二进制和事件驱动的架构,在节能深度学习方面具有巨大的潜力。据我们所知,我们是第一个将snn引入rPPG领域的人,提出了一种混合神经网络(HNN)模型,即spike - physformer,旨在降低功耗。具体来说,所提出的Spiking-PhyFormer由基于人工神经网络的补丁嵌入块、基于snn的变压器块和基于人工神经网络的预测头组成。首先,为了简化变压器块,同时保留其聚合局部和全局时空特征的能力,我们设计了一个并联尖峰变压器块来取代顺序子块。此外,我们提出了一种简化的峰值自注意机制,该机制在不影响模型性能的情况下省略了值参数。在pure、UBFC-rPPG、UBFC-Phys和MMPD四个数据集上进行的实验表明,与PhysFormer相比,该模型的功耗降低了10.1%。此外,变压器块的功耗降低了12.2倍,同时保持了与PhysFormer和其他基于人工神经网络的模型一样的良好性能。
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引用次数: 0
Contrastive Graph Representation Learning with Adversarial Cross-View Reconstruction and Information Bottleneck. 具有对抗性交叉视图重构和信息瓶颈的对比图表示学习。
IF 6 1区 计算机科学 Q1 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE Pub Date : 2025-01-09 DOI: 10.1016/j.neunet.2024.107094
Yuntao Shou, Haozhi Lan, Xiangyong Cao

Graph Neural Networks (GNNs) have received extensive research attention due to their powerful information aggregation capabilities. Despite the success of GNNs, most of them suffer from the popularity bias issue in a graph caused by a small number of popular categories. Additionally, real graph datasets always contain incorrect node labels, which hinders GNNs from learning effective node representations. Graph contrastive learning (GCL) has been shown to be effective in solving the above problems for node classification tasks. Most existing GCL methods are implemented by randomly removing edges and nodes to create multiple contrasting views, and then maximizing the mutual information (MI) between these contrasting views to improve the node feature representation. However, maximizing the mutual information between multiple contrasting views may lead the model to learn some redundant information irrelevant to the node classification task. To tackle this issue, we propose an effective Contrastive Graph Representation Learning with Adversarial Cross-view Reconstruction and Information Bottleneck (CGRL) for node classification, which can adaptively learn to mask the nodes and edges in the graph to obtain the optimal graph structure representation. Furthermore, we innovatively introduce the information bottleneck theory into GCLs to remove redundant information in multiple contrasting views while retaining as much information as possible about node classification. Moreover, we add noise perturbations to the original views and reconstruct the augmented views by constructing adversarial views to improve the robustness of node feature representation. We also verified through theoretical analysis the effectiveness of this cross-attempt reconstruction mechanism and information bottleneck theory in capturing graph structure information and improving model generalization performance. Extensive experiments on real-world public datasets demonstrate that our method significantly outperforms existing state-of-the-art algorithms.

图神经网络因其强大的信息聚合能力而受到广泛的研究关注。尽管gnn取得了成功,但大多数gnn都存在由少数流行类别引起的图中的流行偏差问题。此外,真实的图数据集总是包含不正确的节点标签,这阻碍了gnn学习有效的节点表示。图对比学习(GCL)已被证明可以有效地解决节点分类任务中的上述问题。大多数现有的GCL方法是通过随机移除边缘和节点来创建多个对比视图,然后最大化这些对比视图之间的互信息(MI)来改进节点特征表示。然而,最大化多个对比视图之间的互信息可能会导致模型学习到一些与节点分类任务无关的冗余信息。为了解决这一问题,我们提出了一种有效的基于对抗性交叉视图重构和信息瓶颈(CGRL)的对比图表示学习方法用于节点分类,该方法可以自适应学习对图中的节点和边进行屏蔽,以获得最优的图结构表示。此外,我们创新地将信息瓶颈理论引入到gcl中,在保留尽可能多的节点分类信息的同时,去除多个对比视图中的冗余信息。此外,我们在原始视图中加入噪声扰动,并通过构造对抗视图来重建增强视图,以提高节点特征表示的鲁棒性。通过理论分析验证了这种交叉尝试重构机制和信息瓶颈理论在获取图结构信息和提高模型泛化性能方面的有效性。在真实世界的公共数据集上进行的大量实验表明,我们的方法明显优于现有的最先进的算法。
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引用次数: 0
Sequential recommendation via agent-based irrelevancy skipping. 通过基于代理的不相关性跳过进行顺序推荐。
IF 6 1区 计算机科学 Q1 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE Pub Date : 2025-01-09 DOI: 10.1016/j.neunet.2025.107134
Yu Cheng, Jiawei Zheng, Binquan Wu, Qianli Ma

Sequential Recommendation is based on modelling sequential dependencies in user interactions to produce subsequent recommendation results. However, due to the diversity of users' interests and the uncertainty of their behaviours, not all historical interactions in users' interaction sequences are relevant to their next-interaction intents, which hinders generating accurate sequential recommendations. To this end, a novel Sequential Recommendation method, Dynamic-Skip for Sequential Recommendation (DyS4Rec), is proposed in this study. Specifically, by a Long-Short Term Memory (LSTM) with dynamic skip connections, allows DyS4Rec to skip irrelevant interactions to more accurately capture long-term dependencies, which are related to users' next-interaction intents. Furthermore, a Personalized Module (PM) is designed to guide the skipping process and add more personalization to the recommendation results. In this way, DyS4Rec can adaptively learn to exclude the impact of irrelevant historical interactions to precisely model users' personalized interaction intents and generate more accurate sequential recommendations. Extensive experiments on five public real-world datasets (containing items ranging from a few thousand to hundreds of thousands) showcase that DyS4Rec outperforms other state-of-the-art counterparts (by 1% to 12%). Moreover, visualization analyses demonstrate that DyS4Rec can indeed perform meaningful jumps in modelling user interactions to exclude the influence of irrelevant historical interactions and generate more accurate sequential recommendations.

顺序推荐基于对用户交互中的顺序依赖进行建模,以产生后续推荐结果。然而,由于用户兴趣的多样性和行为的不确定性,用户交互序列中并非所有历史交互都与下一次交互意图相关,这阻碍了生成准确的顺序推荐。为此,本文提出了一种新的顺序推荐方法——动态跳过顺序推荐(DyS4Rec)。具体来说,通过具有动态跳过连接的长短期记忆(LSTM),允许DyS4Rec跳过不相关的交互,以更准确地捕获与用户下一次交互意图相关的长期依赖关系。此外,设计了个性化模块(PM)来指导跳过过程,并为推荐结果添加更多个性化。通过这种方式,DyS4Rec可以自适应学习排除不相关的历史交互的影响,以精确地模拟用户的个性化交互意图,并生成更准确的顺序推荐。在五个公开的真实世界数据集(包含从几千到几十万的项目)上进行的广泛实验表明,DyS4Rec优于其他最先进的同行(1%到12%)。此外,可视化分析表明,DyS4Rec确实可以在建模用户交互方面进行有意义的跳跃,以排除不相关的历史交互的影响,并生成更准确的顺序推荐。
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引用次数: 0
Disentangled Active Learning on Graphs. 图上的解纠缠主动学习。
IF 6 1区 计算机科学 Q1 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE Pub Date : 2025-01-09 DOI: 10.1016/j.neunet.2025.107130
Haoran Yang, Junli Wang, Rui Duan, Changwei Wang, Chungang Yan

Active learning on graphs (ALG) has emerged as a compelling research field due to its capacity to address the challenge of label scarcity. Existing ALG methods incorporate diversity into their query strategies to maximize the gains from node sampling, improving robustness and reducing redundancy in graph learning. However, they often overlook the complex entanglement of latent factors inherent in graph-structured data. This oversight can lead to a sampling process that fails to ensure diversity at a finer-grained level, thereby missing the opportunity to sample more valuable nodes. To this end, we propose a novel approach, Disentangled Active Learning on Graphs (DALG). In this work, we first design the Disenconv-AL layer to learn disentangled feature embedding, then construct the influence graph for each node and create a dedicated "memory list" to store the resultant influence weights. On this basis, our approach aims to make the model not excessively focus on a few latent factors during the sampling phase. Specifically, we prioritize addressing latent factors with the most significant impact on the sampled node in the previous round, thereby ensuring that current sampling can better focus on other latent factors. Compared with existing methodologies, our approach pioneers reach diversity from the latent factor that drives the formation of graph data at a finer-grained level, thereby enabling further improvements in the benefits delivered with a limited labeling budget. Extensive experiments across eight public datasets show that DALG surpasses state-of-the-art graph active learning methods, achieving an improvement of up to approximately 15% in both Micro-F1 and Macro-F1.

图上主动学习(ALG)已经成为一个引人注目的研究领域,因为它能够解决标签稀缺的挑战。现有的ALG方法将多样性纳入其查询策略中,以最大限度地提高节点采样的收益,提高图学习的鲁棒性并减少冗余。然而,他们往往忽略了图结构数据中固有的潜在因素的复杂纠缠。这种疏忽可能导致采样过程无法确保细粒度级别上的多样性,从而失去对更有价值的节点进行采样的机会。为此,我们提出了一种新的方法——图上解纠缠主动学习(DALG)。在这项工作中,我们首先设计disenconvo - al层来学习解纠缠的特征嵌入,然后为每个节点构建影响图,并创建一个专用的“记忆列表”来存储得到的影响权重。在此基础上,我们的方法旨在使模型在采样阶段不会过度关注少数潜在因素。具体来说,我们优先处理对前一轮采样节点影响最大的潜在因素,从而确保当前采样能够更好地关注其他潜在因素。与现有的方法相比,我们的方法从驱动更细粒度的图形数据形成的潜在因素中获得了多样性,从而在有限的标签预算下实现了进一步的改进。在8个公共数据集上进行的广泛实验表明,DALG超越了最先进的图主动学习方法,在Micro-F1和Macro-F1中都实现了大约15%的改进。
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引用次数: 0
VPT: Video portraits transformer for realistic talking face generation. VPT:视频肖像变压器为现实的谈话脸生成。
IF 6 1区 计算机科学 Q1 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE Pub Date : 2025-01-09 DOI: 10.1016/j.neunet.2025.107122
Zhijun Zhang, Jian Zhang, Weijian Mai

Talking face generation is a promising approach within various domains, such as digital assistants, video editing, and virtual video conferences. Previous works with audio-driven talking faces focused primarily on the synchronization between audio and video. However, existing methods still have certain limitations in synthesizing photo-realistic video with high identity preservation, audiovisual synchronization, and facial details like blink movements. To solve these problems, a novel talking face generation framework, termed video portraits transformer (VPT) with controllable blink movements is proposed and applied. It separates the process of video generation into two stages, i.e., audio-to-landmark and landmark-to-face stages. In the audio-to-landmark stage, the transformer encoder serves as the generator used for predicting whole facial landmarks from given audio and continuous eye aspect ratio (EAR). During the landmark-to-face stage, the video-to-video (vid-to-vid) network is employed to transfer landmarks into realistic talking face videos. Moreover, to imitate real blink movements during inference, a transformer-based spontaneous blink generation module is devised to generate the EAR sequence. Extensive experiments demonstrate that the VPT method can produce photo-realistic videos of talking faces with natural blink movements, and the spontaneous blink generation module can generate blink movements close to the real blink duration distribution and frequency.

在许多领域,如数字助理、视频编辑和虚拟视频会议中,语音人脸生成是一种很有前途的方法。之前关于音频驱动的说话脸的工作主要集中在音频和视频之间的同步。然而,现有的方法在合成具有高度身份保持、视听同步和面部细节(如眨眼动作)的逼真视频方面仍然存在一定的局限性。为了解决这些问题,提出并应用了一种具有可控制眨眼运动的视频肖像变换(VPT)说话人脸生成框架。它将视频的生成过程分为两个阶段,即音频到地标和地标到面孔的阶段。在音频-地标阶段,变压器编码器作为发生器,用于从给定的音频和连续眼宽高比(EAR)预测整个面部地标。在地标到人脸阶段,采用视频到视频(video-to-vid)网络将地标转换为逼真的说话人脸视频。此外,为了模拟推理过程中真实的眨眼运动,设计了基于变压器的自发眨眼生成模块来生成EAR序列。大量实验表明,VPT方法可以生成具有自然眨眼运动的说话人脸的逼真视频,自发眨眼生成模块可以生成接近真实眨眼持续时间分布和频率的眨眼运动。
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引用次数: 0
Dual-view global and local category-attentive domain alignment for unsupervised conditional adversarial domain adaptation. 无监督条件对抗域自适应的双视角全局和局部范畴关注域对齐。
IF 6 1区 计算机科学 Q1 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE Pub Date : 2025-01-08 DOI: 10.1016/j.neunet.2025.107129
Jiahua Wu, Yuchun Fang

Conditional adversarial domain adaptation (CADA) is one of the most commonly used unsupervised domain adaptation (UDA) methods. CADA introduces multimodal information to the adversarial learning process to align the distributions of the labeled source domain and unlabeled target domain with mode match. However, CADA provides wrong multimodal information for challenging target features due to utilizing classifier predictions as the multimodal information, leading to distribution mismatch and less robust domain-invariant features. Compared to the recent state-of-the-art UDA methods, CADA also faces poor discriminability on the target domain. To tackle these challenges, we propose a novel unsupervised CADA framework named dual-view global and local category-attentive domain alignment (DV-GLCA). Specifically, to mitigate distribution mismatch and acquire more robust domain-invariant features, we integrate dual-view information into conditional adversarial domain adaptation and then utilize the substantial feature disparity between the two perspectives to better align the multimodal structures of the source and target distributions. Moreover, to learn more discriminative features of the target domain based on dual-view conditional adversarial domain adaptation (DV-CADA), we further propose global category-attentive domain alignment (GCA). We combine coding rate reduction and dual-view centroid alignment in GCA to amplify inter-category domain discrepancies while reducing intra-category domain differences globally. Additionally, to address challenging ambiguous samples during the training phase, we propose local category-attentive domain alignment (LCA). We introduce a new way of using contrastive domain discrepancy in LCA to move ambiguous samples closer to the correct category. Our method demonstrates leading performance on five UDA benchmarks, with extensive experiments showcasing its effectiveness.

条件对抗域自适应(Conditional adversarial domain adaptation, CADA)是一种最常用的无监督域自适应方法。CADA将多模态信息引入到对抗学习过程中,通过模式匹配来对齐标记的源域和未标记的目标域的分布。然而,由于使用分类器预测作为多模态信息,CADA为具有挑战性的目标特征提供了错误的多模态信息,导致分布不匹配和鲁棒性较差的域不变特征。与最近最先进的UDA方法相比,CADA在目标域上也面临着较差的可分辨性。为了解决这些挑战,我们提出了一种新的无监督CADA框架,称为双视图全局和局部类别关注域对齐(DV-GLCA)。具体而言,为了缓解分布不匹配并获得更鲁棒的域不变特征,我们将双视角信息集成到条件对抗域自适应中,然后利用两个视角之间的大量特征差异来更好地对齐源分布和目标分布的多模态结构。此外,为了学习基于双视图条件对抗性领域自适应(DV-CADA)的目标领域的更多判别特征,我们进一步提出了全局类别关注领域对齐(GCA)。在GCA中,我们将编码率降低和双视图质心对齐结合起来,放大了分类域间的差异,同时在全局上减小了分类域内的差异。此外,为了在训练阶段解决具有挑战性的模糊样本,我们提出了局部类别关注域对齐(LCA)。我们介绍了一种利用LCA中对比域差异的新方法,使模糊样本更接近正确的类别。我们的方法在五个UDA基准测试中表现出领先的性能,并通过大量实验证明了其有效性。
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引用次数: 0
Dynamic planning in hierarchical active inference. 分层主动推理中的动态规划。
IF 6 1区 计算机科学 Q1 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE Pub Date : 2025-01-08 DOI: 10.1016/j.neunet.2024.107075
Matteo Priorelli, Ivilin Peev Stoianov

By dynamic planning, we refer to the ability of the human brain to infer and impose motor trajectories related to cognitive decisions. A recent paradigm, active inference, brings fundamental insights into the adaptation of biological organisms, constantly striving to minimize prediction errors to restrict themselves to life-compatible states. Over the past years, many studies have shown how human and animal behaviors could be explained in terms of active inference - either as discrete decision-making or continuous motor control - inspiring innovative solutions in robotics and artificial intelligence. Still, the literature lacks a comprehensive outlook on effectively planning realistic actions in changing environments. Setting ourselves the goal of modeling complex tasks such as tool use, we delve into the topic of dynamic planning in active inference, keeping in mind two crucial aspects of biological behavior: the capacity to understand and exploit affordances for object manipulation, and to learn the hierarchical interactions between the self and the environment, including other agents. We start from a simple unit and gradually describe more advanced structures, comparing recently proposed design choices and providing basic examples. This study distances itself from traditional views centered on neural networks and reinforcement learning, and points toward a yet unexplored direction in active inference: hybrid representations in hierarchical models.

通过动态规划,我们指的是人类大脑推断和施加与认知决策相关的运动轨迹的能力。最近的一种范式,主动推理,带来了对生物有机体适应的基本见解,不断努力减少预测误差,将自己限制在生命相容的状态。在过去的几年里,许多研究表明,人类和动物的行为可以用主动推理来解释——无论是离散决策还是连续运动控制——这激发了机器人和人工智能领域的创新解决方案。尽管如此,文献缺乏在不断变化的环境中有效规划现实行动的全面展望。我们为自己设定了建模复杂任务(如工具使用)的目标,深入研究了主动推理中的动态规划主题,牢记生物行为的两个关键方面:理解和利用对象操作的能力,以及学习自我与环境(包括其他代理)之间的层次相互作用。我们从一个简单的单元开始,逐步描述更高级的结构,比较最近提出的设计选择,并提供基本的例子。这项研究与以神经网络和强化学习为中心的传统观点有所不同,并指出了主动推理中尚未探索的方向:层次模型中的混合表示。
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引用次数: 0
Improved analysis of supervised learning in the RKHS with random features: Beyond least squares. 具有随机特征的RKHS中监督学习的改进分析:超越最小二乘。
IF 6 1区 计算机科学 Q1 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE Pub Date : 2025-01-08 DOI: 10.1016/j.neunet.2024.107091
Jiamin Liu, Lei Wang, Heng Lian

We consider kernel-based supervised learning using random Fourier features, focusing on its statistical error bounds and generalization properties with general loss functions. Beyond the least squares loss, existing results only demonstrate worst-case analysis with rate n-1/2 and the number of features at least comparable to n, and refined-case analysis where it can achieve almost n-1 rate when the kernel's eigenvalue decay is exponential and the number of features is again at least comparable to n. For the least squares loss, the results are much richer and the optimal rates can be achieved under the source and capacity assumptions, with the number of features smaller than n. In this paper, for both losses with Lipschitz derivative and Lipschitz losses, we successfully establish faster rates with number of features much smaller than n, which are the same as the rates and number of features for the least squares loss. More specifically, in the attainable case (the true function is in the RKHS), we obtain the rate n-2ξ2ξ+γ which is the same as the standard method without using approximation, using o(n) features, where ξ characterizes the smoothness of the true function and γ characterizes the decay rate of the eigenvalues of the integral operator. Thus our results answer an important open question regarding random features.

我们考虑使用随机傅立叶特征的基于核的监督学习,重点研究其统计误差范围和具有一般损失函数的泛化性质。除了最小二乘损失之外,现有的结果只证明了速率为n-1/2且特征数量至少与n相当的最坏情况分析,以及细化的情况分析,当核的特征值衰减为指数且特征数量至少与n相当时,它可以实现几乎n-1的速率。对于最小二乘损失,结果更丰富,并且在源和容量假设下可以实现最优速率。在本文中,对于Lipschitz导数损失和Lipschitz损失,我们成功地建立了特征数远小于n的更快的速率,这与最小二乘损失的速率和特征数相同。更具体地说,在可实现的情况下(真函数在RKHS中),我们获得速率n-2ξ2ξ+γ,这与不使用近似的标准方法相同,使用o(n)个特征,其中ξ表征真函数的平滑性,γ表征积分算子的特征值的衰减率。因此,我们的结果回答了一个关于随机特征的重要开放问题。
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引用次数: 0
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Neural Networks
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