arXiv subjects
Publications and source records attributed to Hang Wang.
In this paper we compute the topological K-homology of 2-dimensional crystal groups. Our method focuses on the fixed point of group action and simplifies the calculation of the K-homology of universal space. The result also verifies the Baum-Connes Conjecture of 2-dimensional crystal groups.
We give a complete solution, for discrete countable groups, to the problem of defining and computing a geometric pairing between the left hand side of the Baum-Connes assembly map, given in terms of geometric cycles associated to proper actions on manifolds, and cyclic periodic cohomology of the group algebra. Indeed, for any such group $Γ$ (without any further assumptions on it) we construct an explicit morphism from the Left-Hand side of the Baum-Connes assembly map to the periodic cyclic homology of the group algebra. This morphism, called here the Chern-Baum-Connes assembly map, allows to give a proper and explicit formulation for a Chern-Connes pairing with the periodic cyclic cohomology of the group algebra. Several theorems are needed to formulate the Chern-Baum-Connes assembly map. In particular we establish a delocalised Riemann-Roch theorem, the wrong way functoriality for periodic delocalised cohomology for $Γ$-proper actions, the construction of a Chern morphism between the Left-Hand side of Baum-Connes and a delocalised cohomology group associated to $Γ$ which is an isomorphism once tensoring with $\mathbb{C}$, and the construction of an explicit cohomological assembly map between the delocalised cohomology group associated to $Γ$ and the homology group $H_*(Γ,FΓ)$. We then give an index theoretical formula for the above mentioned pairing (for any $Γ$) in terms of pairings of invariant forms, associated to geometric cycles and given in terms of delocalized Chern and Todd classes, and currents naturally associated to group cocycles using Burghelea's computation. As part of our results we prove that left-Hand side group used in this paper is isomorphic to the usual analytic model for the left-hand side of the assembly map.
E-learning is a widely used learning method, but with the development of society, traditional E-learning method has exposed some shortcomings, such as the boring way of teaching, so that it is difficult to increase the enthusiasm of students and raise their attention in class. The application of serious games in E-learning can make up for these shortcomings and effectively improve the quality of teaching. When applying serious games to E-learning, there are two main considerations: educational goals and game design. A successful serious game should organically combine the two aspects and balance the educational and entertaining nature of serious games. This paper mainly discusses the role of serious games in E-learning, various elements of game design, the classification of the educational goals of serious games and the relationship between educational goals and game design. In addition, we try to classify serious games and match educational goals with game types to provide guidance and assistance in the design of serious games. This paper also summarizes some shortcomings that serious games may have in the application of E-learning.
Metaverse is a new type of Internet application and social form that integrates a variety of new technologies. It has the characteristics of multi-technology, sociality, and hyper spatiotemporality. This paper introduces the development status of Metaverse, from the five perspectives of network infrastructure, management technology, basic common technology, virtual reality object connection, and virtual reality convergence, it introduces the technical framework of Metaverse. This paper also introduces the nature of Metaverse's social and hyper spatiotemporality, and discusses the first application areas of Metaverse and some of the problems and challenges it may face.
Consider a proper, isometric action by a unimodular locally compact group $G$ on a Riemannian manifold $M$ with boundary, such that $M/G$ is compact. For an equivariant, elliptic operator $D$ on $M$, and an element $g \in G$, we define a numerical index $\operatorname{index}_g(D)$, in terms of a parametrix for $D$ and a trace associated to $g$. We prove an equivariant Atiyah-Patodi-Singer index theorem for this index. We first state general analytic conditions under which this theorem holds, and then show that these conditions are satisfied if $g=e$ is the identity element; if $G$ is a finitely generated, discrete group, and the conjugacy class of $g$ has polynomial growth; and if $G$ is a connected, linear, real semisimple Lie group, and $g$ is a semisimple element. In the classical case, where $M$ is compact and $G$ is trivial, our arguments reduce to a relatively short and simple proof of the original Atiyah-Patodi-Singer index theorem. In part II of this series, we prove that, under certain conditions, $\operatorname{index}_g(D)$ can be recovered from a $K$-theoretic index of $D$ via a trace defined by the orbital integral over the conjugacy class of $g$.
In this paper, we introduce several new secondary invariants for Dirac operators on a complete Riemannian manifold with a uniform positive scalar curvature metric outside a compact set and use these secondary invariants to establish a higher index theorem for the Dirac operators. We apply our theory to study the secondary invariants for a manifold with corner with positive scalar curvature metric on each boundary face.
Autonomous highlight detection is crucial for enhancing the efficiency of video browsing on social media platforms. To attain this goal in a data-driven way, one may often face the situation where highlight annotations are not available on the target video category used in practice, while the supervision on another video category (named as source video category) is achievable. In such a situation, one can derive an effective highlight detector on target video category by transferring the highlight knowledge acquired from source video category to the target one. We call this problem cross-category video highlight detection, which has been rarely studied in previous works. For tackling such practical problem, we propose a Dual-Learner-based Video Highlight Detection (DL-VHD) framework. Under this framework, we first design a Set-based Learning module (SL-module) to improve the conventional pair-based learning by assessing the highlight extent of a video segment under a broader context. Based on such learning manner, we introduce two different learners to acquire the basic distinction of target category videos and the characteristics of highlight moments on source video category, respectively. These two types of highlight knowledge are further consolidated via knowledge distillation. Extensive experiments on three benchmark datasets demonstrate the superiority of the proposed SL-module, and the DL-VHD method outperforms five typical Unsupervised Domain Adaptation (UDA) algorithms on various cross-category highlight detection tasks. Our code is available at https://github.com/ChrisAllenMing/Cross_Category_Video_Highlight .
This paper studies unsupervised/self-supervised whole-graph representation learning, which is critical in many tasks such as molecule properties prediction in drug and material discovery. Existing methods mainly focus on preserving the local similarity structure between different graph instances but fail to discover the global semantic structure of the entire data set. In this paper, we propose a unified framework called Local-instance and Global-semantic Learning (GraphLoG) for self-supervised whole-graph representation learning. Specifically, besides preserving the local similarities, GraphLoG introduces the hierarchical prototypes to capture the global semantic clusters. An efficient online expectation-maximization (EM) algorithm is further developed for learning the model. We evaluate GraphLoG by pre-training it on massive unlabeled graphs followed by fine-tuning on downstream tasks. Extensive experiments on both chemical and biological benchmark data sets demonstrate the effectiveness of the proposed approach.
Convolution and self-attention are acting as two fundamental building blocks in deep neural networks, where the former extracts local image features in a linear way while the latter non-locally encodes high-order contextual relationships. Though essentially complementary to each other, i.e., first-/high-order, stat-of-the-art architectures, i.e., CNNs or transformers lack a principled way to simultaneously apply both operations in a single computational module, due to their heterogeneous computing pattern and excessive burden of global dot-product for visual tasks. In this work, we theoretically derive a global self-attention approximation scheme, which approximates a self-attention via the convolution operation on transformed features. Based on the approximated scheme, we establish a multi-branch elementary module composed of both convolution and self-attention operation, capable of unifying both local and non-local feature interaction. Importantly, once trained, this multi-branch module could be conditionally converted into a single standard convolution operation via structural re-parameterization, rendering a pure convolution styled operator named X-volution, ready to be plugged into any modern networks as an atomic operation. Extensive experiments demonstrate that the proposed X-volution, achieves highly competitive visual understanding improvements (+1.2% top-1 accuracy on ImageNet classification, +1.7 box AP and +1.5 mask AP on COCO detection and segmentation).
In this work, we propose a Cross-view Contrastive Learning framework for unsupervised 3D skeleton-based action Representation (CrosSCLR), by leveraging multi-view complementary supervision signal. CrosSCLR consists of both single-view contrastive learning (SkeletonCLR) and cross-view consistent knowledge mining (CVC-KM) modules, integrated in a collaborative learning manner. It is noted that CVC-KM works in such a way that high-confidence positive/negative samples and their distributions are exchanged among views according to their embedding similarity, ensuring cross-view consistency in terms of contrastive context, i.e., similar distributions. Extensive experiments show that CrosSCLR achieves remarkable action recognition results on NTU-60 and NTU-120 datasets under unsupervised settings, with observed higher-quality action representations. Our code is available at https://github.com/LinguoLi/CrosSCLR.
Along with the rapid development of Internet and cyber techniques, the Internet of People (IoP) has been emerging as a novel paradigm which establishes ubiquitous connections between social space and cyberspace. Unlike the Internet of Things (IoT), human nodes in IoP are not only terminal users, but also significant participants bonded with tighter relationships. Note that IoP has deeply influenced our lives. For example, the prosperity of social media enables us to build and maintain new relationships without considering physical boundaries. In this paper, we give a comprehensive overview of IoP by comparing it with IoT, introduce its enabling techniques from aspects of sensing, communication and application. In addition, we summarize and compare popular IoP-enabled platforms according to different functions, and finally envision open issues needed to be further discussed in IoP. It provides constructive suggestions, lays solid foundations, and makes a basic blueprint for the future development of IoP paradigm.
This paper studies distributed Q-learning for Linear Quadratic Regulator (LQR) in a multi-agent network. The existing results often assume that agents can observe the global system state, which may be infeasible in large-scale systems due to privacy concerns or communication constraints. In this work, we consider a setting with unknown system models and no centralized coordinator. We devise a state tracking (ST) based Q-learning algorithm to design optimal controllers for agents. Specifically, we assume that agents maintain local estimates of the global state based on their local information and communications with neighbors. At each step, every agent updates its local global state estimation, based on which it solves an approximate Q-factor locally through policy iteration. Assuming decaying injected excitation noise during the policy evaluation, we prove that the local estimation converges to the true global state, and establish the convergence of the proposed distributed ST-based Q-learning algorithm. The experimental studies corroborate our theoretical results by showing that our proposed method achieves comparable performance with the centralized case.
System identification is a fundamental problem in reinforcement learning, control theory and signal processing, and the non-asymptotic analysis of the corresponding sample complexity is challenging and elusive, even for linear time-varying (LTV) systems. To tackle this challenge, we develop an episodic block model for the LTV system where the model parameters remain constant within each block but change from block to block. Based on the observation that the model parameters across different blocks are related, we treat each episodic block as a learning task and then run meta-learning over many blocks for system identification, using two steps, namely offline meta-learning and online adaptation. We carry out a comprehensive non-asymptotic analysis of the performance of meta-learning based system identification. To deal with the technical challenges rooted in the sample correlation and small sample sizes in each block, we devise a new two-scale martingale small-ball approach for offline meta-learning, for arbitrary model correlation structure across blocks. We then quantify the finite time error of online adaptation by leveraging recent advances in linear stochastic approximation with correlated samples.
Transferring knowledges learned from multiple source domains to target domain is a more practical and challenging task than conventional single-source domain adaptation. Furthermore, the increase of modalities brings more difficulty in aligning feature distributions among multiple domains. To mitigate these problems, we propose a Learning to Combine for Multi-Source Domain Adaptation (LtC-MSDA) framework via exploring interactions among domains. In the nutshell, a knowledge graph is constructed on the prototypes of various domains to realize the information propagation among semantically adjacent representations. On such basis, a graph model is learned to predict query samples under the guidance of correlated prototypes. In addition, we design a Relation Alignment Loss (RAL) to facilitate the consistency of categories' relational interdependency and the compactness of features, which boosts features' intra-class invariance and inter-class separability. Comprehensive results on public benchmark datasets demonstrate that our approach outperforms existing methods with a remarkable margin. Our code is available at \url{https://github.com/ChrisAllenMing/LtC-MSDA}
Consider a proper, isometric action by a unimodular locally compact group $G$ on a Riemannian manifold $M$ with boundary, such that $M/G$ is compact. Then an equivariant Dirac-type operator $D$ on $M$ under a suitable boundary condition has an equivariant index $\operatorname{index}_G(D)$ in the $K$-theory of the reduced group $C^*$-algebra $C^*_rG$ of $G$. This is a common generalisation of the Baum-Connes analytic assembly map and the (equivariant) Atiyah-Patodi-Singer index. In part I of this series, a numerical index $\operatorname{index}_g(D)$ was defined for an element $g \in G$, in terms of a parametrix of $D$ and a trace associated to $g$. An Atiyah-Patodi-Singer type index formula was obtained for this index. In this paper, we show that, under certain conditions, $τ_g(\operatorname{index}_G(D)) = \operatorname{index}_g(D)$, for a trace $τ_g$ defined by the orbital integral over the conjugacy class of $g$. This implies that the index theorem from part I yields information about the $K$-theoretic index $\operatorname{index}_G(D)$. It also shows that $\operatorname{index}_g(D)$ is a homotopy-invariant quantity.
Fundamental group of a manifold gives a deep effect on its underlying smooth structure. In this paper we introduce a new variant of the Donaldson invariant in Yang-Mills gauge theory from twisting by the Picard group of a four manifold in the case when the fundamental group is free abelian. We then generalize it to the general case of fundamental groups by use of the framework of non commutative geometry. We also verify that our invariant distinguishes smooth structures between some homeomorphic four manifolds.
Recently, a backdoor data poisoning attack was proposed, which adds mislabeled examples to the training set, with an embedded backdoor pattern, aiming to have the classifier learn to classify to a target class whenever the backdoor pattern is present in a test sample. Here, we address post-training detection of innocuous perceptible backdoors in DNN image classifiers, wherein the defender does not have access to the poisoned training set, but only to the trained classifier, as well as unpoisoned examples. This problem is challenging because without the poisoned training set, we have no hint about the actual backdoor pattern used during training. This post-training scenario is also of great import because in many practical contexts the DNN user did not train the DNN and does not have access to the training data. We identify two important properties of perceptible backdoor patterns - spatial invariance and robustness - based upon which we propose a novel detector using the maximum achievable misclassification fraction (MAMF) statistic. We detect whether the trained DNN has been backdoor-attacked and infer the source and target classes. Our detector outperforms other existing detectors and, coupled with an imperceptible backdoor detector, helps achieve post-training detection of all evasive backdoors.
Applying the knowledge of an object detector trained on a specific domain directly onto a new domain is risky, as the gap between two domains can severely degrade model's performance. Furthermore, since different instances commonly embody distinct modal information in object detection scenario, the feature alignment of source and target domain is hard to be realized. To mitigate these problems, we propose a Graph-induced Prototype Alignment (GPA) framework to seek for category-level domain alignment via elaborate prototype representations. In the nutshell, more precise instance-level features are obtained through graph-based information propagation among region proposals, and, on such basis, the prototype representation of each class is derived for category-level domain alignment. In addition, in order to alleviate the negative effect of class-imbalance on domain adaptation, we design a Class-reweighted Contrastive Loss to harmonize the adaptation training process. Combining with Faster R-CNN, the proposed framework conducts feature alignment in a two-stage manner. Comprehensive results on various cross-domain detection tasks demonstrate that our approach outperforms existing methods with a remarkable margin. Our code is available at https://github.com/ChrisAllenMing/GPA-detection.