arXiv subjects
Publications and source records attributed to Hang Wang.
We prove an equivariant index theorem on the Euclidean space using a continuous field of $C^*$-algebras. This generalizes the work of Elliott, Natsume and Nest, which is a special case of the algebraic index theorem by Nest-Tsygan. Using our formula, the equivariant index of the Bott-Dirac operator on $\mathbb{R}^{2n}$ can be explicitly calculated.
The contrastive vision-language pre-training, known as CLIP, demonstrates remarkable potential in perceiving open-world visual concepts, enabling effective zero-shot image recognition. Nevertheless, few-shot learning methods based on CLIP typically require offline fine-tuning of the parameters on few-shot samples, resulting in longer inference time and the risk of over-fitting in certain domains. To tackle these challenges, we propose the Meta-Adapter, a lightweight residual-style adapter, to refine the CLIP features guided by the few-shot samples in an online manner. With a few training samples, our method can enable effective few-shot learning capabilities and generalize to unseen data or tasks without additional fine-tuning, achieving competitive performance and high efficiency. Without bells and whistles, our approach outperforms the state-of-the-art online few-shot learning method by an average of 3.6\% on eight image classification datasets with higher inference speed. Furthermore, our model is simple and flexible, serving as a plug-and-play module directly applicable to downstream tasks. Without further fine-tuning, Meta-Adapter obtains notable performance improvements in open-vocabulary object detection and segmentation tasks.
Face forgery techniques have emerged as a forefront concern, and numerous detection approaches have been proposed to address this challenge. However, existing methods predominantly concentrate on single-face manipulation detection, leaving the more intricate and realistic realm of multi-face forgeries relatively unexplored. This paper proposes a novel framework explicitly tailored for multi-face forgery detection,filling a critical gap in the current research. The framework mainly involves two modules:(i) a facial relationships learning module, which generates distinguishable local features for each face within images,(ii) a global feature aggregation module that leverages the mutual constraints between global and local information to enhance forgery detection accuracy.Our experimental results on two publicly available multi-face forgery datasets demonstrate that the proposed approach achieves state-of-the-art performance in multi-face forgery detection scenarios.
Well-known (non-malicious) sources of overfitting in deep neural net (DNN) classifiers include: i) large class imbalances; ii) insufficient training-set diversity; and iii) over-training. In recent work, it was shown that backdoor data-poisoning also induces overfitting, with unusually large classification margins to the attacker's target class, mediated particularly by (unbounded) ReLU activations that allow large signals to propagate in the DNN. Thus, an effective post-training (with no knowledge of the training set or training process) mitigation approach against backdoors was proposed, leveraging a small clean dataset, based on bounding neural activations. Improving upon that work, we threshold activations specifically to limit maximum margins (MMs), which yields performance gains in backdoor mitigation. We also provide some analytical support for this mitigation approach. Most importantly, we show that post-training MM-based regularization substantially mitigates non-malicious overfitting due to class imbalances and overtraining. Thus, unlike adversarial training, which provides some resilience against attacks but which harms clean (attack-free) generalization, we demonstrate an approach originating from adversarial learning that helps clean generalization accuracy. Experiments on CIFAR-10 and CIFAR-100, in comparison with peer methods, demonstrate strong performance of our methods.
Deep neural networks are vulnerable to backdoor attacks (Trojans), where an attacker poisons the training set with backdoor triggers so that the neural network learns to classify test-time triggers to the attacker's designated target class. Recent work shows that backdoor poisoning induces over-fitting (abnormally large activations) in the attacked model, which motivates a general, post-training clipping method for backdoor mitigation, i.e., with bounds on internal-layer activations learned using a small set of clean samples. We devise a new such approach, choosing the activation bounds to explicitly limit classification margins. This method gives superior performance against peer methods for CIFAR-10 image classification. We also show that this method has strong robustness against adaptive attacks, X2X attacks, and on different datasets. Finally, we demonstrate a method extension for test-time detection and correction based on the output differences between the original and activation-bounded networks. The code of our method is online available.
Backdoor attacks are an important type of adversarial threat against deep neural network classifiers, wherein test samples from one or more source classes will be (mis)classified to the attacker's target class when a backdoor pattern is embedded. In this paper, we focus on the post-training backdoor defense scenario commonly considered in the literature, where the defender aims to detect whether a trained classifier was backdoor-attacked without any access to the training set. Many post-training detectors are designed to detect attacks that use either one or a few specific backdoor embedding functions (e.g., patch-replacement or additive attacks). These detectors may fail when the backdoor embedding function used by the attacker (unknown to the defender) is different from the backdoor embedding function assumed by the defender. In contrast, we propose a post-training defense that detects backdoor attacks with arbitrary types of backdoor embeddings, without making any assumptions about the backdoor embedding type. Our detector leverages the influence of the backdoor attack, independent of the backdoor embedding mechanism, on the landscape of the classifier's outputs prior to the softmax layer. For each class, a maximum margin statistic is estimated. Detection inference is then performed by applying an unsupervised anomaly detector to these statistics. Thus, our detector does not need any legitimate clean samples, and can efficiently detect backdoor attacks with arbitrary numbers of source classes. These advantages over several state-of-the-art methods are demonstrated on four datasets, for three different types of backdoor patterns, and for a variety of attack configurations. Finally, we propose a novel, general approach for backdoor mitigation once a detection is made. The mitigation approach was the runner-up at the first IEEE Trojan Removal Competition. The code is online available.
Warm-Start reinforcement learning (RL), aided by a prior policy obtained from offline training, is emerging as a promising RL approach for practical applications. Recent empirical studies have demonstrated that the performance of Warm-Start RL can be improved \textit{quickly} in some cases but become \textit{stagnant} in other cases, especially when the function approximation is used. To this end, the primary objective of this work is to build a fundamental understanding on ``\textit{whether and when online learning can be significantly accelerated by a warm-start policy from offline RL?}''. Specifically, we consider the widely used Actor-Critic (A-C) method with a prior policy. We first quantify the approximation errors in the Actor update and the Critic update, respectively. Next, we cast the Warm-Start A-C algorithm as Newton's method with perturbation, and study the impact of the approximation errors on the finite-time learning performance with inaccurate Actor/Critic updates. Under some general technical conditions, we derive the upper bounds, which shed light on achieving the desired finite-learning performance in the Warm-Start A-C algorithm. In particular, our findings reveal that it is essential to reduce the algorithm bias in online learning. We also obtain lower bounds on the sub-optimality gap of the Warm-Start A-C algorithm to quantify the impact of the bias and error propagation.
The ensemble method is a promising way to mitigate the overestimation issue in Q-learning, where multiple function approximators are used to estimate the action values. It is known that the estimation bias hinges heavily on the ensemble size (i.e., the number of Q-function approximators used in the target), and that determining the `right' ensemble size is highly nontrivial, because of the time-varying nature of the function approximation errors during the learning process. To tackle this challenge, we first derive an upper bound and a lower bound on the estimation bias, based on which the ensemble size is adapted to drive the bias to be nearly zero, thereby coping with the impact of the time-varying approximation errors accordingly. Motivated by the theoretic findings, we advocate that the ensemble method can be combined with Model Identification Adaptive Control (MIAC) for effective ensemble size adaptation. Specifically, we devise Adaptive Ensemble Q-learning (AdaEQ), a generalized ensemble method with two key steps: (a) approximation error characterization which serves as the feedback for flexibly controlling the ensemble size, and (b) ensemble size adaptation tailored towards minimizing the estimation bias. Extensive experiments are carried out to show that AdaEQ can improve the learning performance than the existing methods for the MuJoCo benchmark.
Conversational recommender systems (CRSs) aim to understand the information needs and preferences expressed in a dialogue to recommend suitable items to the user. Most of the existing conversational recommendation datasets are synthesized or simulated with crowdsourcing, which has a large gap with real-world scenarios. To bridge the gap, previous work contributes a dataset E-ConvRec, based on pre-sales dialogues between users and customer service staff in E-commerce scenarios. However, E-ConvRec only supplies coarse-grained annotations and general tasks for making recommendations in pre-sales dialogues. Different from that, we use real user needs as a clue to explore the E-commerce conversational recommendation in complex pre-sales dialogues, namely user needs-centric E-commerce conversational recommendation (UNECR). In this paper, we construct a user needs-centric E-commerce conversational recommendation dataset (U-NEED) from real-world E-commerce scenarios. U-NEED consists of 3 types of resources: (i) 7,698 fine-grained annotated pre-sales dialogues in 5 top categories (ii) 333,879 user behaviors and (iii) 332,148 product knowledge tuples. To facilitate the research of UNECR, we propose 5 critical tasks: (i) pre-sales dialogue understanding (ii) user needs elicitation (iii) user needs-based recommendation (iv) pre-sales dialogue generation and (v) pre-sales dialogue evaluation. We establish baseline methods and evaluation metrics for each task. We report experimental results of 5 tasks on U-NEED. We also report results in 3 typical categories. Experimental results indicate that the challenges of UNECR in various categories are different.
While lightweight ViT framework has made tremendous progress in image super-resolution, its uni-dimensional self-attention modeling, as well as homogeneous aggregation scheme, limit its effective receptive field (ERF) to include more comprehensive interactions from both spatial and channel dimensions. To tackle these drawbacks, this work proposes two enhanced components under a new Omni-SR architecture. First, an Omni Self-Attention (OSA) block is proposed based on dense interaction principle, which can simultaneously model pixel-interaction from both spatial and channel dimensions, mining the potential correlations across omni-axis (i.e., spatial and channel). Coupling with mainstream window partitioning strategies, OSA can achieve superior performance with compelling computational budgets. Second, a multi-scale interaction scheme is proposed to mitigate sub-optimal ERF (i.e., premature saturation) in shallow models, which facilitates local propagation and meso-/global-scale interactions, rendering an omni-scale aggregation building block. Extensive experiments demonstrate that Omni-SR achieves record-high performance on lightweight super-resolution benchmarks (e.g., 26.95 dB@Urban100 $\times 4$ with only 792K parameters). Our code is available at \url{https://github.com/Francis0625/Omni-SR}.
We consider a complete Riemannian manifold, which consists of a compact interior and one or more $φ$-cusps: infinitely long ends of a type that includes cylindrical ends and hyperbolic cusps. Here $φ$ is a function of the radial coordinate that describes the shape of such an end. Given an action by a compact Lie group on such a manifold, we obtain an equivariant index theorem for Dirac operators, under conditions on $φ$. These conditions hold in the cases of cylindrical ends and hyperbolic cusps. In the case of cylindrical ends, the cusp contribution equals the delocalised $η$-invariant, and the index theorem reduces to Donnelly's equivariant index theory on compact manifolds with boundary. In general, we find that the cusp contribution is zero if the spectrum of the relevant Dirac operator on a hypersurface is symmetric around zero.
A Dirac operator on a complete manifold is Fredholm if it is invertible outside a compact set. Assuming a compact group to act on all relevant structure, and the manifold to have a warped product structure outside such a compact set, we express the equivariant index of such a Dirac operator as an Atiyah-Segal-Singer type contribution from inside this compact set, and a contribution from outside this set. Consequences include equivariant versions of the relative index theorem of Gromov and Lawson, in the case of manifolds with warped product structures at infinity, and the Atiyah-Patodi-Singer index theorem.
Digital twin has recently attracted growing attention, leading to intensive research and applications. Along with this, a new research area, dubbed as "human digital twin" (HDT), has emerged. Similar to the conception of digital twin, HDT is referred to as the replica of a physical-world human in the digital world. Nevertheless, HDT is much more complicated and delicate compared to digital twins of any physical systems and processes, due to humans' dynamic and evolutionary nature, including physical, behavioral, social, physiological, psychological, cognitive, and biological dimensions. Studies on HDT are limited, and the research is still in its infancy. In this paper, we first examine the inception, development, and application of the digital twin concept, providing a context within which we formally define and characterize HDT based on the similarities and differences between digital twin and HDT. Then we conduct an extensive literature review on HDT research, analyzing underpinning technologies and establishing typical frameworks in which the core HDT functions or components are organized. Built upon the findings from the above work, we propose a generic architecture for the HDT system and describe the core function blocks and corresponding technologies. Following this, we present the state of the art of HDT technologies and applications in the healthcare, industry, and daily life domain. Finally, we discuss various issues related to the development of HDT and point out the trends and challenges of future HDT research and development.
Depth map super-resolution (DSR) has been a fundamental task for 3D computer vision. While arbitrary scale DSR is a more realistic setting in this scenario, previous approaches predominantly suffer from the issue of inefficient real-numbered scale upsampling. To explicitly address this issue, we propose a novel continuous depth representation for DSR. The heart of this representation is our proposed Geometric Spatial Aggregator (GSA), which exploits a distance field modulated by arbitrarily upsampled target gridding, through which the geometric information is explicitly introduced into feature aggregation and target generation. Furthermore, bricking with GSA, we present a transformer-style backbone named GeoDSR, which possesses a principled way to construct the functional mapping between local coordinates and the high-resolution output results, empowering our model with the advantage of arbitrary shape transformation ready to help diverse zooming demand. Extensive experimental results on standard depth map benchmarks, e.g., NYU v2, have demonstrated that the proposed framework achieves significant restoration gain in arbitrary scale depth map super-resolution compared with the prior art. Our codes are available at https://github.com/nana01219/GeoDSR.
We produce an explicit description of the K-theory and K-homology of the pure braid group on $n$ strands. We describe the Baum--Connes correspondence between the generators of the left- and right-hand sides for $n=4$. Using functoriality of the assembly map and direct computations, we recover Oyono-Oyono's result on the Baum--Connes conjecture for pure braid groups. We also discuss the case of the full braid group $B_3$.
In this paper, we establish an equivariant version of Dai-Zhang's Toeplitz index theorem for compact odd-dimensional spin manifolds with even-dimensional boundary.
Multi-Source Domain Adaptation (MSDA) focuses on transferring the knowledge from multiple source domains to the target domain, which is a more practical and challenging problem compared to the conventional single-source domain adaptation. In this problem, it is essential to model multiple source domains and target domain jointly, and an effective domain combination scheme is also highly required. The graphical structure among different domains is useful to tackle these challenges, in which the interdependency among various instances/categories can be effectively modeled. In this work, we propose two types of graphical models, i.e. Conditional Random Field for MSDA (CRF-MSDA) and Markov Random Field for MSDA (MRF-MSDA), for cross-domain joint modeling and learnable domain combination. In a nutshell, given an observation set composed of a query sample and the semantic prototypes (i.e. representative category embeddings) on various domains, the CRF-MSDA model seeks to learn the joint distribution of labels conditioned on the observations. We attain this goal by constructing a relational graph over all observations and conducting local message passing on it. By comparison, MRF-MSDA aims to model the joint distribution of observations over different Markov networks via an energy-based formulation, and it can naturally perform label prediction by summing the joint likelihoods over several specific networks. Compared to the CRF-MSDA counterpart, the MRF-MSDA model is more expressive and possesses lower computational cost. We evaluate these two models on four standard benchmark data sets of MSDA with distinct domain shift and data complexity, and both models achieve superior performance over existing methods on all benchmarks. In addition, the analytical studies illustrate the effect of different model components and provide insights about how the cross-domain joint modeling performs.
Deep Neural Networks (DNNs) have been shown vulnerable to Test-Time Evasion attacks (TTEs, or adversarial examples), which, by making small changes to the input, alter the DNN's decision. We propose an unsupervised attack detector on DNN classifiers based on class-conditional Generative Adversarial Networks (GANs). We model the distribution of clean data conditioned on the predicted class label by an Auxiliary Classifier GAN (AC-GAN). Given a test sample and its predicted class, three detection statistics are calculated based on the AC-GAN Generator and Discriminator. Experiments on image classification datasets under various TTE attacks show that our method outperforms previous detection methods. We also investigate the effectiveness of anomaly detection using different DNN layers (input features or internal-layer features) and demonstrate, as one might expect, that anomalies are harder to detect using features closer to the DNN's output layer.