arXiv subjects

Hang Wang

Publications and source records attributed to Hang Wang.

At least 55 records · Page 3Linked to original sources

arXiv2025

A higher index and rapidly decaying kernels

We construct an index of first-order, self-adjoint, elliptic differential operators in the $K$-theory of a Fréchet algebra of smooth kernels with faster than exponential off-diagonal decay. We show that this index can be represented by an idempotent involving heat operators. The rapid decay of the kernels in the algebra used is helpful in proving convergence of pairings with cyclic cocycles. Representing the index in terms of heat operators allows one to use heat kernel asymptotics to compute such pairings. We give a link to von Neumann algebras and $L^2$-index theorems as an immediate application, and work out further applications in other papers.

math.KT↗

arXiv2025

The equivalence between Einstein and Jordan frames: a study based on the inflationary magnetogenesis model

The equivalence of the Jordan and Einstein frames has been a subject of considerable interest in the field. In this paper, within the context of $f(R)$ gravity, we explore the inflationary magnetogenesis model, focusing on the magnetic field energy density and its spectrum in both the Jordan and Einstein frames to elucidate the equivalence between these two reference frames. Our analysis reveals that during the inflationary epoch, while the magnetic field exhibits a scale-invariant spectrum in the Einstein frame, it demonstrates a blue spectrum in the Jordan frame. Additionally, we investigate the post-inflationary evolution of the magnetic field's energy density in both frames, uncovering that for scale-invariant spectra in the Einstein frame during inflation, the magnetic field transitions to a blue spectrum, whereas in the Jordan frame, it evolves into a red spectrum. We also establish the conditions under which both frames may exhibit scale-invariant spectra simultaneously during the inflationary period.

astro-ph.CO↗

arXiv2025

Manifold-valued function approximation from multiple tangent spaces

Approximating a manifold-valued function from samples of input-output pairs consists of modeling the relationship between an input from a vector space and an output on a Riemannian manifold. We propose a function approximation method that leverages and unifies two prior techniques: (i) approximating a pullback to the tangent space, and (ii) the Riemannian moving least squares method. The core idea of the new scheme is to combine pullbacks to multiple tangent spaces with a weighted Fréchet mean. The effectiveness of this approach is illustrated with numerical experiments on model problems from parametric model order reduction.

math.NA↗

arXiv2025

CEPA: Consensus Embedded Perturbation for Agnostic Detection and Inversion of Backdoors

A variety of defenses have been proposed against Trojans planted in (backdoor attacks on) deep neural network (DNN) classifiers. Backdoor-agnostic methods seek to reliably detect and/or to mitigate backdoors irrespective of the incorporation mechanism used by the attacker, while inversion methods explicitly assume one. In this paper, we describe a new detector that: relies on embedded feature representations to estimate (invert) the backdoor and to identify its target class; can operate without access to the training dataset; and is highly effective for various incorporation mechanisms (i.e., is backdoor agnostic). Our detection approach is evaluated -- and found to be favorable - in comparison with an array of published defenses for a variety of different attacks on the CIFAR-10 and CIFAR-100 image-classification domains.

cs.CR↗

arXiv2025

Heterogeneous Decision Making in Mixed Traffic: Uncertainty-aware Planning and Bounded Rationality

The past few years have witnessed a rapid growth of the deployment of automated vehicles (AVs). Clearly, AVs and human-driven vehicles (HVs) will co-exist for many years, and AVs will have to operate around HVs, pedestrians, cyclists, and more, calling for fundamental breakthroughs in AI designed for mixed traffic to achieve mixed autonomy. Thus motivated, we study heterogeneous decision making by AVs and HVs in a mixed traffic environment, aiming to capture the interactions between human and machine decision-making and develop an AI foundation that enables vehicles to operate safely and efficiently. There are a number of challenges to achieve mixed autonomy, including 1) humans drivers make driving decisions with bounded rationality, and it remains open to develop accurate models for HVs' decision making; and 2) uncertainty-aware planning plays a critical role for AVs to take safety maneuvers in response to the human behavior. In this paper, we introduce a formulation of AV-HV interaction, where the HV makes decisions with bounded rationality and the AV employs uncertainty-aware planning based on the prediction on HV's future actions. We conduct a comprehensive analysis on AV and HV's learning regret to answer the questions: 1) {How does the learning performance depend on HV's bounded rationality and AV's planning}; 2) {How do different decision making strategies impact the overall learning performance}? Our findings reveal some intriguing phenomena, such as Goodhart's Law in AV's learning performance and compounding effects in HV's decision making process. By examining the dynamics of the regrets, we gain insights into the interplay between human and machine decision making.

cs.MA↗

arXiv2025

Discussion on "Resurrecting a Neglected Measurement Technique for Air-Water Flows"

Over the last years, there has been a renewed interest in differentiating various contributions to the air concentration in high Froude-number self-aerated flows, see for example Kramer (2024), comprising entrained and entrapped air. The former is characterized by entrained air packets and bubbles, while entrapped air corresponds to air transported along wave peaks and troughs. Entrapped air was first measured by Killen (1968) using a so-called dipping probe, while a physical interpretation of the dipping probe signals was provided only later by Wilhelms and Gulliver (2005). Since then, it has been commonly accepted that two different measurement instruments, for example a dipping probe and a common phase-detection probe, are required to fully quantify entrained and entrapped air. Recently, an article entitled "Resurrecting a Neglected Measurement Technique for Air-Water Flows" was published by Wilhelms and Gulliver (2024), who re-iterated the importance of applying these concepts for cavitation prevention and air-water gas transfer, as well as the need for two separate measurement instruments. The authors are congratulated for their seminal works on entrained and entrapped air (Wilhelms and Gulliver 2005; Wilhelms and Gulliver 2024), and it is stipulated that these concepts have been overlooked in the last two decades. In this discussion, a simple discrimination technique for phase-detection probe signals is proposed, which allows to differentiate entrained and entrapped air from existing datasets, recorded with a state-of-the-art dual-tip phase-detection probe. It is believed that this novel signal processing method will make Killen's (1968) dipping probe redundant, and that it will be useful for the validation of non-intrusive measurements of entrapped air, as well as for the development of physics-based models for air-water mass transfer in self-aerated flows.

physics.flu-dyn↗

arXiv2025

AdaWM: Adaptive World Model based Planning for Autonomous Driving

World model based reinforcement learning (RL) has emerged as a promising approach for autonomous driving, which learns a latent dynamics model and uses it to train a planning policy. To speed up the learning process, the pretrain-finetune paradigm is often used, where online RL is initialized by a pretrained model and a policy learned offline. However, naively performing such initialization in RL may result in dramatic performance degradation during the online interactions in the new task. To tackle this challenge, we first analyze the performance degradation and identify two primary root causes therein: the mismatch of the planning policy and the mismatch of the dynamics model, due to distribution shift. We further analyze the effects of these factors on performance degradation during finetuning, and our findings reveal that the choice of finetuning strategies plays a pivotal role in mitigating these effects. We then introduce AdaWM, an Adaptive World Model based planning method, featuring two key steps: (a) mismatch identification, which quantifies the mismatches and informs the finetuning strategy, and (b) alignment-driven finetuning, which selectively updates either the policy or the model as needed using efficient low-rank updates. Extensive experiments on the challenging CARLA driving tasks demonstrate that AdaWM significantly improves the finetuning process, resulting in more robust and efficient performance in autonomous driving systems.

cs.RO↗

arXiv2024

Towards Unraveling and Improving Generalization in World Models

World models have recently emerged as a promising approach to reinforcement learning (RL), achieving state-of-the-art performance across a wide range of visual control tasks. This work aims to obtain a deep understanding of the robustness and generalization capabilities of world models. Thus motivated, we develop a stochastic differential equation formulation by treating the world model learning as a stochastic dynamical system, and characterize the impact of latent representation errors on robustness and generalization, for both cases with zero-drift representation errors and with non-zero-drift representation errors. Our somewhat surprising findings, based on both theoretic and experimental studies, reveal that for the case with zero drift, modest latent representation errors can in fact function as implicit regularization and hence result in improved robustness. We further propose a Jacobian regularization scheme to mitigate the compounding error propagation effects of non-zero drift, thereby enhancing training stability and robustness. Our experimental studies corroborate that this regularization approach not only stabilizes training but also accelerates convergence and improves accuracy of long-horizon prediction.

cs.LG↗

arXiv2024

Research on Cervical Cancer p16/Ki-67 Immunohistochemical Dual-Staining Image Recognition Algorithm Based on YOLO

The p16/Ki-67 dual staining method is a new approach for cervical cancer screening with high sensitivity and specificity. However, there are issues of mis-detection and inaccurate recognition when the YOLOv5s algorithm is directly applied to dual-stained cell images. This paper Proposes a novel cervical cancer dual-stained image recognition (DSIR-YOLO) model based on an YOLOv5. By fusing the Swin-Transformer module, GAM attention mechanism, multi-scale feature fusion, and EIoU loss function, the detection performance is significantly improved, with mAP@0.5 and mAP@0.5:0.95 reaching 92.6% and 70.5%, respectively. Compared with YOLOv5s in five-fold cross-validation, the accuracy, recall, mAP@0.5, and mAP@0.5:0.95 of the improved algorithm are increased by 2.3%, 4.1%, 4.3%, and 8.0%, respectively, with smaller variances and higher stability. Compared with other detection algorithms, DSIR-YOLO in this paper sacrifices some performance requirements to improve the network recognition effect. In addition, the influence of dataset quality on the detection results is studied. By controlling the sealing property of pixels, scale difference, unlabelled cells, and diagonal annotation, the model detection accuracy, recall, mAP@0.5, and mAP@0.5:0.95 are improved by 13.3%, 15.3%, 18.3%, and 30.5%, respectively.

cs.AI↗

arXiv2024

MSSIDD: A Benchmark for Multi-Sensor Denoising

The cameras equipped on mobile terminals employ different sensors in different photograph modes, and the transferability of raw domain denoising models between these sensors is significant but remains sufficient exploration. Industrial solutions either develop distinct training strategies and models for different sensors or ignore the differences between sensors and simply extend existing models to new sensors, which leads to tedious training or unsatisfactory performance. In this paper, we introduce a new benchmark, the Multi-Sensor SIDD (MSSIDD) dataset, which is the first raw-domain dataset designed to evaluate the sensor transferability of denoising models. The MSSIDD dataset consists of 60,000 raw images of six distinct sensors, derived through the degeneration of sRGB images via different camera sensor parameters. Furthermore, we propose a sensor consistency training framework that enables denoising models to learn the sensor-invariant features, thereby facilitating the generalization of the consistent model to unseen sensors. We evaluate previous arts on the newly proposed MSSIDD dataset, and the experimental results validate the effectiveness of our proposed method. Our dataset is available at https://www.kaggle.com/datasets/sjtuwh/mssidd.

cs.CV↗

arXiv2024

Equivariant Poincaré-Hopf theorem

In this paper, we employ the framework of localization algebras to compute the equivariant K-homology class of the Euler characteristic operator, a central object in studying equivariant index theory on manifolds. This approach provides a powerful algebraic language for analyzing differential operators on equivariant structures and allows for the application of Witten deformation techniques in a K-homological context. Utilizing these results, we establish an equivariant version of the Poincaré-Hopf theorem, extending classical topological insights to the equivariant case, inspired by the results of Lück-Rosenberg. This work thus offers a new perspective on the localization techniques in the equivariant K-homology, highlighting their utility in deriving explicit formulas for index-theoretic invariants.

math.AT↗

arXiv2024

A geometric Elliott invariant and noncommutative rigidity of mapping tori

We prove a rigidity property for mapping tori associated to minimal topological dynamical systems using tools from noncommutative geometry. More precisely, we show that under mild geometric assumptions, an orientation-preserving leafwise homotopy equivalence of two mapping tori associated to $\mathbb{Z}^d$-actions on a compact space can be lifted to an isomorphism of their foliation $C^*$-algebras. This property is a noncommutative analogue of topological rigidity in the context of foliated spaces whose space of leaves is singular, where isomorphism type of the $C^*$-algebra replaces homeomorphism type. Our technique is to develop a geometric approach to the Elliott invariant that relies on topological and index-theoretic data from the mapping torus. We also discuss how our construction can be extended to slightly more general homotopy quotients arising from actions of discrete cocompact subgroups of simply connected solvable Lie groups, as well as how the theory can be applied to the magnetic gap-labelling problem for certain Cantor minimal systems.

math.OA↗

arXiv2024

CarDreamer: Open-Source Learning Platform for World Model based Autonomous Driving

To safely navigate intricate real-world scenarios, autonomous vehicles must be able to adapt to diverse road conditions and anticipate future events. World model (WM) based reinforcement learning (RL) has emerged as a promising approach by learning and predicting the complex dynamics of various environments. Nevertheless, to the best of our knowledge, there does not exist an accessible platform for training and testing such algorithms in sophisticated driving environments. To fill this void, we introduce CarDreamer, the first open-source learning platform designed specifically for developing WM based autonomous driving algorithms. It comprises three key components: 1) World model backbone: CarDreamer has integrated some state-of-the-art WMs, which simplifies the reproduction of RL algorithms. The backbone is decoupled from the rest and communicates using the standard Gym interface, so that users can easily integrate and test their own algorithms. 2) Built-in tasks: CarDreamer offers a comprehensive set of highly configurable driving tasks which are compatible with Gym interfaces and are equipped with empirically optimized reward functions. 3) Task development suite: This suite streamlines the creation of driving tasks, enabling easy definition of traffic flows and vehicle routes, along with automatic collection of multi-modal observation data. A visualization server allows users to trace real-time agent driving videos and performance metrics through a browser. Furthermore, we conduct extensive experiments using built-in tasks to evaluate the performance and potential of WMs in autonomous driving. Thanks to the richness and flexibility of CarDreamer, we also systematically study the impact of observation modality, observability, and sharing of vehicle intentions on AV safety and efficiency. All code and documents are accessible on https://github.com/ucd-dare/CarDreamer.

cs.RO↗

arXiv2024

Persistence approximation property for $L^p$ operator algebras

In this paper, we study the persistence approximation property for quantitative $K$-theory of filtered $L^p$ operator algebras. Moreover, we define quantitative assembly maps for $L^p$ operator algebras when $p\in [1,\infty)$. Finally, in the case of $L^{p}$ crossed products and $L^{p}$ Roe algebras, we find sufficient conditions for the persistence approximation property. This allows us to give some applications involving the $L^{p}$ (coarse) Baum-Connes conjecture.

math.OA↗

arXiv2024

Equivariant Spectral Flow and Equivariant $η$-invariants on Manifolds With Boundary

In this article, we study several closely related invariants associated to Dirac operators on odd-dimensional manifolds with boundary with an action of the compact group $H$ of isometries. In particular, the equality between equivariant winding numbers, equivariant spectral flow, and equivariant Maslov indices is established. We also study equivariant $η$-invariants which play a fundamental role in the equivariant analog of Getzler's spectral flow formula. As a consequence, we establish a relation between equivariant $η$-invariants and equivariant Maslov triple indices in the splitting of manifolds.

math.DG↗

arXiv2024

IVAC-P2L: Leveraging Irregular Repetition Priors for Improving Video Action Counting

Video Action Counting (VAC) is crucial in analyzing sports, fitness, and everyday activities by quantifying repetitive actions in videos. However, traditional VAC methods have overlooked the complexity of action repetitions, such as interruptions and the variability in cycle duration. Our research addresses the shortfall by introducing a novel approach to VAC, called Irregular Video Action Counting (IVAC). IVAC prioritizes modeling irregular repetition patterns in videos, which we define through two primary aspects: Inter-cycle Consistency and Cycle-interval Inconsistency. Inter-cycle Consistency ensures homogeneity in the spatial-temporal representations of cycle segments, signifying action uniformity within cycles. Cycle-interval inconsistency highlights the importance of distinguishing between cycle segments and intervals based on their inherent content differences. To encapsulate these principles, we propose a new methodology that includes consistency and inconsistency modules, supported by a unique pull-push loss (P2L) mechanism. The IVAC-P2L model applies a pull loss to promote coherence among cycle segment features and a push loss to clearly distinguish features of cycle segments from interval segments. Empirical evaluations conducted on the RepCount dataset demonstrate that the IVAC-P2L model sets a new benchmark in VAC task performance. Furthermore, the model demonstrates exceptional adaptability and generalization across various video contents, outperforming existing models on two additional datasets, UCFRep and Countix, without the need for dataset-specific optimization. These results confirm the efficacy of our approach in addressing irregular repetitions in videos and pave the way for further advancements in video analysis and understanding.

cs.CV↗

arXiv2024

Activating Wider Areas in Image Super-Resolution

The prevalence of convolution neural networks (CNNs) and vision transformers (ViTs) has markedly revolutionized the area of single-image super-resolution (SISR). To further boost the SR performances, several techniques, such as residual learning and attention mechanism, are introduced, which can be largely attributed to a wider range of activated area, that is, the input pixels that strongly influence the SR results. However, the possibility of further improving SR performance through another versatile vision backbone remains an unresolved challenge. To address this issue, in this paper, we unleash the representation potential of the modern state space model, i.e., Vision Mamba (Vim), in the context of SISR. Specifically, we present three recipes for better utilization of Vim-based models: 1) Integration into a MetaFormer-style block; 2) Pre-training on a larger and broader dataset; 3) Employing complementary attention mechanism, upon which we introduce the MMA. The resulting network MMA is capable of finding the most relevant and representative input pixels to reconstruct the corresponding high-resolution images. Comprehensive experimental analysis reveals that MMA not only achieves competitive or even superior performance compared to state-of-the-art SISR methods but also maintains relatively low memory and computational overheads (e.g., +0.5 dB PSNR elevation on Manga109 dataset with 19.8 M parameters at the scale of 2). Furthermore, MMA proves its versatility in lightweight SR applications. Through this work, we aim to illuminate the potential applications of state space models in the broader realm of image processing rather than SISR, encouraging further exploration in this innovative direction.

cs.CV↗

arXiv2024

Index theorem for homogenous spaces of Lie groups

We study index theory on homogeneous spaces associated to an almost connected Lie group in terms of the topological aspect and the analytic aspect. On the topological aspect, we obtain a topological formula as a result of the Riemann-Roch formula for proper cocompact actions of the Lie group, inspired by the work of Paradan and Vergne. On the analytic aspect, we apply heat kernel methods to obtain a local index formula representing the higher indices of equivariant elliptic operators with respect to a proper cocompact actions of the Lie group.

math.DG↗