arXiv subjects

Xingyu Zhu

Publications and source records attributed to Xingyu Zhu.

At least 73 records · Page 4Linked to original sources

arXiv2024

Positive Scalar Curvature Meets Ricci Limit Spaces

We investigate the influence of uniformly positive scalar curvature on the size of a non-collapsed Ricci limit space coming from a sequence of $n$-manifolds with non-negative Ricci curvature and uniformly positive scalar curvature. We prove that such a limit space splits at most $n-2$ lines or $\mathbb{R}$-factors. When this maximal splitting occurs, we obtain a uniform upper bound on the diameter of the non-splitting factor. Moreover, we obtain a volume gap estimate and a volume growth order estimate of geodesic balls on such manifolds.

math.DG↗

arXiv2024

Achieving Resolution-Agnostic DNN-based Image Watermarking: A Novel Perspective of Implicit Neural Representation

DNN-based watermarking methods are rapidly developing and delivering impressive performances. Recent advances achieve resolution-agnostic image watermarking by reducing the variant resolution watermarking problem to a fixed resolution watermarking problem. However, such a reduction process can potentially introduce artifacts and low robustness. To address this issue, we propose the first, to the best of our knowledge, Resolution-Agnostic Image WaterMarking (RAIMark) framework by watermarking the implicit neural representation (INR) of image. Unlike previous methods, our method does not rely on the previous reduction process by directly watermarking the continuous signal instead of image pixels, thus achieving resolution-agnostic watermarking. Precisely, given an arbitrary-resolution image, we fit an INR for the target image. As a continuous signal, such an INR can be sampled to obtain images with variant resolutions. Then, we quickly fine-tune the fitted INR to get a watermarked INR conditioned on a binary secret message. A pre-trained watermark decoder extracts the hidden message from any sampled images with arbitrary resolutions. By directly watermarking INR, we achieve resolution-agnostic watermarking with increased robustness. Extensive experiments show that our method outperforms previous methods with significant improvements: averagely improved bit accuracy by 7%$\sim$29%. Notably, we observe that previous methods are vulnerable to at least one watermarking attack (e.g. JPEG, crop, resize), while ours are robust against all watermarking attacks.

cs.CR↗

arXiv2024

Selective Vision-Language Subspace Projection for Few-shot CLIP

Vision-language models such as CLIP are capable of mapping the different modality data into a unified feature space, enabling zero/few-shot inference by measuring the similarity of given images and texts. However, most existing methods overlook modality gaps in CLIP's encoded features, which is shown as the text and image features lie far apart from each other, resulting in limited classification performance. To tackle this issue, we introduce a method called Selective Vision-Language Subspace Projection (SSP), which incorporates local image features and utilizes them as a bridge to enhance the alignment between image-text pairs. Specifically, our SSP framework comprises two parallel modules: a vision projector and a language projector. Both projectors utilize local image features to span the respective subspaces for image and texts, thereby projecting the image and text features into their respective subspaces to achieve alignment. Moreover, our approach entails only training-free matrix calculations and can be seamlessly integrated into advanced CLIP-based few-shot learning frameworks. Extensive experiments on 11 datasets have demonstrated SSP's superior text-image alignment capabilities, outperforming the state-of-the-art alignment methods. The code is available at https://github.com/zhuhsingyuu/SSP

cs.CV↗

arXiv2024

On the geometry at infinity of manifolds with linear volume growth and nonnegative Ricci curvature

We prove that an open manifold with nonnegative Ricci curvature, linear volume growth and noncollapsed ends always splits off a line at infinity. This completes the final step to prove the existence of isoperimetric sets given large volumes in the above setting. We also find that under our assumptions, the diameter of the level sets of any Busemann function are uniformly bounded as opposed to a classical result stating that they can have sublinear growth when ends are collapsing. Moreover, some equivalent characterizations of linear volume growth are given. Finally, we construct an example to show that for manifolds in our setting, although their limit spaces at infinity are always cylinders, the cross sections can be nonhomeomorphic.

math.DG↗

arXiv2024

Boosting Few-Shot Learning via Attentive Feature Regularization

Few-shot learning (FSL) based on manifold regularization aims to improve the recognition capacity of novel objects with limited training samples by mixing two samples from different categories with a blending factor. However, this mixing operation weakens the feature representation due to the linear interpolation and the overlooking of the importance of specific channels. To solve these issues, this paper proposes attentive feature regularization (AFR) which aims to improve the feature representativeness and discriminability. In our approach, we first calculate the relations between different categories of semantic labels to pick out the related features used for regularization. Then, we design two attention-based calculations at both the instance and channel levels. These calculations enable the regularization procedure to focus on two crucial aspects: the feature complementarity through adaptive interpolation in related categories and the emphasis on specific feature channels. Finally, we combine these regularization strategies to significantly improve the classifier performance. Empirical studies on several popular FSL benchmarks demonstrate the effectiveness of AFR, which improves the recognition accuracy of novel categories without the need to retrain any feature extractor, especially in the 1-shot setting. Furthermore, the proposed AFR can seamlessly integrate into other FSL methods to improve classification performance.

cs.CV↗

arXiv2024

Characterization of Turbulent Fluctuations in the Sub-Alfvenic Solar Wind

Parker Solar Probe (PSP) observed sub-Alfvenic solar wind intervals during encounters 8 - 14, and low-frequency magnetohydrodynamic turbulence in these regions may differ from that in super-Alfvenic wind. We apply a new mode-decomposition analysis (Zank et al 2023) to the sub-Alfvénic flow observed by PSP on 2021 April 28, identifying and characterizing entropy, magnetic islands, forward and backward Alfvén waves, including weakly/non-propagating Alfvén vortices, forward and backward fast and slow magnetosonic modes. Density fluctuations are primarily and almost equally entropy and backward propagating slow magnetosonic modes. The mode-decomposition provides phase information (frequency and wavenumber k) for each mode. Entropy-density fluctuations have a wavenumber anisotropy k_{||} >> k_{perp} whereas slow mode density fluctuations have k_{perp} > k_{||}. Magnetic field fluctuations are primarily magnetic island modes (delta B^i) with an O(1) smaller contribution from uni-directionally propagating Alfven waves (delta B^{A+}) giving a variance anisotropy of <{δB^i}^2> / = 4.1. Incompressible magnetic fluctuations dominate compressible contributions from fast and slow magnetosonic modes. The magnetic island spectrum is Kolmogorov-like k_{perp}^{-1.6} in perpendicular wavenumber and the uni-directional Alfven wave spectra are k_{||}^{-1.6} and k_{perp}^{-1.5}. Fast magnetosonic modes propagate at essentially the Alfvén speed with anti-correlated transverse velocity and magnetic field fluctuations and are almost exclusively magnetic due to beta_p<<1. Transverse velocity fluctuations are the dominant velocity component in fast magnetosonic modes and longitudinal fluctuations dominate in slow modes. Mode-decomposition is an effective tool in identifying the basic building blocks of MHD turbulence and provides detailed phase information about each of the modes.

astro-ph.SR↗

arXiv2023

Rethinking Mesh Watermark: Towards Highly Robust and Adaptable Deep 3D Mesh Watermarking

The goal of 3D mesh watermarking is to embed the message in 3D meshes that can withstand various attacks imperceptibly and reconstruct the message accurately from watermarked meshes. The watermarking algorithm is supposed to withstand multiple attacks, and the complexity should not grow significantly with the mesh size. Unfortunately, previous methods are less robust against attacks and lack of adaptability. In this paper, we propose a robust and adaptable deep 3D mesh watermarking Deep3DMark that leverages attention-based convolutions in watermarking tasks to embed binary messages in vertex distributions without texture assistance. Furthermore, our Deep3DMark exploits the property that simplified meshes inherit similar relations from the original ones, where the relation is the offset vector directed from one vertex to its neighbor. By doing so, our method can be trained on simplified meshes but remains effective on large size meshes (size adaptable) and unseen categories of meshes (geometry adaptable). Extensive experiments demonstrate our method remains efficient and effective even if the mesh size is 190x increased. Under mesh attacks, Deep3DMark achieves 10%~50% higher accuracy than traditional methods, and 2x higher SNR and 8% higher accuracy than previous DNN-based methods.

cs.CR↗

arXiv2023

A characterization of non-collapsed $RCD(K, N)$ spaces via Einstein tensors

We investigate the second principal term in the expansion of metrics $c(n)t^{(n+2)/2}g_t$ induced by heat kernel embedding into $L^2$ on a compact $RCD(K, N)$ space. We prove that the divergence free property of this term in the weak, asymptotic sense if and only if the space is non-collapsed up to multiplying a constant to the reference measure. This seems new even for weighted Riemannian manifolds. Moreover an example tells us that the result cannot be generalized to the noncompact case. In this sense, our result is sharp.

math.DG↗

arXiv2023

Regulation of Proton-$α$ Differential Flow by Compressive Fluctuations and Ion-scale Instabilities in the Solar Wind

Large-scale compressive slow-mode-like fluctuations can cause variations in the density, temperature, and magnetic-field magnitude in the solar wind. In addition, they also lead to fluctuations in the differential flow $U_{\rm pα}$ between $α$-particles and protons ($p$), which is a common source of free energy for the driving of ion-scale instabilities. If the amplitude of the compressive fluctuations is sufficiently large, the fluctuating $U_{\rm pα}$ intermittently drives the plasma across the instability threshold, leading to the excitation of ion-scale instabilities and thus the growth of corresponding ion-scale waves. The unstable waves scatter particles and reduce the average value of $U_{\rm pα}$. We propose that this "fluctuating-beam effect" maintains the average value of $U_{\rm pα}$ well below the marginal instability threshold. We model the large-scale compressive fluctuations in the solar wind as long-wavelength slow-mode waves using a multi-fluid model. We numerically quantify the fluctuating-beam effect for the Alfvén/ion-cyclotron (A/IC) and fast-magnetosonic/whistler (FM/W) instabilities. We show that measurements of the proton-$α$ differential flow and compressive fluctuations from the {\it Wind} spacecraft are consistent with our predictions for the fluctuating-beam effect. This effect creates a new channel for a direct cross-scale energy transfer from large-scale compressions to ion-scale fluctuations.

physics.space-ph↗

arXiv2023

Clothes Grasping and Unfolding Based on RGB-D Semantic Segmentation

Clothes grasping and unfolding is a core step in robotic-assisted dressing. Most existing works leverage depth images of clothes to train a deep learning-based model to recognize suitable grasping points. These methods often utilize physics engines to synthesize depth images to reduce the cost of real labeled data collection. However, the natural domain gap between synthetic and real images often leads to poor performance of these methods on real data. Furthermore, these approaches often struggle in scenarios where grasping points are occluded by the clothing item itself. To address the above challenges, we propose a novel Bi-directional Fractal Cross Fusion Network (BiFCNet) for semantic segmentation, enabling recognition of graspable regions in order to provide more possibilities for grasping. Instead of using depth images only, we also utilize RGB images with rich color features as input to our network in which the Fractal Cross Fusion (FCF) module fuses RGB and depth data by considering global complex features based on fractal geometry. To reduce the cost of real data collection, we further propose a data augmentation method based on an adversarial strategy, in which the color and geometric transformations simultaneously process RGB and depth data while maintaining the label correspondence. Finally, we present a pipeline for clothes grasping and unfolding from the perspective of semantic segmentation, through the addition of a strategy for grasp point selection from segmentation regions based on clothing flatness measures, while taking into account the grasping direction. We evaluate our BiFCNet on the public dataset NYUDv2 and obtained comparable performance to current state-of-the-art models. We also deploy our model on a Baxter robot, running extensive grasping and unfolding experiments as part of our ablation studies, achieving an 84% success rate.

cs.CV↗

arXiv2023

Optimal diameter estimates of three-dimensional Ricci limit spaces

In this note, we prove that positive scalar curvature can pass to three dimensional Ricci limit spaces of non-negative Ricci curvature when it splits off a line. As a corollary, we obtain an optimal Bonnet-Myers type upper bound. Moreover, we obtain a similar statement in all dimensions for Alexandrov spaces of non-negative curvature.

math.DG↗

arXiv2023

Understanding Edge-of-Stability Training Dynamics with a Minimalist Example

Recently, researchers observed that gradient descent for deep neural networks operates in an ``edge-of-stability'' (EoS) regime: the sharpness (maximum eigenvalue of the Hessian) is often larger than stability threshold $2/η$ (where $η$ is the step size). Despite this, the loss oscillates and converges in the long run, and the sharpness at the end is just slightly below $2/η$. While many other well-understood nonconvex objectives such as matrix factorization or two-layer networks can also converge despite large sharpness, there is often a larger gap between sharpness of the endpoint and $2/η$. In this paper, we study EoS phenomenon by constructing a simple function that has the same behavior. We give rigorous analysis for its training dynamics in a large local region and explain why the final converging point has sharpness close to $2/η$. Globally we observe that the training dynamics for our example has an interesting bifurcating behavior, which was also observed in the training of neural nets.

cs.LG↗

arXiv2023

Fairness in the Assignment Problem with Uncertain Priorities

In the assignment problem, a set of items must be allocated to unit-demand agents who express ordinal preferences (rankings) over the items. In the assignment problem with priorities, agents with higher priority are entitled to their preferred goods with respect to lower priority agents. A priority can be naturally represented as a ranking and an uncertain priority as a distribution over rankings. For example, this models the problem of assigning student applicants to university seats or job applicants to job openings when the admitting body is uncertain about the true priority over applicants. This uncertainty can express the possibility of bias in the generation of the priority ranking. We believe we are the first to explicitly formulate and study the assignment problem with uncertain priorities. We introduce two natural notions of fairness in this problem: stochastic envy-freeness (SEF) and likelihood envy-freeness (LEF). We show that SEF and LEF are incompatible and that LEF is incompatible with ordinal efficiency. We describe two algorithms, Cycle Elimination (CE) and Unit-Time Eating (UTE) that satisfy ordinal efficiency (a form of ex-ante Pareto optimality) and SEF; the well known random serial dictatorship algorithm satisfies LEF and the weaker efficiency guarantee of ex-post Pareto optimality. We also show that CE satisfies a relaxation of LEF that we term 1-LEF which applies only to certain comparisons of priority, while UTE satisfies a version of proportional allocations with ranks. We conclude by demonstrating how a mediator can model a problem of school admission in the face of bias as an assignment problem with uncertain priority.

cs.GT↗

arXiv2022

Dissecting Hessian: Understanding Common Structure of Hessian in Neural Networks

Hessian captures important properties of the deep neural network loss landscape. Previous works have observed low rank structure in the Hessians of neural networks. In this paper, we propose a decoupling conjecture that decomposes the layer-wise Hessians of a network as the Kronecker product of two smaller matrices. We can analyze the properties of these smaller matrices and prove the structure of top eigenspace random 2-layer networks. The decoupling conjecture has several other interesting implications - top eigenspaces for different models have surprisingly high overlap, and top eigenvectors form low rank matrices when they are reshaped into the same shape as the corresponding weight matrix. All of these can be verified empirically for deeper networks. Finally, we use the structure of layer-wise Hessian to get better explicit generalization bounds for neural networks.

cs.LG↗

arXiv2022

On the intrinsic and extrinsic boundary for metric measure spaces with lower curvature bounds

We show that if an Alexandrov space $X$ has an Alexandrov subspace $\bar Ω$ of the same dimension disjoint from the boundary of $X$, then the topological boundary of $\bar Ω$ coincides with its Alexandrov boundary. Similarly, if a noncollapsed RCD(K,N) space $X$ has a noncollapsed RCD(K,N) subspace $\bar Ω$ disjoint from boundary of $X$ and with mild boundary condition, then the topological boundary of $\bar Ω$ coincides with its De Philippis-Gigli boundary. We then discuss some consequences about convexity of such type of equivalence.

math.MG↗

arXiv2022

Weakly non-collapsed RCD spaces are strongly non-collapsed

We prove that any weakly non-collapsed RCD space is actually non-collapsed, up to a renormalization of the measure. This confirms a conjecture raised by De Philippis and the second named author in full generality. One of the auxiliary results of independent interest that we obtain is about the link between the properties $\quad$- $\mathrm{tr}(\mathrm{Hess}f)=Δf$ on $U\subset\mathsf{X}$ for every $f$ sufficiently regular, $\quad$- $\mathfrak{m}=c\mathscr{H}^n$ on $U\subset\mathsf{X}$ for some $c>0$, where $U\subset \mathsf{X}$ is open and $\mathsf{X}$ is a - possibly collapsed - RCD space of essential dimension $n$.

math.DG↗

arXiv2022

Coherence of ion cyclotron resonance for damping ion cyclotron waves in space plasmas

Ion cyclotron resonance is one of the fundamental energy conversion processes through field-particle interaction in collisionless plasmas. However, the key evidence for ion cyclotron resonance (i.e., the coherence between electromagnetic fields and the ion phase space density) and the resulting damping of ion cyclotron waves (ICWs) has not yet been directly observed. Investigating the high-quality measurements of space plasmas by the Magnetospheric Multiscale (MMS) satellites, we find that both the wave electromagnetic field vectors and the bulk velocity of the disturbed ion velocity distribution rotate around the background magnetic field. Moreover, we find that the absolute gyro-phase angle difference between the center of the fluctuations in the ion velocity distribution functions and the wave electric field vectors falls in the range of (0, 90) degrees, consistent with the ongoing energy conversion from wave-fields to particles. By invoking plasma kinetic theory, we demonstrate that the field-particle correlation for the damping ion cyclotron waves in our theoretical model matches well with our observations. Furthermore, the wave electric field vectors ($δ\mathbf{E'}_{\mathrm {wave,\perp}}$), the ion current density ($δ\mathbf{J}_\mathrm {i,\perp}$) and the energy transfer rate ($δ\mathbf{J}_\mathrm {i,\perp}\cdot δ\mathbf{E'}_{\mathrm {wave,\perp}}$) exhibit quasi-periodic oscillations, and the integrated work done by the electromagnetic field on the ions are positive, indicates that ions are mainly energized by the perpendicular component of the electric field via cyclotron resonance. Therefore, our combined analysis of MMS observations and kinetic theory provides direct, thorough, and comprehensive evidence for ICW damping in space plasmas.

physics.plasm-ph↗

arXiv2021

Observations of rapidly growing whistler waves in front of space plasma shock

Whistler mode wave is a fundamental perturbation of electromagnetic fields and plasmas in various environments including planetary space, laboratory and astrophysics. The origin and evolution of the waves are a long-standing question due to the limited instrumental capability in resolving highly variable plasma and electromagnetic fields. Here, we analyse data with the high time resolution from the multi-scale magnetospheric spacecraft in the weak magnetic environment (i.e., foreshock) enabling a relatively long gyro-period of whistler mode wave. Moreover, we develop a novel approach to separate the three-dimensional fluctuating electron velocity distributions from their background, and have successfully captured the coherent resonance between electrons and electromagnetic fields at high frequency, providing the resultant growth rate of unstable whistler waves. Regarding the energy origin for the waves, the ion distributions are found to also play crucial roles in determining the eigenmode disturbances of fields and electrons. The quantification of wave growth rate can significantly advance the understandings of the wave evolution and the energy conversion with particles.

physics.space-ph↗