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Zipeng Wang

Publications and source records attributed to Zipeng Wang.

At least 55 records · Page 3Linked to original sources
arXiv2025

Quantifying the Capability Boundary of DeepSeek Models: An Application-Driven Performance Analysis

DeepSeek-R1, known for its low training cost and exceptional reasoning capabilities, has achieved state-of-the-art performance on various benchmarks. However, detailed evaluations for DeepSeek Series models from the perspective of real-world applications are lacking, making it challenging for users to select the most suitable DeepSeek models for their specific needs. To address this gap, we presents the first comprehensive evaluation of the DeepSeek and its related models (including DeepSeek-V3, DeepSeek-R1, DeepSeek-R1-Distill-Qwen series, DeepSeek-R1-Distill-Llama series, their corresponding 4-bit quantized models, and the reasoning model QwQ-32B) using our enhanced A-Eval benchmark, A-Eval-2.0. Our systematic analysis reveals several key insights: (1) Given identical model architectures and training data, larger parameter models demonstrate superior performance, aligning with the scaling law. However, smaller models may achieve enhanced capabilities when employing optimized training strategies and higher-quality data; (2) Reasoning-enhanced model show significant performance gains in logical reasoning tasks but may underperform in text understanding and generation tasks; (3) As the data difficulty increases, distillation or reasoning enhancements yield higher performance gains for the models. Interestingly, reasoning enhancements can even have a negative impact on simpler problems; (4) Quantization impacts different capabilities unevenly, with significant drop on logical reasoning and minimal impact on text generation. Based on these results and findings, we design an model selection handbook enabling users to select the most cost-effective models without efforts.

cs.AI↗
arXiv2025

Da Lio-Rivière-Wettstein-type inequality for weighted Bergman spaces

In this paper, inspired by the work of Da Lio-Rivière-Wettstein, we investigate the boundary-value characterizations of weighted Bergman spaces and establish a weighted Da Lio-Rivière-Wettstein inequality. In addition, we obtain analogous results on the upper plane which does not seem to be a direct consequence of the ones on the unit disk.

math.CV↗
arXiv2025

The one-weight inequality for $\mathcal{H}$-harmonic Bergman projection

Let $n\geqslant 3$ be an integer. For the Bekollé-Bonami weight $ω$ on the real unit ball $\mathbb{B}_n$, we obtain the following sharp one-weight estimate for the $\mathcal{H}$-harmonic Bergman projection: for $1<p<\infty$ and $-1<α<\infty$, \[||P_α||_{ L^p(ωdν_α)\longrightarrow L^p(ωdν_α)}\leqslant C [ω]_{p,α}^{\max\left\{1,\frac{1}{p-1}\right\}}, \] where $[ω]_{p,α}$ is the Bekollé-Bonami constant. Our proof is inspired by the dyadic harmonic analysis, and the key ingredient involves the discretization of the Bergman kernel for the $\mathcal{H}$-harmonic Bergman spaces.

math.FA↗
arXiv2025

Fractional integrals associated with Zygmund dilations

We study a family of fractional integral operators defined in $\mathbb{R}^3$ whose kernels are distributions associated with Zygmund dilations: $(x_1, x_2, x_3) \rightarrow (δ_1 x_1, δ_2 x_2, δ_1δ_2 x_3)$ for $δ_1,δ_2>0$ having singularity on every coordinate subspace. As a result, we obtain a Hardy-Littlewood-Sobolev type inequality.

math.CA↗
arXiv2025

Three-body scattering hypervolume of two-component fermions in three dimensions

We study the zero-energy collision of three fermions, two of which are in the spin-down ($\downarrow$) state and one of which is in the spin-up ($\uparrow$) state. Assuming that the two-body and the three-body interactions have a finite range, we find a parameter, $D$, called the three-body scattering hypervolume. We study the three-body wave function asymptotically when three fermions are far apart or one spin-$\uparrow$ (spin-$\downarrow$) fermion and one pair, formed by the other two fermions, are far apart, and derive three asymptotic expansions of the wave function. The three-body scattering hypervolume $D$ appears in the coefficients of such expansions at the order of $B^{-5}$, where $B=\sqrt{(s_1^2+s_2^2+s_3^2)/2}$ is the hyperradius of the triangle formed by the three fermions (we assume that the three fermions have the same mass), and $s_1,s_2,s_3$ are the sides of the triangle. We compute the $T$-matrix element for three such fermions colliding at low energy in terms of $D$ in the absence of two-body interactions. When the interactions are weak, we calculate $D$ approximately using the Born expansion. We also analyze the energy shift of three two-component fermions in a large periodic cube due to $D$ and generalize this result to the many-fermion system. $D$ also determines the three-body recombination rates in two-component Fermi gases, and we calculate the three-body recombination rates in terms of $D$ and the density and temperature of the gas.

cond-mat.quant-gas↗
arXiv2025

A family of convolution operators, part two

We study a family of convolution operators. Their regarding Fourier multipliers are defined in terms of distributions having singularity on the light-cone in $\mathbb{R}^{n+1}$. As a result, we give a new approach to the Bochner-Riesz summability.

math.CA↗
arXiv2024

ViMoE: An Empirical Study of Designing Vision Mixture-of-Experts

Mixture-of-Experts (MoE) models embody the divide-and-conquer concept and are a promising approach for increasing model capacity, demonstrating excellent scalability across multiple domains. In this paper, we integrate the MoE structure into the classic Vision Transformer (ViT), naming it ViMoE, and explore the potential of applying MoE to vision through a comprehensive study on image classification and semantic segmentation. However, we observe that the performance is sensitive to the configuration of MoE layers, making it challenging to obtain optimal results without careful design. The underlying cause is that inappropriate MoE layers lead to unreliable routing and hinder experts from effectively acquiring helpful information. To address this, we introduce a shared expert to learn and capture common knowledge, serving as an effective way to construct stable ViMoE. Furthermore, we demonstrate how to analyze expert routing behavior, revealing which MoE layers are capable of specializing in handling specific information and which are not. This provides guidance for retaining the critical layers while removing redundancies, thereby advancing ViMoE to be more efficient without sacrificing accuracy. We aspire for this work to offer new insights into the design of vision MoE models and provide valuable empirical guidance for future research.

cs.CV↗
arXiv2024

Gravitational Magnus effect from scalar dark matter

In fluid dynamics, the Magnus effect is the force perpendicular to the motion of a spinning object as it moves through a medium. In general relativity, an analogous effect exists for a spinning compact object moving through matter, purely as a result of gravitational interactions. In this work we consider a Kerr black hole moving at relativistic velocities through scalar dark matter that is at rest. We simulate the system numerically and extract the total spin-curvature force on the black hole perpendicular to its motion. We confirm that the force scales linearly with the dimensionless spin parameter $a/M$ of the black hole up to $a/M = 0.99$, and measure its dependence on the speed $v$ of the black hole in the range $0.1 \le v \le 0.55$ for a fixed spin. Compared to previous analytic work applicable at small $v$, higher-order corrections in the velocity are found to be important: the total force is nonzero, and the dependence is not linear in $v$. We find that in all cases the total force is in the opposite direction to the hydrodynamical analogue, although at low speeds it appears to approach the expectation that the Weyl and Magnus components cancel. Spin-curvature effects may leave an imprint on gravitational wave signals from extreme mass-ratio inspirals, where the secondary black hole has a nonnegligible spin and moves in the presence of a dark matter cloud. We hope that our simulations can be used to support and extend the limits of analytic results, which are necessary to better quantify such effects in the relativistic regime.

gr-qc↗
arXiv2024

Modeling, Design, and Verification of An Active Transmissive RIS

Reconfigurable Intelligent Surface (RIS) is a promising technology that may effectively improve the quality of signals in wireless communications. In practice, however, the ``double fading'' effect undermines the application of RIS and constitutes a significant challenge to its commercialization. To address this problem, we present a novel 2-bit programmable amplifying transmissive RIS with a power amplification function to enhance the transmission of electromagnetic signals. The transmissive function is achieved through a pair of radiation patches located on the upper and lower surfaces, respectively, while a microstrip line connects two patches. A power amplifier, SP4T switch, and directional coupler provide signal amplification and a 2-bit phase shift. To characterize the signal enhancement of active transmissive RIS, we propose a dual radar cross section (RCS)-based path loss model to predict the power of the received signal for active transmissive RIS-aided wireless communication systems. Simulation and experimental results verify the reliability of the RIS design, and the proposed path loss model is validated by measurements. Compared with the traditional passive RIS, the signal power gain in this design achieves 11.9 dB.

eess.SP↗
arXiv2024

Regularity of Fourier integrals on product spaces

We study a family of Fourier integral operators by allowing their symbols to satisfy a multi-parameter differential inequality on R^N. We show that these operators of order -(N-1)/2 are bounded from classical, atom decomposable H^1-Hardy space to L^1(R^N). Consequently, we obtain a sharp L^p-regularity result due to Seeger, Sogge and Stein.

math.CA↗
arXiv2024

Boundedness of New Type Fourier Integral Operators with Product Structure

We investigate a class of Fourier integral operators with weakened symbols, which satisfy a multi-parameter differential inequality in $\R^n$. We establish that these operators retain the classical $L^p$ boundedness and the $H^1$ to $L^1$ boundedness. Notably, the Hardy space considered here is the traditional single-parameter Hardy space rather than a product Hardy space.

math.FA↗
arXiv2024

Revisit Event Generation Model: Self-Supervised Learning of Event-to-Video Reconstruction with Implicit Neural Representations

Reconstructing intensity frames from event data while maintaining high temporal resolution and dynamic range is crucial for bridging the gap between event-based and frame-based computer vision. Previous approaches have depended on supervised learning on synthetic data, which lacks interpretability and risk over-fitting to the setting of the event simulator. Recently, self-supervised learning (SSL) based methods, which primarily utilize per-frame optical flow to estimate intensity via photometric constancy, has been actively investigated. However, they are vulnerable to errors in the case of inaccurate optical flow. This paper proposes a novel SSL event-to-video reconstruction approach, dubbed EvINR, which eliminates the need for labeled data or optical flow estimation. Our core idea is to reconstruct intensity frames by directly addressing the event generation model, essentially a partial differential equation (PDE) that describes how events are generated based on the time-varying brightness signals. Specifically, we utilize an implicit neural representation (INR), which takes in spatiotemporal coordinate $(x, y, t)$ and predicts intensity values, to represent the solution of the event generation equation. The INR, parameterized as a fully-connected Multi-layer Perceptron (MLP), can be optimized with its temporal derivatives supervised by events. To make EvINR feasible for online requisites, we propose several acceleration techniques that substantially expedite the training process. Comprehensive experiments demonstrate that our EvINR surpasses previous SSL methods by 38% w.r.t. Mean Squared Error (MSE) and is comparable or superior to SoTA supervised methods. Project page: https://vlislab22.github.io/EvINR/.

cs.CV↗
arXiv2024

Self-absorption of Hankel systems on monoids --a seemingly universal property

Given any cancellative monoid $\mathcal{M}$, we study the Hankel system determined by its multiplication table. We prove that the Hankel system admits self-absorption property provided that the monoid $\mathcal{M}$ has the local algebraic structure: \[ \big(ax = by, cx=dy, az=bw \,\, \text{in $\mathcal{M}$}\big)\Longrightarrow \big(cz=dw \,\, \text{in $\mathcal{M}$}\big). \] Our result holds for all group-embeddable monoids and goes beyond. In particular, it works for all cancellative Abelian monoids and most common non-Abelian cancellative monoids such as $$ \mathrm{SL}_d(\mathbb{N}): = \big\{[a_{ij}]_{1\le i,j\le d}\in \mathrm{SL}_d(\mathbb{Z})\big| a_{ij} \in \mathbb{N}\big\}. $$ The Hankel system determined by the multiplication table of a monoid is further generalized to that determined by level sets of any abstract two-variable map. We introduce an algebraic notion of lunar maps and establish a stronger hereditary self-absorption property for the corresponding generalized Hankel systems. As a consequence, we prove the self-absorption property for arbitrary spatial compression of the regular representation system $\{λ_G(g)\}_{g\in G}$ of any discrete group $G$, as well as the Hankel system $\{Γ_\ell^Φ\}$ determined by the level sets of any rational map of the form $Φ(x,y)=a x^m + b y^n$ with $a,b,m,n\in \mathbb{Z}^*$: \[ Γ_\ell^Φ(x, y)= \mathbf{1}(a x^m + b y^n= \ell), \quad x, y\in \mathbb{N}^*, \, \ell\in Φ(\mathbb{N}^*\times \mathbb{N}^*). \] The self-absorption property is applied to the study of completely bounded Fourier multipliers between Hardy spaces. Further applications are: i) exact complete bounded norm of the Carleman embedding in any dimension; ii) mixed Fourier-Schur multiplier inequalities with critical exponent $4/3$; iii) failure of hyper-complete-contractivity for the Poisson semigroup.

math.FA↗
arXiv2024

PyGS: Large-scale Scene Representation with Pyramidal 3D Gaussian Splatting

Neural Radiance Fields (NeRFs) have demonstrated remarkable proficiency in synthesizing photorealistic images of large-scale scenes. However, they are often plagued by a loss of fine details and long rendering durations. 3D Gaussian Splatting has recently been introduced as a potent alternative, achieving both high-fidelity visual results and accelerated rendering performance. Nonetheless, scaling 3D Gaussian Splatting is fraught with challenges. Specifically, large-scale scenes grapples with the integration of objects across multiple scales and disparate viewpoints, which often leads to compromised efficacy as the Gaussians need to balance between detail levels. Furthermore, the generation of initialization points via COLMAP from large-scale dataset is both computationally demanding and prone to incomplete reconstructions. To address these challenges, we present Pyramidal 3D Gaussian Splatting (PyGS) with NeRF Initialization. Our approach represent the scene with a hierarchical assembly of Gaussians arranged in a pyramidal fashion. The top level of the pyramid is composed of a few large Gaussians, while each subsequent layer accommodates a denser collection of smaller Gaussians. We effectively initialize these pyramidal Gaussians through sampling a rapidly trained grid-based NeRF at various frequencies. We group these pyramidal Gaussians into clusters and use a compact weighting network to dynamically determine the influence of each pyramid level of each cluster considering camera viewpoint during rendering. Our method achieves a significant performance leap across multiple large-scale datasets and attains a rendering time that is over 400 times faster than current state-of-the-art approaches.

cs.CV↗
arXiv2024

Co-Occ: Coupling Explicit Feature Fusion with Volume Rendering Regularization for Multi-Modal 3D Semantic Occupancy Prediction

3D semantic occupancy prediction is a pivotal task in the field of autonomous driving. Recent approaches have made great advances in 3D semantic occupancy predictions on a single modality. However, multi-modal semantic occupancy prediction approaches have encountered difficulties in dealing with the modality heterogeneity, modality misalignment, and insufficient modality interactions that arise during the fusion of different modalities data, which may result in the loss of important geometric and semantic information. This letter presents a novel multi-modal, i.e., LiDAR-camera 3D semantic occupancy prediction framework, dubbed Co-Occ, which couples explicit LiDAR-camera feature fusion with implicit volume rendering regularization. The key insight is that volume rendering in the feature space can proficiently bridge the gap between 3D LiDAR sweeps and 2D images while serving as a physical regularization to enhance LiDAR-camera fused volumetric representation. Specifically, we first propose a Geometric- and Semantic-aware Fusion (GSFusion) module to explicitly enhance LiDAR features by incorporating neighboring camera features through a K-nearest neighbors (KNN) search. Then, we employ volume rendering to project the fused feature back to the image planes for reconstructing color and depth maps. These maps are then supervised by input images from the camera and depth estimations derived from LiDAR, respectively. Extensive experiments on the popular nuScenes and SemanticKITTI benchmarks verify the effectiveness of our Co-Occ for 3D semantic occupancy prediction. The project page is available at https://rorisis.github.io/Co-Occ_project-page/.

cs.CV↗
arXiv2024

Singular Integrals associated with Reflection Groups on Euclidean Space

In the field of harmonic analysis, geometric considerations are frequently crucial. Specially, group actions such as translations, dilations and rotations on Euclidean space are instrumental. The objective of this paper is to extend the study of singular integrals to include the effects of group reflections on Euclidean space, and to establish the T1 theorem for these singular integrals.

math.CA↗
arXiv2024

P2Seg: Pointly-supervised Segmentation via Mutual Distillation

Point-level Supervised Instance Segmentation (PSIS) aims to enhance the applicability and scalability of instance segmentation by utilizing low-cost yet instance-informative annotations. Existing PSIS methods usually rely on positional information to distinguish objects, but predicting precise boundaries remains challenging due to the lack of contour annotations. Nevertheless, weakly supervised semantic segmentation methods are proficient in utilizing intra-class feature consistency to capture the boundary contours of the same semantic regions. In this paper, we design a Mutual Distillation Module (MDM) to leverage the complementary strengths of both instance position and semantic information and achieve accurate instance-level object perception. The MDM consists of Semantic to Instance (S2I) and Instance to Semantic (I2S). S2I is guided by the precise boundaries of semantic regions to learn the association between annotated points and instance contours. I2S leverages discriminative relationships between instances to facilitate the differentiation of various objects within the semantic map. Extensive experiments substantiate the efficacy of MDM in fostering the synergy between instance and semantic information, consequently improving the quality of instance-level object representations. Our method achieves 55.7 mAP$_{50}$ and 17.6 mAP on the PASCAL VOC and MS COCO datasets, significantly outperforming recent PSIS methods and several box-supervised instance segmentation competitors.

cs.CV↗