Searcharxiv⌕ Search

arXiv subjects

Zipeng Wang

Publications and source records attributed to Zipeng Wang.

At least 37 records · Page 2Linked to original sources
arXiv2026

HeroGS: Hierarchical Guidance for Robust 3D Gaussian Splatting under Sparse Views

3D Gaussian Splatting (3DGS) has recently emerged as a promising approach in novel view synthesis, combining photorealistic rendering with real-time efficiency. However, its success heavily relies on dense camera coverage; under sparse-view conditions, insufficient supervision leads to irregular Gaussian distributions, characterized by globally sparse coverage, blurred background, and distorted high-frequency areas. To address this, we propose HeroGS, Hierarchical Guidance for Robust 3D Gaussian Splatting, a unified framework that establishes hierarchical guidance across the image, feature, and parameter levels. At the image level, sparse supervision is converted into pseudo-dense guidance, globally regularizing the Gaussian distributions and forming a consistent foundation for subsequent optimization. Building upon this, Feature-Adaptive Densification and Pruning (FADP) at the feature level leverages low-level features to refine high-frequency details and adaptively densifies Gaussians in background regions. The optimized distributions then support Co-Pruned Geometry Consistency (CPG) at parameter level, which guides geometric consistency through parameter freezing and co-pruning, effectively removing inconsistent splats. The hierarchical guidance strategy effectively constrains and optimizes the overall Gaussian distributions, thereby enhancing both structural fidelity and rendering quality. Extensive experiments demonstrate that HeroGS achieves high-fidelity reconstructions and consistently surpasses state-of-the-art baselines under sparse-view conditions.

cs.CV↗
arXiv2026

The optimal hypercontractive constants for $\mathbb{Z}_3$ and biased Bernoulli random variables

We resolve a folklore problem of determining the optimal hypercontractive constants $r_{p,q}(\mathbb{Z}_3)$ for the cyclic group $\mathbb{Z}_3$ for all $1 < p < q < \infty$. More precisely, we have \[ r_{p,q}(\mathbb{Z}_3) = \frac{(1 + 2x)(1 - y)}{(1 + 2y)(1 - x)}, \] where $(x,y)$ is the unique solution in the open unit square $(0,1)\times (0,1)$ to the system of equations \begin{align*} \left\{ \begin{aligned} &\frac{1}{1+2x}\Big(\frac{1+2x^p}{3}\Big)^{\frac{1}{p}}=\frac{1}{1+2y}\Big(\frac{1+2y^q}{3}\Big)^{\frac{1}{q}},\\ &\frac{(1-x)(1-x^{p-1})}{1+2x^p}=\frac{(1-y)(1-y^{q-1})}{1+2y^q}. \end{aligned} \right. \end{align*} Consequently, for rational $p, q\in \mathbb{Q}$, the constants $r_{p,q}(\mathbb{Z}_3)$ are algebraic numbers which generally admit no radical expressions, since their often rather complicated minimal polynomials may have non-solvable Galois groups. Our formalism relies on a key observation: the existence of nontrivial critical extremizers. This approach can also be adapted to resolve a long-standing open problem -- determining all optimal $(p,q)$-hypercontractive constants for biased Bernoulli random variables, which are closely related to noise operators. Several noteworthy phenomena emerge from numerical simulations: the monotonicity of the hypercontractive constants in the parameters, and the appearance of intriguing limit shapes. These phenomena merit further investigation.

math.FA↗
arXiv2026

$L^p$--$L^q$ estimates for Shimorin-type integral operators

Let $ν$ be a positive measure on $[0,1]$. A Shimorin-type operator $T_ν$ is an integral operator on the unit disk given by \[ T_νf(z) = \int_{\mathbb{D}} \frac{1}{1 - z\overlineλ} \left( \int_0^1 \frac{dν(r)}{1 - r z \overlineλ} \right) f(λ) \, dA(λ), \] which originates from Shimorin's work on Bergman-type kernel representations for logarithmically subharmonic weighted Bergman spaces. In this paper, we study $L^p$--$L^q$ estimates for $T_ν$. Unlike classical Bergman-type operators, the critical line on the $(1/p,1/q)$-plane that separates the boundedness and unboundedness regions of $T_ν$ is not immediately evident. Moreover, even along this line, new phenomena arise. In the present work, by introducing a quantity $c_ν$, \begin{itemize} \item we first determine the critical boundary in the $(1/p,1/q)$-plane for bounded $T_ν$; \item furthermore, on this critical line, we establish necessary and sufficient conditions for $T_ν$ which have standard Bergman-type $L^p$--$L^q$ estimates, meaning that it is bounded in the interior of the region and admits weak-type and BMO-type estimates at endpoints. \end{itemize}

math.CV↗
arXiv2025

Fractional integration with singularity on the light-cone

We study a family of convolution operators whose symbols and kernels have singularity on the light-cone in $\mathbb{R}^{n+1}$. First, we prove a desired ${\bf L}^p\to {\bf L}^q$ norm inequality which has been left open. Moreover, we obtain certain sharp regularity results for the cone multiplier problem of negative order.

math.CA↗
arXiv2025

A multi-parameter family of Fourier integral operators

We study a new class of Fourier integral operators defined in R^N. Their symbols are allowed to satisfy a differential inequality with certain multi-parameter characteristic. We prove these operators of order -(N-1)/2 bounded from the classical, atom decomposable H^1-Hardy space to L^1(R^N). As a result, we obtain a sharp L^p-estimate. Simultaneously, a generalized Sobolev Lp-space is introduced. We establish the Sobolev Lp-norm inequality for convolutions with a distribution having singularity on the unit sphere. As an application, we give a new a priori estimate for the solution of wave equations by requiring less regularity on the source term and initial data.

math.CA↗
arXiv2025

Stein-Weiss inequality revisit on Heisenberg group

We study a family of fractional integral operators defined on Heisenberg group whose kernels satisfy Zygmund dilation. We give a characterization between a two-weight norm inequality and the necessary constraints by considering the weights to be suitable powers. As a result, we obtain a Stein-Weiss inequality on Heisenberg group.

math.CA↗
arXiv2025

PSTF-AttControl: Per-Subject-Tuning-Free Personalized Image Generation with Controllable Face Attributes

Recent advancements in personalized image generation have significantly improved facial identity preservation, particularly in fields such as entertainment and social media. However, existing methods still struggle to achieve precise control over facial attributes in a per-subject-tuning-free (PSTF) way. Tuning-based techniques like PreciseControl have shown promise by providing fine-grained control over facial features, but they often require extensive technical expertise and additional training data, limiting their accessibility. In contrast, PSTF approaches simplify the process by enabling image generation from a single facial input, but they lack precise control over facial attributes. In this paper, we introduce a novel, PSTF method that enables both precise control over facial attributes and high-fidelity preservation of facial identity. Our approach utilizes a face recognition model to extract facial identity features, which are then mapped into the $W^+$ latent space of StyleGAN2 using the e4e encoder. We further enhance the model with a Triplet-Decoupled Cross-Attention module, which integrates facial identity, attribute features, and text embeddings into the UNet architecture, ensuring clean separation of identity and attribute information. Trained on the FFHQ dataset, our method allows for the generation of personalized images with fine-grained control over facial attributes, while without requiring additional fine-tuning or training data for individual identities. We demonstrate that our approach successfully balances personalization with precise facial attribute control, offering a more efficient and user-friendly solution for high-quality, adaptable facial image synthesis. The code is publicly available at https://github.com/UnicomAI/PSTF-AttControl.

cs.CV↗
arXiv2025

HR-INR: Continuous Space-Time Video Super-Resolution via Event Camera

Continuous space-time video super-resolution (C-STVSR) aims to simultaneously enhance video resolution and frame rate at an arbitrary scale. Recently, implicit neural representation (INR) has been applied to video restoration, representing videos as implicit fields that can be decoded at an arbitrary scale. However, existing INR-based C-STVSR methods typically rely on only two frames as input, leading to insufficient inter-frame motion information. Consequently, they struggle to capture fast, complex motion and long-term dependencies (spanning more than three frames), hindering their performance in dynamic scenes. In this paper, we propose a novel C-STVSR framework, named HR-INR, which captures both holistic dependencies and regional motions based on INR. It is assisted by an event camera -- a novel sensor renowned for its high temporal resolution and low latency. To fully utilize the rich temporal information from events, we design a feature extraction consisting of (1) a regional event feature extractor -- taking events as inputs via the proposed event temporal pyramid representation to capture the regional nonlinear motion and (2) a holistic event-frame feature extractor for long-term dependence and continuity motion. We then propose a novel INR-based decoder with spatiotemporal embeddings to capture long-term dependencies with a larger temporal perception field. We validate the effectiveness and generalization of our method on four datasets (both simulated and real data), showing the superiority of our method. The project page is available at https://github.com/yunfanLu/HR-INR

cs.CV↗
arXiv2025

Fuzzy Reasoning Chain (FRC): An Innovative Reasoning Framework from Fuzziness to Clarity

With the rapid advancement of large language models (LLMs), natural language processing (NLP) has achieved remarkable progress. Nonetheless, significant challenges remain in handling texts with ambiguity, polysemy, or uncertainty. We introduce the Fuzzy Reasoning Chain (FRC) framework, which integrates LLM semantic priors with continuous fuzzy membership degrees, creating an explicit interaction between probability-based reasoning and fuzzy membership reasoning. This transition allows ambiguous inputs to be gradually transformed into clear and interpretable decisions while capturing conflicting or uncertain signals that traditional probability-based methods cannot. We validate FRC on sentiment analysis tasks, where both theoretical analysis and empirical results show that it ensures stable reasoning and facilitates knowledge transfer across different model scales. These findings indicate that FRC provides a general mechanism for managing subtle and ambiguous expressions with improved interpretability and robustness.

cs.CL↗
arXiv2025

VER-Bench: Evaluating MLLMs on Reasoning with Fine-Grained Visual Evidence

With the rapid development of MLLMs, evaluating their visual capabilities has become increasingly crucial. Current benchmarks primarily fall into two main types: basic perception benchmarks, which focus on local details but lack deep reasoning (e.g., "what is in the image?"), and mainstream reasoning benchmarks, which concentrate on prominent image elements but may fail to assess subtle clues requiring intricate analysis. However, profound visual understanding and complex reasoning depend more on interpreting subtle, inconspicuous local details than on perceiving salient, macro-level objects. These details, though occupying minimal image area, often contain richer, more critical information for robust analysis. To bridge this gap, we introduce the VER-Bench, a novel framework to evaluate MLLMs' ability to: 1) identify fine-grained visual clues, often occupying on average just 0.25% of the image area; 2) integrate these clues with world knowledge for complex reasoning. Comprising 374 carefully designed questions across Geospatial, Temporal, Situational, Intent, System State, and Symbolic reasoning, each question in VER-Bench is accompanied by structured evidence: visual clues and question-related reasoning derived from them. VER-Bench reveals current models' limitations in extracting subtle visual evidence and constructing evidence-based arguments, highlighting the need to enhance models's capabilities in fine-grained visual evidence extraction, integration, and reasoning for genuine visual understanding and human-like analysis. Dataset and additional materials are available https://github.com/verbta/ACMMM-25-Materials.

cs.CV↗
arXiv2025

HyRF: Hybrid Radiance Fields for Memory-efficient and High-quality Novel View Synthesis

Recently, 3D Gaussian Splatting (3DGS) has emerged as a powerful alternative to NeRF-based approaches, enabling real-time, high-quality novel view synthesis through explicit, optimizable 3D Gaussians. However, 3DGS suffers from significant memory overhead due to its reliance on per-Gaussian parameters to model view-dependent effects and anisotropic shapes. While recent works propose compressing 3DGS with neural fields, these methods struggle to capture high-frequency spatial variations in Gaussian properties, leading to degraded reconstruction of fine details. We present Hybrid Radiance Fields (HyRF), a novel scene representation that combines the strengths of explicit Gaussians and neural fields. HyRF decomposes the scene into (1) a compact set of explicit Gaussians storing only critical high-frequency parameters and (2) grid-based neural fields that predict remaining properties. To enhance representational capacity, we introduce a decoupled neural field architecture, separately modeling geometry (scale, opacity, rotation) and view-dependent color. Additionally, we propose a hybrid rendering scheme that composites Gaussian splatting with a neural field-predicted background, addressing limitations in distant scene representation. Experiments demonstrate that HyRF achieves state-of-the-art rendering quality while reducing model size by over 20 times compared to 3DGS and maintaining real-time performance. Our project page is available at https://wzpscott.github.io/hyrf/.

cs.CV↗
arXiv2025

On the end-point of Stein-Weiss inequality

This paper has two purposes. First, we show that the classical Stein-Weiss inequality is true for p=1. Second, by considering a family of strong fractional integral operators whose kernels have singularity on every coordinate subspace, we extend this end-point result to the multi-parameter setting.

math.CA↗
arXiv2025

Microcanonical cascades and random homeomorphisms

We give a complete solution to the Mandelbrot-Kahane problem for the microcanonical cascade measures by determing their exact Fourier dimensions. We also discuss the Frostman regularity as well as the bi-Hölder continuity of the Dubins-Freedman random homeomorphisms.

math.PR↗
arXiv2025

Harmonic analysis of Mandelbrot cascades -- in the context of vector-valued martingales

We solve a long-standing open problem of determining the Fourier dimension of the Mandelbrot canonical cascade measure (MCCM). This problem of significant interest was raised by Mandelbrot in 1976 and reiterated by Kahane in 1993. Specifically, we derive the exact formula for the Fourier dimension of the MCCM for random weights $W$ satisfying the condition $\mathbb{E}[W^t]<\infty$ for all $t>0$. As a corollary, we prove that the MCCM is Salem if and only if the random weight has a specific two-point distribution. In addition, we show that the MCCM is Rajchman with polynomial Fourier decay whenever the random weight satisfies $\mathbb{E}[W^{1+δ}]<\infty$ for some $δ>0$. As a consequence, we discover that, in the Biggins-Kyprianou's boundary case, the Fourier dimension of the MCCM exhibits a second order phase transition at the inverse temperature $β= 1/2$; we establish the upper Frostman regularity for MCCM; and we obtain a Fourier restriction estimate for MCCM. The major novelty of this paper is the discovery of putting the fine analysis of Fourier decay for multiplicative chaos measures into the theory of vector-valued martingales. This new viewpoint is of fundamental importance in the study of Fourier decay of multiplicative chaos measures. Indeed, in the sequel to this paper, combining the vector-valued martingale methods and ideas from Littlewood-Paley theory, the precise Fourier dimensions will be established for various classical models of multiplicative chaos measures including GMC of all dimensions, microcanonical Mandelbrot cascades, Mandelbrot random coverings, as well as Fourier-Walsh analysis of these models.

math.PR↗