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Qifan Li

Publications and source records attributed to Qifan Li.

18 recordsLinked to original sources
arXiv2026

On the Local boundedness and higher integrability for the subcritical doubly nonlinear parabolic systems

We consider the inhomogeneous doubly nonlinear parabolic systems of the form \begin{equation*}\partial_t (|u|^{q-1}u)-\operatorname{div}(|Du|^{p-2}Du)=\operatorname{div}(|F|^{p-2}F)\end{equation*} in a bounded space-time cylinder $\Omega_T=\Omega\times(0,T)\subset \mathbb{R}^{N+1}$. We study the local regularity properties for weak solutions in the subcritical range $p\leq\frac{N(q+1)}{N+q+1}$ and $0 0$. In addition, we prove local higher integrability of $|Du|$ in the range $p=\frac{N(q+1)}{N+q+1}$ and $\frac{N+p}{N-p}<q<\frac{N+2}{N-2}$, provided that $|u|\in L_{\loc}^{\rr}(\Omega_T)$ holds.

math.AP↗
arXiv2026

Learning Adaptive Semantic Gaussian Allocation for 3D Occupancy

Semantic 3D Gaussians provide a compact representation for 3D semantic occupancy prediction by rendering semantic primitives into a voxel volume under voxel-wise supervision. Recent methods have improved the modeling ability and efficiency of this representation through more flexible primitive shapes, geometry-guided initialization, and progressive densification. However, these advances mainly determine how primitives are represented, initialized, or added, and do not explicitly address how to select the most useful Gaussians when their total number must be limited to control memory and computation. This imbalance creates an allocation bottleneck: redundant Gaussians remain in simple regions, while difficult regions receive insufficient semantic support. We propose the Semantic Gaussian Allocation Transformer (SAGFormer), which uses Gaussian attributes and local geometric-semantic features to score candidates and select a fixed final Gaussian set. Experiments on nuScenes-SurroundOcc and SSCBench-KITTI-360 show that SAGFormer improves occupancy prediction under the evaluated protocols and yields more semantically consistent and better-utilized Gaussian representations. Under similar final counts and raw coverage, it reduces semantic mixing, strengthens class-consistent voxel support, and produces fewer unused Gaussians. The results indicate that explicit capacity allocation is a useful complement to Gaussian refinement for semantic occupancy prediction.

cs.CV↗
arXiv2026

Hyperbolic Distillation: Geometry-Guided Cross-Modal Transfer for Robust 3D Object Detection

Cross-modal knowledge distillation has emerged as an effective strategy for integrating point cloud and image features in 3D perception tasks. However, the modality heterogeneity, spatial misalignment, and the representation crisis of multiple modalities often limit the efficient of these cross-modal distillation methods. To address these limitations in existing approaches, we propose a hyperbolic constrained cross-modal distillation method for multimodal 3D object detection (HGC-Det). The proposed HGC-Det framework includes an image branch and a point cloud branch to extract semantic features from two different modalities. The point cloud branch comprises three core components: a 2D semantic-guided voxel optimization component (SGVO), a hyperbolic geometry constrained cross-modal feature transfer component (HFT), and a feature aggregation-based geometry optimization component (FAGO). Specifically, the SGVO component adaptively refines the spatial representation of the 3D branch by leveraging semantic cues from the image branch, thereby mitigating the issue of inadequate representation fusion. The HFT component exploits the intrinsic geometric properties of hyperbolic space to alleviate semantic loss during the fusion of high-dimensional image features and low-dimensional point cloud features. Finally, the FAGO compensates for potential spatial feature degradation introduced by the 2D semantic-guided voxel optimization component. Extensive experiments on indoor datasets (SUN RGB-D, ARKitScenes) and outdoor datasets (KITTI, nuScenes) demonstrate that our method achieves a better trade-off between detection accuracy and computational cost.

cs.CV↗
arXiv2026

Taming Sampling Perturbations with Variance Expansion Loss for Latent Diffusion Models

Latent diffusion models have emerged as the dominant framework for high-fidelity and efficient image generation, owing to their ability to learn diffusion processes in compact latent spaces. However, while previous research has focused primarily on reconstruction accuracy and semantic alignment of the latent space, we observe that another critical factor, robustness to sampling perturbations, also plays a crucial role in determining generation quality. Through empirical and theoretical analyses, we show that the commonly used $\beta$-VAE-based tokenizers in latent diffusion models, tend to produce overly compact latent manifolds that are highly sensitive to stochastic perturbations during diffusion sampling, leading to visual degradation. To address this issue, we propose a simple yet effective solution that constructs a latent space robust to sampling perturbations while maintaining strong reconstruction fidelity. This is achieved by introducing a Variance Expansion loss that counteracts variance collapse and leverages the adversarial interplay between reconstruction and variance expansion to achieve an adaptive balance that preserves reconstruction accuracy while improving robustness to stochastic sampling. Extensive experiments demonstrate that our approach consistently enhances generation quality across different latent diffusion architectures, confirming that robustness in latent space is a key missing ingredient for stable and faithful diffusion sampling.

cs.CV↗
arXiv2025

Guiding a Diffusion Transformer with the Internal Dynamics of Itself

The diffusion model presents a powerful ability to capture the entire (conditional) data distribution. However, due to the lack of sufficient training and data to learn to cover low-probability areas, the model will be penalized for failing to generate high-quality images corresponding to these areas. To achieve better generation quality, guidance strategies such as classifier free guidance (CFG) can guide the samples to the high-probability areas during the sampling stage. However, the standard CFG often leads to over-simplified or distorted samples. On the other hand, the alternative line of guiding diffusion model with its bad version is limited by carefully designed degradation strategies, extra training and additional sampling steps. In this paper, we proposed a simple yet effective strategy Internal Guidance (IG), which introduces an auxiliary supervision on the intermediate layer during training process and extrapolates the intermediate and deep layer's outputs to obtain generative results during sampling process. This simple strategy yields significant improvements in both training efficiency and generation quality on various baselines. On ImageNet 256x256, SiT-XL/2+IG achieves FID=5.31 and FID=1.75 at 80 and 800 epochs. More impressively, LightningDiT-XL/1+IG achieves FID=1.34 which achieves a large margin between all of these methods. Combined with CFG, LightningDiT-XL/1+IG achieves the current state-of-the-art FID of 1.19.

cs.CV↗
arXiv2025

Texture Vector-Quantization and Reconstruction Aware Prediction for Generative Super-Resolution

Vector-quantized based models have recently demonstrated strong potential for visual prior modeling. However, existing VQ-based methods simply encode visual features with nearest codebook items and train index predictor with code-level supervision. Due to the richness of visual signal, VQ encoding often leads to large quantization error. Furthermore, training predictor with code-level supervision can not take the final reconstruction errors into consideration, result in sub-optimal prior modeling accuracy. In this paper we address the above two issues and propose a Texture Vector-Quantization and a Reconstruction Aware Prediction strategy. The texture vector-quantization strategy leverages the task character of super-resolution and only introduce codebook to model the prior of missing textures. While the reconstruction aware prediction strategy makes use of the straight-through estimator to directly train index predictor with image-level supervision. Our proposed generative SR model (TVQ&RAP) is able to deliver photo-realistic SR results with small computational cost.

cs.CV↗
arXiv2025

H\"older regularity of weak solutions to nonlocal doubly degenerate parabolic equations

We study local regularity for nonlocal doubly degenerate parabolic equations. The model equation is \begin{equation*}\begin{split} \partial_t(|u|^{q-1}u)+\mathrm{P}.\mathrm{V}.\int_{\mathbb{R}^n}\frac{|u(x,t)-u(y,t)|^{p-2}(u(x,t)-u(y,t))}{|x-y|^{n+sp}}\,\mathrm{d}y=0, \end{split} \end{equation*} where $0 2$ and $0<q<p-1$. Under a parabolic tail condition, we show that any locally bounded and sign-changing solution is locally H\"older continuous. Our proof is based on a nonlocal version of De Giorgi technique and the method of intrinsic scaling.

math.AP↗
arXiv2025

RouteWinFormer: A Route-Window Transformer for Middle-range Attention in Image Restoration

Transformer models have recently garnered significant attention in image restoration due to their ability to capture long-range pixel dependencies. However, long-range attention often results in computational overhead without practical necessity, as degradation and context are typically localized. Normalized average attention distance across various degradation datasets shows that middle-range attention is enough for image restoration. Building on this insight, we propose RouteWinFormer, a novel window-based Transformer that models middle-range context for image restoration. RouteWinFormer incorporates Route-Windows Attnetion Module, which dynamically selects relevant nearby windows based on regional similarity for attention aggregation, extending the receptive field to a mid-range size efficiently. In addition, we introduce Multi-Scale Structure Regularization during training, enabling the sub-scale of the U-shaped network to focus on structural information, while the original-scale learns degradation patterns based on generalized image structure priors. Extensive experiments demonstrate that RouteWinFormer outperforms state-of-the-art methods across 9 datasets in various image restoration tasks.

cs.CV↗
arXiv2023

Continuity estimates for doubly degenerate parabolic equations with lower order terms via nonlinear potentials

This article studies the continuity of bounded nonnegative weak solutions to inhomogeneous doubly nonlinear parabolic equations. A model equation is \begin{equation*}\partial_t u-\operatorname{div}(u^{m-1}|Du|^{p-2}Du)=f\qquad \text{in}\quadΩ\times(-T,0)\subset \mathbb{R}^{n+1}.\end{equation*} Here, we consider the case $m>1$ and $2<p<n$. We establish a continuity estimate for $u$ in terms of elliptic Riesz potentials of the right-hand side of the equation.

math.AP↗
arXiv2022

Partial regularity for degenerate parabolic systems with non-standard growth and discontinuous coefficients

This article studies the partial Hölder continuity of weak solutions to certain degenerate parabolic systems whose model is the differentiable parabolic $p(x,t)$-Laplacian system, \begin{equation*}\partial_t u-\operatorname{div}[μ(z)(1+|Du|^2)^{\frac{p(z)-2}{2}}Du]=0,\qquad p(z)\geq2.\end{equation*} Here, the exponential function $p(z)$ satisfies a logarithmic continuity condition. We show that if $μ(z)$ satisfies a certain VMO-type condition, then $u$ is locally Hölder continuous except for a measure zero set.

math.AP↗
arXiv2019

High Performance Metallic Amorphous Magnetic Flake-based Magnetodielectric Inductors

Flake-shaped FeSi-based metallic amorphous alloy particles, having an aspect ratio as high as 175 to 1, were prepared by ball milling gas atomized amorphous powders of an effective diameter of 20 micrometers. The starting powder had a saturation magnetic flux density, Bs, of 1.5 T and a coercivity, Hc, of 94 A/m. The aspect ratio of the flakes, as well as their magnetic properties, were controlled by milling process parameters, such as duration, speed, and the type, mass and diameter of the milling balls. To minimize the oxidation of the charge, the powders were handled in an argon gas-purged glove box, milled in toluene, and subsequently dried in vacuo. Subsequently, soft magnetodielectric composites were prepared by suspending and aligning the FeSi-based powders in paraffin wax or epoxy resin. The composites were then pressed into toroids for measurements of their high frequency complex permeability by a vector network analyzer. The influence of the flake aspect ratio and volume loading fraction on the permeability of the composites were investigated. Results indicate that the composite permeability increases with the flake aspect ratio. For example, for a given loading factor of 30 vol.%, the composite permeability at 0.1 GHz nearly tripled and approached the value of 10 by increasing the aspect ratio of the FeSi-based inclusions from 1 (spheres) to greater than 175 to 1 (flakes).

physics.app-ph↗
arXiv2018

On the continuity of solutions to doubly singular parabolic equations

This paper considers a certain doubly singular parabolic equations with one singularity occurs in the time derivative, whose model is \begin{equation*} \partial_tβ(u)-\operatorname{div}|Du|^{p-2}Du\ni0,\qquad \text{in}\quad Ω\times(0,T)\end{equation*} where $Ω\subset\mathbb{R}^N$ and $N\geq3$. We show that the bounded weak solutions are locally continuous in the range $$2-ε_0\leq p<2,$$ provided $ε_0>0$ is small enough, and the continuity is stable as $p\to2$.

math.AP↗
arXiv2017

Weak Harnack estimates for supersolutions to doubly degenerate parabolic equations

We establish weak Harnack inequalities for positive, weak supersolutions to certain doubly degenerate parabolic equations. The prototype of this kind of equations is $$\partial_tu-\operatorname{div}|u|^{m-1}|Du|^{p-2}Du=0,\quad p>2,\quad m+p>3.$$ Our proof is based on Caccioppoli inequalities, De Giorgi's estimates and Moser's iterative method.

math.AP↗
arXiv2016

Very weak solutions of subquadratic parabolic systems with non-standard $p(x,t)$-growth

The aim of this paper is to establish a higher integrability result for very weak solutions of certain parabolic systems whose model is the parabolic $p(x,t)$-Laplacian system. Under assumptions on the exponent function $p:Ω_T=Ω\times (0,T)\to\left(\frac{2n}{n+2},2\right]$, it is shown that any very weak solution $u:Ω_T\rightarrow\mathbb{R}^N$ with $|Du|^{p(\cdot)(1-\varepsilon)}\in L^1(Ω_T)$ belongs to the natural energy spaces, i.e. $|Du|^{p(\cdot)}\in L^1_{\operatorname{loc}}(Ω_T)$, provided $ε>0$ is small enough. This extends the main result of [V. Bögelein and Q. Li, Nonlinear Anal., 98 (2014), pp. 190-225] to the subquadratic case.

math.AP↗
arXiv2010

A Bourgain type bilinear estimate for a class of water-wave models

The bilinear estimtate in proposition 7.15 [J. Bourgain, Fourier restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations, Parts II, Geometric Funct. Anal. 3(3) (1993) 209-262.] plays an essential role in the study of the nonlinear term of KdV equation. In this paper, this estimate is extended to the a more general water-vave equations. We hope this result could shed some light on the estimates of nonlinear terms of water-vave equations.

math.CA↗
arXiv2009

Littlewood-Paley characterization for $Q_α(R^n)$ spaces

In Baraka's paper [2], he obtained the Littlewood-Paley characterization of Campanato spaces $L^{2,λ}$ and introduced $\mathcal {L}^{p,λ,s}$ spaces. He showed that $\mathcal {L}^{2,λ,s}=(-\triangle)^{-\frac{s}{2}}L^{2,λ}$ for $0\leqλ<n+2$. In [7], by using the properties of fractional Carleson measures, J Xiao proved that for $n\geq2$, $0<α<1$. $(-\triangle)^{-\fracα{2}}L^{2,n-2α}$ is essential the $Q_α(\mathbb{R}^n)$ spaces which were introduced in [4]. Then we could conclude that $Q_α(\mathbb{R}^n)=\mathcal {L}^{2,n-2α,α}$ for $0<α<1$. In fact, this result could be also obtained directly by using the method in [2]. In this paper, We proved this result in the spirit of [2]. This paper could be considered as the supplement of Baraka's work [2].

math.CA↗