arXiv subjects

Siran Li

Publications and source records attributed to Siran Li.

At least 37 records · Page 2Linked to original sources

arXiv2026

Questions beyond Pixels: Integrating Commonsense Knowledge in Visual Question Generation for Remote Sensing

With the rapid development of remote sensing image archives, asking questions about images has become an effective way of gathering specific information or performing semantic image retrieval. However, current automatically generated questions tend to be simplistic and template-based, which hinders the deployment of question answering or visual dialogue systems for real-world applications. To enrich and diversify the questions with both image content and commonsense knowledge, we propose a Knowledge-aware Remote Sensing Visual Question Generation model (KRSVQG). The proposed model incorporates related knowledge triplets from external knowledge sources to broaden the question content, while employing image captioning as an intermediary representation to ground questions to the corresponding images. Moreover, KRSVQG utilizes a vision-language pre-training and fine-tuning strategy, enabling the model's adaptation to low data regimes. To evaluate the proposed KRSVQG model, we construct two knowledge-aware remote sensing visual question generation datasets: the NWPU-300 dataset and the TextRS-300 dataset. Evaluations, including metrics and human assessment, demonstrate that KRSVQG outperforms existing methods and leads to rich questions, grounded in both image and domain knowledge. As a key practice in vision-language research, knowledge-aware visual question generation advances the understanding of image content beyond pixels, facilitating the development of knowledge-enriched vision-language systems with vision-grounded human commonsense.

cs.CV↗

arXiv2026

Knowledge-aware Visual Question Generation for Remote Sensing Images

With the rapid development of remote sensing image archives, asking questions about images has become an effective way of gathering specific information or performing image retrieval. However, automatically generated image-based questions tend to be simplistic and template-based, which hinders the real deployment of question answering or visual dialogue systems. To enrich and diversify the questions, we propose a knowledge-aware remote sensing visual question generation model, KRSVQG, that incorporates external knowledge related to the image content to improve the quality and contextual understanding of the generated questions. The model takes an image and a related knowledge triplet from external knowledge sources as inputs and leverages image captioning as an intermediary representation to enhance the image grounding of the generated questions. To assess the performance of KRSVQG, we utilized two datasets that we manually annotated: NWPU-300 and TextRS-300. Results on these two datasets demonstrate that KRSVQG outperforms existing methods and leads to knowledge-enriched questions, grounded in both image and domain knowledge.

cs.CV↗

arXiv2026

Global well-posedness for one-dimensional compressible Navier--Stokes system in dynamic combustion with small $BV\cap L^1$ initial data

We establish the global well-posedness theory of small BV weak solutions to a one-dimensional compressible Navier--Stokes model for reacting gas mixtures in dynamic combustion. The unknowns of the PDE system consist of the specific volume, velocity, temperature, and mass fraction of the reactant. For initial data that are small perturbations around the constant equilibrium state $(1, 0, 1, 0)$ in the $L^1(\mathbb{R}) \cap {\rm BV}(\mathbb{R})$-norm, we establish the local-in-time existence of weak solutions via an iterative scheme, show the stability and uniqueness of local weak solutions, and prove the global-in-time existence of solutions for initial data with small BV-norm via an analysis of the Green's function of the linearised system. The large-time behaviour of the global BV weak solutions is also characterised. This work is motivated by and extends the recent global well-posedness theory for BV weak solutions to the one-dimensional isentropic Navier--Stokes and Navier--Stokes--Fourier systems developed in [T.-P. Liu, S.-H. Yu, Commun. Pure Appl. Math. 75 (2022), 223--348] and [H. Wang, S.-H. Yu, X. Zhang, Arch. Ration. Mech. Anal. 245 (2022), 375--477].

math.AP↗

arXiv2026

A note for double Hölder regularity of the hydrodynamic pressure for weak solutions of Euler equations

We give an elementary proof for the interior double Hölder regularity of the hydrodynamic pressure for weak solutions of the Euler Equations in a bounded $C^2$-domain $Ω\subset \mathbb{R}^d$; $d\geq 3$. That is, for velocity $u \in C^{0,γ}(Ω;\mathbb{R}^d)$ with some $0<γ<1/2$, we show that the pressure $p \in C^{0,2γ}_{\rm int}(Ω)$. This is motivated by the studies of turbulence and anomalous dissipation in mathematical hydrodynamics and, recently, has been established in [L. De Rosa, M. Latocca, and G. Stefani, Int. Math. Res. Not. 2024.3 (2024), 2511--2560] over $C^{2,1}$-domains by means of pseudodifferential calculus. Our approach involves only standard elliptic PDE techniques, and relies on a variant of the modified pressure introduced in [C. W. Bardos, D. W. Boutros, and E. S. Titi, Hölder regularity of the pressure for weak solutions of the 3D Euler equations in bounded domains, Arch. Rational Mech. Anal. 249 (2025), 28] and the potential estimates in [L. Silvestre, unpublished notes]. The key novel ingredient of our proof is the introduction of two cutoff functions whose localisation parameters are carefully chosen as a power of the distance to $\partialΩ$.

math.AP↗

arXiv2025

Benchmarking is Broken -- Don't Let AI be its Own Judge

The meteoric rise of AI, with its rapidly expanding market capitalization, presents both transformative opportunities and critical challenges. Chief among these is the urgent need for a new, unified paradigm for trustworthy evaluation, as current benchmarks increasingly reveal critical vulnerabilities. Issues like data contamination and selective reporting by model developers fuel hype, while inadequate data quality control can lead to biased evaluations that, even if unintentionally, may favor specific approaches. As a flood of participants enters the AI space, this "Wild West" of assessment makes distinguishing genuine progress from exaggerated claims exceptionally difficult. Such ambiguity blurs scientific signals and erodes public confidence, much as unchecked claims would destabilize financial markets reliant on credible oversight from agencies like Moody's. In high-stakes human examinations (e.g., SAT, GRE), substantial effort is devoted to ensuring fairness and credibility; why settle for less in evaluating AI, especially given its profound societal impact? This position paper argues that the current laissez-faire approach is unsustainable. We contend that true, sustainable AI advancement demands a paradigm shift: a unified, live, and quality-controlled benchmarking framework robust by construction, not by mere courtesy and goodwill. To this end, we dissect the systemic flaws undermining today's AI evaluation, distill the essential requirements for a new generation of assessments, and introduce PeerBench (with its prototype implementation at https://www.peerbench.ai/), a community-governed, proctored evaluation blueprint that embodies this paradigm through sealed execution, item banking with rolling renewal, and delayed transparency. Our goal is to pave the way for evaluations that can restore integrity and deliver genuinely trustworthy measures of AI progress.

cs.AI↗

arXiv2025

GarmageNet: A Multimodal Generative Framework for Sewing Pattern Design and Generic Garment Modeling

Realistic digital garment modeling remains a labor-intensive task due to the intricate process of translating 2D sewing patterns into high-fidelity, simulation-ready 3D garments. We introduce GarmageNet, a unified generative framework that automates the creation of 2D sewing patterns, the construction of sewing relationships, and the synthesis of 3D garment initializations compatible with physics-based simulation. Central to our approach is Garmage, a novel garment representation that encodes each panel as a structured geometry image, effectively bridging the semantic and geometric gap between 2D structural patterns and 3D garment geometries. Followed by GarmageNet, a latent diffusion transformer to synthesize panel-wise geometry images and GarmageJigsaw, a neural module for predicting point-to-point sewing connections along panel contours. To support training and evaluation, we build GarmageSet, a large-scale dataset comprising 14,801 professionally designed garments with detailed structural and style annotations. Our method demonstrates versatility and efficacy across multiple application scenarios, including scalable garment generation from multi-modal design concepts (text prompts, sketches, photographs), automatic modeling from raw flat sewing patterns, pattern recovery from unstructured point clouds, and progressive garment editing using conventional instructions, laying the foundation for fully automated, production-ready pipelines in digital fashion. Project page: https://style3d.github.io/garmagenet/.

cs.GR↗

arXiv2025

Restricted Path Characteristic Function Determines the Law of Stochastic Processes

A central question in rough path theory is characterising the law of stochastic processes on path spaces. It is established in [I. Chevyrev & T. Lyons, Characteristic functions of measures on geometric rough paths, Ann. Probab. 44 (2016), 4049--4082] that the characteristic function of a probability measure on group-like elements, which is a subspace of the extended tensor algebra $\mathcal{T}\left(\mathbb{R}^d\right) = \prod_{n=0}^\infty\left(\mathbb{R}^d\right)^{\otimes n}$, uniquely determines the measure. In this work, we show that the characteristic function restricted to special orthogonal Lie algebra $\mathfrak{so}(n)$ is sufficient to achieve this goal. The key to our arguments is an explicit algorithm -- as opposed to the non-constructive approach in [I. Chevyrev & T. Lyons, op. cit.] -- for determining a generic element $X \in \mathcal{T}\left(\mathbb{R}^d\right)$ from its generating function when restricting its domain to a sparse subspace of real tridiagonal skew-symmetric matrices. Our only assumption is that $X$ has a non-zero ROC, which relaxes the condition of having an infinite ROC in the literature. As an application, we propose the restricted path characteristic function distance (RPCFD), a novel distance function for probability measures on the path space that serves as the sparse counterpart of path characteristic function distance. It has enormous advantages in dimension reduction and potential in generative modeling for synthetic time series generation, validated in this paper via hypothesis testing on fractional Brownian motions.

math.PR↗

arXiv2025

Spacetime decay of mild solutions and conditional quantitative transfer of regularity of the incompressible Navier--Stokes Equations from $\mathbb{R}^n$ to bounded domains

We are concerned with the "transfer of regularity" phenomenon for the incompressible Navier--Stokes Equations (NSE) in dimension $n \geq 3$; that is, the strong solutions of NSE on $\mathbb{R}^n$ can be nicely approximated by those on sufficiently large domains $Ω\subset \mathbb{R}^n$ under the no-slip boundary condition. Based on the space-time decay estimates of mild solutions of NSE established by [On space-time decay properties of nonstationary incompressible Navier-Stokes flows in $\mathbb{R}^n$, Funkcial. Ekvac. 43 (2000);$L^2$ decay for weak solutions of the Navier-Stokes equations, Arch. Rational Mech. Anal. 88 (1985)] and others, we obtain quantitative estimates for the ``transfer of regularity'' on higher-order derivatives of velocity and pressure under the smallness assumptions of the Stokes' system and/or the initial velocity, thus complementing the results obtained by [Using periodic boundary conditions to approximate the Navier-Stokes equations on $\mathbb{R}^n$ and the transfer of regularity, Nonlinearity 34 (2021)] and [Quantitative transfer of regularity of the incompressible Navier-Stokes equations from $\Bbb R^3$ to the case of a bounded domain, J. Math. Fluid Mech. 23 (2021)].

math.AP↗

arXiv2025

On local solubility of Bao--Ratiu equations on surfaces related to the geometry of diffeomorphism group

We are concerned with the existence of asymptotic directions for the group of volume-preserving diffeomorphisms of a closed 2-dimensional surface $(Σ,g)$ within the full diffeomorphism group, described by the Bao--Ratiu equations, a system of second-order PDEs introduced in [On a non-linear equation related to the geometry of the diffeomorphism group, Pacific J. Math. 158 (1993); On the geometric origin and the solvability of a degenerate Monge--Ampere equation, Proc. Symp. Pure Math. 54 (1993)]. It is known [The Bao--Ratiu equations on surfaces, Proc. R. Soc. Lond. A 449 (1995)] that asymptotic directions cannot exist globally on any $Σ$ with positive curvature. To complement this result, we prove that asymptotic directions always exist locally about a point $x_0 \in Σ$ in either of the following cases (where $K$ is the Gaussian curvature on $Σ$): (a), $K(x_0)>0$; (b) $K(x_0)<0$; or (c), $K$ changes sign cleanly at $x_0$, i.e., $K(x_0)=0$ and $\nabla K(x_0) \neq 0$. The key ingredient of the proof is the analysis following Han [On the isometric embedding of surfaces with Gauss curvature changing sign cleanly, Comm. Pure Appl. Math. 58 (2005)] of a degenerate Monge--Ampère equation -- which is of the elliptic, hyperbolic, and mixed types in cases (a), (b), and (c), respectively -- locally equivalent to the Bao--Ratiu equations.

math.DG↗

arXiv2025

Enhancing Retrieval-Augmented Generation: A Study of Best Practices

Retrieval-Augmented Generation (RAG) systems have recently shown remarkable advancements by integrating retrieval mechanisms into language models, enhancing their ability to produce more accurate and contextually relevant responses. However, the influence of various components and configurations within RAG systems remains underexplored. A comprehensive understanding of these elements is essential for tailoring RAG systems to complex retrieval tasks and ensuring optimal performance across diverse applications. In this paper, we develop several advanced RAG system designs that incorporate query expansion, various novel retrieval strategies, and a novel Contrastive In-Context Learning RAG. Our study systematically investigates key factors, including language model size, prompt design, document chunk size, knowledge base size, retrieval stride, query expansion techniques, Contrastive In-Context Learning knowledge bases, multilingual knowledge bases, and Focus Mode retrieving relevant context at sentence-level. Through extensive experimentation, we provide a detailed analysis of how these factors influence response quality. Our findings offer actionable insights for developing RAG systems, striking a balance between contextual richness and retrieval-generation efficiency, thereby paving the way for more adaptable and high-performing RAG frameworks in diverse real-world scenarios. Our code and implementation details are publicly available.

cs.CL↗

arXiv2024

Some recent developments on isometric immersions via compensated compactness and gauge transforms

We survey recent developments on the analysis of Gauss--Codazzi--Ricci equations, the first-order PDE system arising from the classical problem of isometric immersions in differential geometry, especially in the regime of low Sobolev regularity. Such equations are not purely elliptic, parabolic, or hyperbolic in general, hence calling for analytical tools for PDEs of mixed types. We discuss various recent contributions -- in line with the pioneering works by G.-Q. Chen, M. Slemrod, and D. Wang [Proc. Amer. Math. Soc. (2010); Comm. Math. Phys. (2010)] -- on the weak continuity of Gauss--Codazzi--Ricci equations, the weak stability of isometric immersions, and the fundamental theorem of submanifold theory with low regularity. Two mixed-type PDE techniques are emphasised throughout these developments: the method of compensated compactness and the theory of Coulomb--Uhlenbeck gauges.

math.AP↗

arXiv2024

Path Development Network with Finite-dimensional Lie Group Representation

Signature, lying at the heart of rough path theory, is a central tool for analysing controlled differential equations driven by irregular paths. Recently it has also found extensive applications in machine learning and data science as a mathematically principled, universal feature that boosts the performance of deep learning-based models in sequential data tasks. It, nevertheless, suffers from the curse of dimensionality when paths are high-dimensional. We propose a novel, trainable path development layer, which exploits representations of sequential data through finite-dimensional Lie groups, thus resulting in dimension reduction. Its backpropagation algorithm is designed via optimization on manifolds. Our proposed layer, analogous to recurrent neural networks (RNN), possesses an explicit, simple recurrent unit that alleviates the gradient issues. Our layer demonstrates its strength in irregular time series modelling. Empirical results on a range of datasets show that the development layer consistently and significantly outperforms signature features on accuracy and dimensionality. The compact hybrid model (stacking one-layer LSTM with the development layer) achieves state-of-the-art against various RNN and continuous time series models. Our layer also enhances the performance of modelling dynamics constrained to Lie groups. Code is available at https://github.com/PDevNet/DevNet.git.

cs.LG↗

arXiv2024

On the fundamental theorem of submanifold theory and isometric immersions with supercritical low regularity

A fundamental result in global analysis and nonlinear elasticity asserts that given a solution $\mathfrak{S}$ to the Gauss--Codazzi--Ricci equations over a simply-connected closed manifold $(\mathcal{M}^n,g)$, one may find an isometric immersion $ι$ of $(\mathcal{M}^n,g)$ into the Euclidean space $\mathbb{R}^{n+k}$ whose extrinsic geometry coincides with $\mathfrak{S}$. Here the dimension $n$ and the codimension $k$ are arbitrary. Abundant literature has been devoted to relaxing the regularity assumptions on $\mathfrak{S}$ and $ι$. The best result up to date is $\mathfrak{S} \in L^p$ and $ι\in W^{2,p}$ for $p>n \geq 3$ or $p=n=2$. In this paper, we extend the above result to $ι\in \mathcal{X}$ whose topology is strictly weaker than $W^{2,n}$ for $n \geq 3$. Indeed, $\mathcal{X}$ is the weak Morrey space $L^{p, n-p}_{2,w}$ with arbitrary $p \in ]2,n]$. This appears to be first supercritical result in the literature on the existence of isometric immersions with low regularity, given the solubility of the Gauss--Codazzi--Ricci equations. Our proof essentially utilises the theory of Uhlenbeck gauges -- in particular, Rivière--Struwe's work [Partial regularity for harmonic maps and related problems, Comm. Pure Appl. Math. 61 (2008)] on harmonic maps in arbitrary dimensions and codimensions -- and compensated compactness.

math.DG↗

arXiv2024

PCF-GAN: generating sequential data via the characteristic function of measures on the path space

Generating high-fidelity time series data using generative adversarial networks (GANs) remains a challenging task, as it is difficult to capture the temporal dependence of joint probability distributions induced by time-series data. Towards this goal, a key step is the development of an effective discriminator to distinguish between time series distributions. We propose the so-called PCF-GAN, a novel GAN that incorporates the path characteristic function (PCF) as the principled representation of time series distribution into the discriminator to enhance its generative performance. On the one hand, we establish theoretical foundations of the PCF distance by proving its characteristicity, boundedness, differentiability with respect to generator parameters, and weak continuity, which ensure the stability and feasibility of training the PCF-GAN. On the other hand, we design efficient initialisation and optimisation schemes for PCFs to strengthen the discriminative power and accelerate training efficiency. To further boost the capabilities of complex time series generation, we integrate the auto-encoder structure via sequential embedding into the PCF-GAN, which provides additional reconstruction functionality. Extensive numerical experiments on various datasets demonstrate the consistently superior performance of PCF-GAN over state-of-the-art baselines, in both generation and reconstruction quality. Code is available at https://github.com/DeepIntoStreams/PCF-GAN.

cs.LG↗

arXiv2023

A dynamical--topological obstruction for smooth isometric embeddings of Riemannian manifolds via incompressible Euler equations

We obtain a dynamical--topological obstruction for the existence of isometric embedding of a Riemannian manifold-with-boundary $(M,g)$: if the first real homology of $M$ is nontrivial, if the centre of the fundamental group is trivial, and if $M$ is isometrically embedded into a Euclidean space of dimension at least $3$, then the isometric embedding must violate a certain dynamical, kinetic energy-related condition (the "rigid isotopy extension property" in Definition 1.1). The arguments are motivated by the incompressible Euler equations with prescribed initial and terminal configurations in hydrodynamics.

math.DG↗

arXiv2023

A smooth isotopy of volume-preserving diffeomorphisms on unit cube saving energy through extra dimensions

We construct an explicit example of a smooth isotopy $\{ξ_t\}_{t \in [0,1]}$ of volume- and orientation-preserving diffeomorphisms on $[0,1]^n$ ($n \geq 3$) that has infinite total kinetic energy. This isotopy has no self-cancellation and is supported on countably many disjoint tubular neighbourhoods of homothetic copies of the isometrically embedded image of $(M,g)$, a "topologically complicated" Riemannian manifold-with-boundary. However, there exists another smooth isotopy that coincides with $\{ξ_t\}$ at $t=0$ and $t=1$ but of finite total kinetic energy.

math.DG↗

arXiv2023

Characterisations for the depletion of reactant in a one-dimensional dynamic combustion model

In this paper, a novel observation is made on a one-dimensional compressible Navier--Stokes model for the dynamic combustion of a reacting mixture of $γ$-law gases ($γ>1$) with discontinuous Arrhenius reaction rate function, on both bounded and unbounded domains. We show that the mass fraction of the reactant (denoted as $Z$) satisfies a weighted gradient estimate $Z_y/ \sqrt{Z} \in L^\infty_t L^2_y$, provided that at time zero the density is Lipschitz continuous and bounded strictly away from zero and infinity. Consequently, the graph of $Z$ cannot form cusps or corners near the points where the reactant in the combustion process is completely depleted at any instant, and the entropy of $Z$ is bounded from above. The key ingredient of the proof is a new estimate based on the Fisher information, first exploited by [2, 7] with applications to PDEs in chemorepulsion and thermoelasticity. Along the way, we also establish a Lipschitz estimate for the density.

math.AP↗

arXiv2023

Scores for Multivariate Distributions and Level Sets

Forecasts of multivariate probability distributions are required for a variety of applications. Scoring rules enable the evaluation of forecast accuracy, and comparison between forecasting methods. We propose a theoretical framework for scoring rules for multivariate distributions, which encompasses the existing quadratic score and multivariate continuous ranked probability score. We demonstrate how this framework can be used to generate new scoring rules. In some multivariate contexts, it is a forecast of a level set that is needed, such as a density level set for anomaly detection or the level set of the cumulative distribution as a measure of risk. This motivates consideration of scoring functions for such level sets. For univariate distributions, it is well-established that the continuous ranked probability score can be expressed as the integral over a quantile score. We show that, in a similar way, scoring rules for multivariate distributions can be decomposed to obtain scoring functions for level sets. Using this, we present scoring functions for different types of level set, including density level sets and level sets for cumulative distributions. To compute the scores, we propose a simple numerical algorithm. We perform a simulation study to support our proposals, and we use real data to illustrate usefulness for forecast combining and CoVaR estimation.

math.ST↗