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Yao Yuan

Publications and source records attributed to Yao Yuan.

At least 19 recordsLinked to original sources
arXiv2026

Lefschetz filtration and Perverse filtration on the compactified Jacobian

Let $C$ be a complex integral curve with plannar singularities. Let $J$ be the compactified Jacobian of $C$. There are two filtrations on the cohomology group $H^*(J)$. One is obtained by the nilpotent morphism defined by cupping a certain ample divisor on $J$, which we call the Lefschetz filtration. To obtain the other filtration, we put $C$ into a family of curves $\mathcal{C}\rightarrow B$ so that $J$ can be embedded into a family $f:\mathcal{J}\rightarrow B$, and we let $B, \mathcal{C},\mathcal{J}$ be smooth. Then $Rf_*(\mathbb{Q}_{\mathcal{J}})$ decomposes into a direct sum of its (shifted) perverse cohomologies. Restricting this decomposition to fibers, we get a filtration on $H^*(J)$ called the perverse filtration. We show in this paper that these two filtrations are opposite to each other as conjectured by Maulik-Yun.

math.AG↗
arXiv2026

Measurement of Differential Static Polarizability and Frequency of an Inner-Shell Orbital Clock Transition in Lattice-Trapped 174Yb

Additional clock transitions of ytterbium atoms based on inner-shell orbital transition could benefit the search for new physics beyond the Standard Model. Observation of these transitions with high resolution is a prerequisite for making precise frequency measurements. Here, we observe 4.3 Hz-linewidth spectra of the inner-shell orbital transition at 431 nm in lattice-trapped 174Yb. With high-resolution spectra, we precisely determine the differential static polarizability of the transition to be -2.10(4) kHz/(kV/cm)^2. The magnitude of this polarizability is approximately 1/17 of that of the well-known clock transition in 171Yb at 578 nm, indicating a reduced sensitivity to blackbody radiation. We carry out a frequency ratio measurement between the two clock transitions of ytterbium atoms with an uncertainty of 9E-15. The frequency of the 431 nm transition is determined to be 695 175 030 801 776.5(6.3) Hz. These results represent a step forward in future studies on the search for new physics beyond the Standard Model.

physics.atom-ph↗
arXiv2025

Scaling Spatial Reasoning in MLLMs through Programmatic Data Synthesis

Embodied intelligence, a grand challenge in artificial intelligence, is fundamentally constrained by the limited spatial understanding and reasoning capabilities of current models. Prevailing efforts to address this through enhancing Vision-Language Models (VLMs) are trapped in a dilemma: template-based datasets are scalable but structurally rigid, while manual annotation is linguistically diverse but unscalable and, critically, computationally imprecise. We introduce SPRITE, a novel framework that overcomes this dilemma by leveraging simulators and large models to programmatically synthesize scalable, diverse, and high-quality spatial reasoning data. The core innovation of SPRITE is to reframe ground-truth generation as a code-generation task. We utilize LLMs to compile complex spatial questions into executable programs, which are then verified against high-precision scene meta-information extracted from simulators. This ensures our ground truth is both computationally precise and verifiable, while the generative power of LLMs provides vast linguistic diversity. Leveraging this pipeline, we have curated a dataset encompassing 3 simulators, 11k+ scenes, and 300k+ image/video instruction-tuning pairs. We demonstrate that a VLM trained on our data achieves significant performance gains on multiple spatial benchmarks and outperforms other open-source datasets of equivalent size. Furthermore, a scalability analysis confirms our hypothesis that overcoming the low-diversity nature of traditional template methods is essential for building robust, generalizable spatial intelligence. We will make the SPRITE framework code and the full 300k+ dataset publicly available to facilitate future research in spatial intelligence.

cs.AI↗
arXiv2025

Uncertainty Guided Refinement for Fine-Grained Salient Object Detection

Recently, salient object detection (SOD) methods have achieved impressive performance. However, salient regions predicted by existing methods usually contain unsaturated regions and shadows, which limits the model for reliable fine-grained predictions. To address this, we introduce the uncertainty guidance learning approach to SOD, intended to enhance the model's perception of uncertain regions. Specifically, we design a novel Uncertainty Guided Refinement Attention Network (UGRAN), which incorporates three important components, i.e., the Multilevel Interaction Attention (MIA) module, the Scale Spatial-Consistent Attention (SSCA) module, and the Uncertainty Refinement Attention (URA) module. Unlike conventional methods dedicated to enhancing features, the proposed MIA facilitates the interaction and perception of multilevel features, leveraging the complementary characteristics among multilevel features. Then, through the proposed SSCA, the salient information across diverse scales within the aggregated features can be integrated more comprehensively and integrally. In the subsequent steps, we utilize the uncertainty map generated from the saliency prediction map to enhance the model's perception capability of uncertain regions, generating a highly-saturated fine-grained saliency prediction map. Additionally, we devise an adaptive dynamic partition (ADP) mechanism to minimize the computational overhead of the URA module and improve the utilization of uncertainty guidance. Experiments on seven benchmark datasets demonstrate the superiority of the proposed UGRAN over the state-of-the-art methodologies. Codes will be released at https://github.com/I2-Multimedia-Lab/UGRAN.

cs.CV↗
arXiv2025

LeanGaussian: Breaking Pixel or Point Cloud Correspondence in Modeling 3D Gaussians

Recently, Gaussian splatting has demonstrated significant success in novel view synthesis. Current methods often regress Gaussians with pixel or point cloud correspondence, linking each Gaussian with a pixel or a 3D point. This leads to the redundancy of Gaussians being used to overfit the correspondence rather than the objects represented by the 3D Gaussians themselves, consequently wasting resources and lacking accurate geometries or textures. In this paper, we introduce LeanGaussian, a novel approach that treats each query in deformable Transformer as one 3D Gaussian ellipsoid, breaking the pixel or point cloud correspondence constraints. We leverage deformable decoder to iteratively refine the Gaussians layer-by-layer with the image features as keys and values. Notably, the center of each 3D Gaussian is defined as 3D reference points, which are then projected onto the image for deformable attention in 2D space. On both the ShapeNet SRN dataset (category level) and the Google Scanned Objects dataset (open-category level, trained with the Objaverse dataset), our approach, outperforms prior methods by approximately 6.1%, achieving a PSNR of 25.44 and 22.36, respectively. Additionally, our method achieves a 3D reconstruction speed of 7.2 FPS and rendering speed 500 FPS. Codes are available at https://github.com/jwubz123/LeanGaussian.

cs.CV↗
arXiv2024

Higher direct images of the structure sheaf via the Hilbert-Chow morphism

Let $X$ be a projective smooth surface over $\mathbb{C}$ with $H^2(\mathcal{O}_X)=0$. Let $M=M(L,χ)$ be the moduli space of 1-dimensional semistable sheaves with determinant $\mathcal{O}_X(L)$ and Euler characteristic $χ$. We have the Hilbert-Chow morphism $π:M\rightarrow |L|$. We give explicit forms of the higher direct images $R^iπ_*\mathcal{O}_M$ under some mild conditions on $M$ and $|L|$. Our result shows that $R^iπ_*\mathcal{O}_M$ are direct sums of line bundles. In particular, using our result one gets explicit formulas for the Euler characteristic of $π^*\mathcal{O}_{|L|}(m)$, which in $X=\mathbb{P}^2$ case was once conjectured by Chung-Moon.

math.AG↗
arXiv2024

Unified Unsupervised Salient Object Detection via Knowledge Transfer

Recently, unsupervised salient object detection (USOD) has gained increasing attention due to its annotation-free nature. However, current methods mainly focus on specific tasks such as RGB and RGB-D, neglecting the potential for task migration. In this paper, we propose a unified USOD framework for generic USOD tasks. Firstly, we propose a Progressive Curriculum Learning-based Saliency Distilling (PCL-SD) mechanism to extract saliency cues from a pre-trained deep network. This mechanism starts with easy samples and progressively moves towards harder ones, to avoid initial interference caused by hard samples. Afterwards, the obtained saliency cues are utilized to train a saliency detector, and we employ a Self-rectify Pseudo-label Refinement (SPR) mechanism to improve the quality of pseudo-labels. Finally, an adapter-tuning method is devised to transfer the acquired saliency knowledge, leveraging shared knowledge to attain superior transferring performance on the target tasks. Extensive experiments on five representative SOD tasks confirm the effectiveness and feasibility of our proposed method. Code and supplement materials are available at https://github.com/I2-Multimedia-Lab/A2S-v3.

cs.CV↗
arXiv2023

On the perverse filtration of the moduli spaces of 1-dimensional sheaves on $\mathbb{P}^2$ and P=C conjecture

Let $M(d,χ)$ be the moduli space of semistable 1-dimensional sheaves supported at curves of degree $d$ on $\mathbb{P}^2$, with Euler characteristic $χ$. We have the Hilbert-Chow morphism $π: M(d,χ)\rightarrow |dH|$ sending each sheaf to its support. We study the perverse filtration on $H^*(M(d,χ),\mathbb{Q})$ via map $π$, especially the P=C conjecture posed by Kononov-Pi-Shen. We show that P=C conjecture holds for $H^{*\leq 4}(M(d,χ),\mathbb{Q})$ for any $d\geq 4$, $(d,χ)=1$. The main strategy is to relate $M(d,χ)$ to the Hilbert scheme $S^{[n]}$ of $n$-points and transfer the problem to some properties on $H^*(S^{[n]},\mathbb{Q})$. We use induction on $n$ to achieve the desired properties. Our proof involves some complicated calculations.

math.AG↗
arXiv2023

M$^3$Net: Multilevel, Mixed and Multistage Attention Network for Salient Object Detection

Most existing salient object detection methods mostly use U-Net or feature pyramid structure, which simply aggregates feature maps of different scales, ignoring the uniqueness and interdependence of them and their respective contributions to the final prediction. To overcome these, we propose the M$^3$Net, i.e., the Multilevel, Mixed and Multistage attention network for Salient Object Detection (SOD). Firstly, we propose Multiscale Interaction Block which innovatively introduces the cross-attention approach to achieve the interaction between multilevel features, allowing high-level features to guide low-level feature learning and thus enhancing salient regions. Secondly, considering the fact that previous Transformer based SOD methods locate salient regions only using global self-attention while inevitably overlooking the details of complex objects, we propose the Mixed Attention Block. This block combines global self-attention and window self-attention, aiming at modeling context at both global and local levels to further improve the accuracy of the prediction map. Finally, we proposed a multilevel supervision strategy to optimize the aggregated feature stage-by-stage. Experiments on six challenging datasets demonstrate that the proposed M$^3$Net surpasses recent CNN and Transformer-based SOD arts in terms of four metrics. Codes are available at https://github.com/I2-Multimedia-Lab/M3Net.

cs.CV↗
arXiv2023

SegPrompt: Using Segmentation Map as a Better Prompt to Finetune Deep Models for Kidney Stone Classification

Recently, deep learning has produced encouraging results for kidney stone classification using endoscope images. However, the shortage of annotated training data poses a severe problem in improving the performance and generalization ability of the trained model. It is thus crucial to fully exploit the limited data at hand. In this paper, we propose SegPrompt to alleviate the data shortage problems by exploiting segmentation maps from two aspects. First, SegPrompt integrates segmentation maps to facilitate classification training so that the classification model is aware of the regions of interest. The proposed method allows the image and segmentation tokens to interact with each other to fully utilize the segmentation map information. Second, we use the segmentation maps as prompts to tune the pretrained deep model, resulting in much fewer trainable parameters than vanilla finetuning. We perform extensive experiments on the collected kidney stone dataset. The results show that SegPrompt can achieve an advantageous balance between the model fitting ability and the generalization ability, eventually leading to an effective model with limited training data.

cs.CV↗
arXiv2023

Some Betti numbers of the moduli of 1-dimensional sheaves on $\mathbb{P}^2$

Let $M(d,χ)$ with $(d,χ)=1$ be the moduli space of semistable sheaves on $\mathbb{P}^2$ supported on curves of degree $d$ and with Euler characteristic $χ$. The cohomology ring $H^*(M(d,χ),\mathbb{Z})$ of $M(d,χ)$ is isomorphic to its Chow ring $A^*(M(d,χ))$ by Markman's result. W. Pi and J. Shen have described a minimal generating set of $A^*(M(d,χ))$ consisting of $3d-7$ generators, which they also showed to have no relation in $A^{\geq d-2}(M(d,χ))$. We compute the two Betti numbers $b_{2(d-1)}$ and $b_{2d}$ of $M(d,χ)$ and as a corollary we show that the generators given by Pi-Shen have no relations in $A^{\geq d-1}(M(d,χ))$ but do have three linearly independent relations in $A^d(M(d,χ))$.

math.AG↗
arXiv2021

Sheaves on non-reduced curves in a projective surface

Sheaves on non-reduced curves can appear in moduli space of 1-dimensional semistable sheaves over a surface, and moduli space of Higgs bundles as well. We estimate the dimension of the stack $\mathbf{M}_{X}(nC,χ)$ of pure sheaves supported at the non-reduced curve $nC~(n\geq 2)$ with $C$ an integral curve on $X$. We prove that the Hilbert-Chow morphism $h_{L,χ}:\mathcal{M}^H_X(L,χ)\rightarrow |L|$ sending each semistable 1-dimensional sheaf to its support have all its fibers of the same dimension for $X$ Fano or with trivial canonical line bundle and $|L|$ contains integral curves.

math.AG↗
arXiv2018

Strange duality on $\mathbb{P}^2$ via quiver representations

We study Le Potier's strange duality conjecture on $\mathbb{P}^2$. We focus on the strange duality map $SD_{c_n^r,d}$ which involves the moduli space of rank $r$ sheaves with trivial first Chern class and second Chern class $n$, and the moduli space of 1-dimensional sheaves with determinant $\mathcal{O}_{\mathbb{P}^2}(d)$ and Euler characteristic 0. By using tools in quiver representation theory, we show that $SD_{c^r_n,d}$ is an isomorphisms for $r=n$ or $r=n-1$ or $d\leq 3$, and in general $SD_{c^r_n,d}$ is injective for any $n\geq r>0$ and $d>0$.

math.AG↗
arXiv2017

Moduli spaces of 1-dimensional semi-stable sheaves and Strange duality on $\mathbb{P}^2$

We study Le Potier's strange duality conjecture on $\mathbb{P}^2$. We show the conjecture is true for the pair ($W(2,0,2),~M(d,0)$) with $d>0$, where $W(2,0,2)$ is the moduli space of semistable sheaves of rank 2, zero first Chern class and second Chern class 2, and $M(d,0)$ is the moduli space of 1-dimensional semistable sheaves of first Chern class $dH$ and Euler characteristic 0.

math.AG↗
arXiv2017

Strange duality on rational surfaces II: higher rank cases

We study Le Potier's strange duality conjecture on a rational surface. We focus on the strange duality map $SD_{c_n^r,L}$ which involves the moduli space of rank $r$ sheaves with trivial first Chern class and second Chern class $n$, and the moduli space of 1-dimensional sheaves with determinant $L$ and Euler characteristic 0. We show there is an exact sequence relating the map $SD_{c_r^r,L}$ to $SD_{c^{r-1}_{r},L}$ and $SD_{c_r^r,L\otimes K_X}$ for all $r\geq1$ under some conditions on $X$ and $L$ which applies to a large number of cases on $\p^2$ or Hirzebruch surfaces . Also on $\mathbb{P}^2$ we show that for any $r>0$, $SD_{c^r_r,dH}$ is an isomorphism for $d=1,2$, injective for $d=3$ and moreover $SD_{c_3^3,rH}$ and $SD_{c_3^2,rH}$ are injective. At the end we prove that the map $SD_{c_n^2,L}$ ($n\geq2$) is an isomorphism for $X=\mathbb{P}^2$ or Fano rational ruled surfaces and $g_L=3$, and hence so is $SD_{c_3^3,L}$ as a corollary of our main result.

math.AG↗
arXiv2016

Strange duality on rational surfaces

We study Le Potier's strange duality conjecture on a rational surface. We focus on the case involving the moduli space of rank 2 sheaves with trivial first Chern class and second Chern class 2, and the moduli space of 1-dimensional sheaves with determinant $L$ and Euler characteristic 0. We show the conjecture for this case is true under some suitable conditions on $L$, which applies to $L$ ample on any Hirzebruch surface $Σ_e:=\mathbb{P}(\mathcal{O}_{\mathbb{P}^1}\oplus\mathcal{O}_{\mathbb{P}^1}(e))$ except for $e=1$. When $e=1$, our result applies to $L=aG+bF$ with $b\geq a+[a/2]$, where $F$ is the fiber class, $G$ is the section class with $G^2=-1$ and $[a/2]$ is the integral part of $a/2$.

math.AG↗