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Yujie Xu

Publications and source records attributed to Yujie Xu.

At least 19 recordsLinked to original sources
arXiv2026

A generic categorical local Langlands correspondence for quasi-split reductive groups

We $\textit{unconditionally}$ prove a $\textit{generic}$ categorical local Langlands conjecture for a large class of quasi-split reductive $p$-adic groups $G$, including all quasi-split classical groups and some non-classical groups. More precisely, we construct a natural fully faithful functor from the stable $\infty$-category of $\textit{generic}$ Bernstein blocks on the automorphic side to the stable $\infty$-category of ind-coherent sheaves on the moduli stack of (arithmetic) $L$-parameters, generalizing earlier work of the first author with Ben-Zvi, Chen and Nadler [BZCHN24] for $\mathrm{GL}_n$. Moreover, for an $\textit{arbitrary}$ quasi-split reductive $p$-adic group $G$, we formulate a classical local Langlands framework under which a classical correspondence can be lifted to an $\infty$-categorical correspondence. Our result builds upon the phenomenal recent work of Zhu [Zhu25] on the unipotent block, as well as structure results such as [Sol22] on the automorphic side and [DHKM25] on the spectral side. In particular, our work establishes [HM26,Conjecture 8.2.1], which implies that the conditional proof of [HM26] for the Fargues-Scholze categorical local Langlands equivalence [FS24] (conditional on the conjectured compatibility of the Fargues-Scholze construction with spectral Eisenstein series) applies as well to a large class of quasi-split reductive $p$-adic groups $G$.

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arXiv2026

Goal-Oriented Framework for Optical Flow-based Multi-User Multi-Task Video Transmission

Efficient multi-user multi-task video transmission is an important research topic within the realm of current wireless communication systems. To reduce the transmission burden and save communication resources, we propose a goal-oriented semantic communication framework for optical flow-based multi-user multi-task video transmission (OF-GSC). At the transmitter, we design a semantic encoder that consists of a motion extractor and a patch-level optical flow-based semantic representation extractor to effectively identify and select important semantic representations. At the receiver, we design a transformer-based semantic decoder for high-quality video reconstruction and video classification tasks. To minimize the communication time, we develop a deep deterministic policy gradient (DDPG)-based bandwidth allocation algorithm for multi-user transmission. For video reconstruction tasks, our OF-GSC framework achieves a significant improvement in the received video quality, as evidenced by a 13.47% increase in the structural similarity index measure (SSIM) score in comparison to DeepJSCC. For video classification tasks, OF-GSC achieves a Top-1 accuracy slightly surpassing the performance of VideoMAE with only 25% required data under the same mask ratio of 0.3. For bandwidth allocation optimization, our DDPG-based algorithm reduces the maximum transmission time by 25.97% compared with the baseline equal-bandwidth allocation scheme.

eess.IV↗
arXiv2025

StyleQoRA: Quality-Aware Low-Rank Adaptation for Few-Shot Multi-Style Editing

In recent years, image editing has garnered growing attention. However, general image editing models often fail to produce satisfactory results when confronted with new styles. The challenge lies in how to effectively fine-tune general image editing models to new styles using only a limited amount of paired data and a minimum number of parameters. To address this issue, this paper proposes a novel few-shot multi-style editing framework. For this task, we construct a benchmark dataset that encompasses five distinct styles. Correspondingly, we propose Quality-Aware Low-Rank Adaptation for few-shot multi-style editing (StyleQoRA). Our StyleQoRA can automatically determine the optimal rank for each layer through a novel approach that estimates the importance score of each single-rank component using an image quality metric. To balance specialization and knowledge sharing, we design a Mixture-of-Experts (MoE) LoRA with hybrid routing in our StyleQoRA, consisting of style-specific routing to prevent cross-style confusion and style-shared routing to capture common transformation patterns. Additionally, we explore the optimal location to insert LoRA within the Diffusion in Transformer (DiT) model and integrate adversarial learning and flow matching to guide the diffusion training process. Experimental results demonstrate that our proposed method outperforms existing state-of-the-art approaches with significantly fewer LoRA parameters. Our code and dataset are available at https://github.com/cao-cong/FSMSE.

cs.CV↗
arXiv2025

$p$-integrability

In this short note, we prove the equivalence of Grothendieck-Katz $p$-curvature Conjecture with Conjecture F in Ekedahl-Shepherd-Barron-Taylor. More precisely, we show that Conjecture F implies the $p$-curvature conjecture, and that the $p$-curvature Conjecture implies Conjecture F for the foliation attached to a vector bundle with integrable connection.

math.AG↗
arXiv2025

Similar Formation Control of Multi-Agent Systems over Directed Acyclic Graphs via Matrix-Weighted Laplacian

This brief proposes a distributed formation control strategy via matrix-weighted Laplacian that can achieve a similar formation in 2-D planar using inter-agent relative displacement measurement. Formation patterns that include translation, rotation, and scaling can be characterized by the null space of the matrix-weighted Laplacian associated with the topological graph. The main contribution of this brief is to extend the similar formation problem of undirected graphs to directed acyclic graphs and provide the necessary algebraic criteria for leader selection. Stability analysis, illustrative examples, and simulation results are provided.

eess.SY↗
arXiv2025

On depth-zero characters of p-adic groups

We show new properties of the Langlands correspondence for arbitrary tori over local fields. Furthermore, we give a detailed analysis of depth-zero characters of reductive p-adic groups, for groups that may be wildly ramified. We present several different definitions of ``depth-zero'' for characters, and show that these notions are in fact equivalent. These results are useful for proving new cases of local Langlands correspondences, in particular for depth zero representations.

math.NT↗
arXiv2025

Threshold Attention Network for Semantic Segmentation of Remote Sensing Images

Semantic segmentation of remote sensing images is essential for various applications, including vegetation monitoring, disaster management, and urban planning. Previous studies have demonstrated that the self-attention mechanism (SA) is an effective approach for designing segmentation networks that can capture long-range pixel dependencies. SA enables the network to model the global dependencies between the input features, resulting in improved segmentation outcomes. However, the high density of attentional feature maps used in this mechanism causes exponential increases in computational complexity. Additionally, it introduces redundant information that negatively impacts the feature representation. Inspired by traditional threshold segmentation algorithms, we propose a novel threshold attention mechanism (TAM). This mechanism significantly reduces computational effort while also better modeling the correlation between different regions of the feature map. Based on TAM, we present a threshold attention network (TANet) for semantic segmentation. TANet consists of an attentional feature enhancement module (AFEM) for global feature enhancement of shallow features and a threshold attention pyramid pooling module (TAPP) for acquiring feature information at different scales for deep features. We have conducted extensive experiments on the ISPRS Vaihingen and Potsdam datasets. The results demonstrate the validity and superiority of our proposed TANet compared to the most state-of-the-art models.

cs.CV↗
arXiv2024

Hecke algebras and local Langlands correspondence for non-singular depth-zero representations

Let G be a connected reductive group over a non-archimedean local field. We say that an irreducible depth-zero (complex) G-representation is non-singular if its cuspidal support is non-singular. We establish a Local Langlands Correspondence for all such representations. We obtain it as a specialization from a categorical version: an equivalence between the category of finite-length non-singular depth-zero G-representations and the category of finite-length right modules of a direct sum of twisted affine Hecke algebras constructed from Langlands parameters. We also show that our LLC and our equivalence of categories have several nice properties, for example compatibility with parabolic induction.

math.RT↗
arXiv2024

Prismatic $F$-Gauges and Fontaine--Laffaille modules

Let $k$ be a perfect field of characteristic $p$ and $W(k)$ its ring of Witt vectors. We construct an equivalence of categories between the full subcategory of the derived category of quasi-coherent sheaves on the syntomification of $W(k)$ spanned by objects whose Hodge-Tate weights are between $[0,p-2]$ and an appropriate derived category of Fontaine-Laffaille modules.

math.NT↗
arXiv2023

Uniformizing the moduli stacks of global $G$-Shtukas II

We show that the moduli spaces of bounded global $\mathcal{G}$-Shtukas with pairwise colliding legs admit $p$-adic uniformization isomorphisms by Rapoport-Zink spaces. Here $\mathcal{G}$ is a smooth affine group scheme with connected fibers and reductive generic fiber, i.e. we do not assume it to be parahoric, or even hyperspecial. Moreover, we deduce the Langlands-Rapoport Conjecture over function fields in the case of colliding legs using our uniformization theorem.

math.NT↗
arXiv2023

Task-Oriented Semantics-Aware Communication for Wireless UAV Control and Command Transmission

To guarantee the safety and smooth control of Unmanned Aerial Vehicle (UAV) operation, the new control and command (C&C) data type imposes stringent quality of service (QoS) requirements on the cellular network. However, the existing bit-oriented communication framework is already approaching the Shannon capacity limit, which can hardly guarantee the ultra-reliable low latency communications (URLLC) service for C&C transmission. To solve the problem, task-oriented semantics-aware (TOSA) communication has been proposed recently by jointly exploiting the context of data and its importance to the UAV control task. However, to the best of our knowledge, an explicit and systematic TOSA communication framework for emerging C&C data type remains unknown. Therefore, in this paper, we propose a TOSA communication framework for C&C transmission and define its value of information based on both the similarity and age of information (AoI) of C&C signals. We also propose a deep reinforcement learning (DRL) algorithm to maximize the TOSA information. Last but not least, we present the simulation results to validate the effectiveness of our proposed TOSA communication framework.

eess.SY↗
arXiv2023

Refined Selmer equations for the thrice-punctured line in depth two

In [Kim05], Kim gave a new proof of Siegel's Theorem that there are only finitely many $S$-integral points on $\mathbb P^1_{\mathbb Z}\setminus\{0,1,\infty\}$. One advantage of Kim's method is that it in principle allows one to actually find these points, but the calculations grow vastly more complicated as the size of $S$ increases. In this paper, we implement a refinement of Kim's method to explicitly compute various examples where $S$ has size $2$ which has been introduced in [BD19]. In so doing, we exhibit new examples of a natural generalisation of a conjecture of Kim.

math.NT↗
arXiv2023

The Explicit Local Langlands Correspondence for $G_2$

We develop a general strategy for constructing the explicit Local Langlands Correspondences for $p$-adic reductive groups via reduction to LLC for supercuspidal representations of proper Levi subgroups, using Hecke algebra techniques. As an example of our general strategy, we construct the explicit Local Langlands Correspondence for the exceptional group $G_2$ over a nonarchimedean local field, with explicit $L$-packets and explicit matching between the group and Galois sides. We also give a list of characterizing properties for our LLC. In \cite{G2-stability}, we complete unique characterization using stability property of our $L$-packets. For intermediate series, we build on our previous results on Hecke algebras. For principal series, we improve previous works of Muic etc. and obtain more explicit descriptions on both group and Galois sides. Moreover, we show the existence of non-unipotent \textit{singular} supercuspidal representations of $G_2$, and exhibit them in \textit{mixed} $L$-packets mixing supercuspidal representations with non-supercuspidal ones. Furthermore, our LLC satisfies a list of expected properties, including the compatibility with cuspidal support.

math.RT↗
arXiv2022

Geometrization of the Satake transform for mod $p$ Hecke algebras

We geometrize the mod $p$ Satake isomorphism of Herzig and Henniart-Vign\'eras using Witt vector affine flag varieties for reductive groups in mixed characteristic. We deduce this as a special case of a formula, stated in terms of the geometry of generalized Mirkovi\'c-Vilonen cycles, for the Satake transform of an arbitrary pararhoric mod $p$ Hecke algebra with respect to an arbitrary Levi subgroup. Moreover, we prove an explicit formula for the convolution product in an arbitrary parahoric mod $p$ Hecke algebra. Our methods involve the constant term functors inspired from the geometric Langlands program, and we also treat the case of reductive groups in equal characteristic. We expect this to be a first step towards a geometrization of a mod $p$ Local Langlands Correspondence.

math.NT↗
arXiv2022

The connected components of affine Deligne--Lusztig varieties

We compute the connected components of arbitrary parahoric level affine Deligne-Lusztig varieties and local Shimura varieties, thus resolving a folklore conjecture in full generality (even for non-quasisplit groups). We achieve this by relating them to the connected components of infinite level moduli spaces of p-adic shtukas, where we use v-sheaf-theoretic techniques such as the specialization map of kimberlites. Along the way, we give a p-adic Hodge-theoretic characterization of HN-irreducibility. As applications, we obtain many results on the geometry of integral models of Shimura varieties of Hodge type at arbitrary stabilizer-parahoric levels. In particular, we deduce new CM lifting results on integral models of Shimura varieties for quasisplit groups at parahoric levels that arise as stabilizer Bruhat-Tits group schemes.

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arXiv2022

Surjectivity of Galois Representations in Rational Families of Abelian Varieties

In this article, we show that for any non-isotrivial family of abelian varieties over a rational base with big monodromy, those members that have adelic Galois representation with image as large as possible form a density-$1$ subset. Our results can be applied to a number of interesting families of abelian varieties, such as rational families dominating the moduli of Jacobians of hyperelliptic curves, trigonal curves, or plane curves. As a consequence, we prove that for any dimension $g \geq 3$, there are infinitely many abelian varieties over $\mathbb Q$ with adelic Galois representation having image equal to all of $\operatorname{GSp}_{2g}(\widehat{\mathbb Z})$.

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