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Xun Lin

Publications and source records attributed to Xun Lin.

At least 19 recordsLinked to original sources
arXiv2026

Categorical Torelli and Fourier-Mukai partners of hypersurfaces

Let $X\subset\PP^{M-1}$ be a smooth hypersurface of degree $d<M$, and let $\Ku(X)$ be its Kuznetsov component, the orthogonal complement of the line bundles $\OO_X,\dots,\OO_X(M-d-1)$ in the derived category. We prove that $\Ku(X)$ determines $X$ for every smooth quartic in $\PP^{4k+1}$, $k\geq1$; together with earlier work, this gives categorical Torelli for every smooth hypersurface of degree $d<M$ with $d\nmid M$. The same algebraic reconstruction proves the classical generic Torelli theorem for these quartics, which completes generic Torelli for smooth hypersurfaces whose degree does not divide $M$, cubic surfaces excepted. When $d$ divides $M$, the Kuznetsov component is a Calabi--Yau category, as for cubic fourfolds, where categorical Torelli is known to fail. We show that, apart from cubic fourfolds, such a hypersurface has a number of Fourier--Mukai partners bounded by a constant depending only on $d$ and $M$, and that categorical Torelli holds in sufficiently large degree, in every dimension. The main tool is a deformation theorem: when geometric deformations surject onto the second Hochschild cohomology of the Kuznetsov components, an equivalence deforms together with the hypersurfaces, so statements proved for general hypersurfaces extend to all smooth ones.

math.AG↗
arXiv2026

Infinitesimal Torelli problems for special Gushel-Mukai and related Fano threefolds: Hodge theoretical and categorical perspectives

A hyperelliptic curve is the classical example of a variety for which the global Torelli theorem holds while the differential of the period map has a kernel, forced by the extra involution. We study the analogous phenomenon for Fano threefolds that are double covers of rigid Fano threefolds branched along a K3 surface, mainly special Gushel--Mukai threefolds. We prove that the part of the infinitesimal period map invariant under the covering involution is injective, so that the kernel is exactly the three-dimensional space of anti-invariant deformations, one more than for ordinary Gushel--Mukai threefolds. We give a Hodge-theoretic proof, which reduces to a twisted infinitesimal Torelli theorem for the branch K3 surface, and a categorical proof, based on Kuznetsov's normal Hochschild cohomology, which also applies in genus eight and identifies the kernel with the tangent space to a distinguished point of a Bridgeland moduli space. The two descriptions of the kernel are related directly through the Plücker net and the conic of special lines of the quintic del Pezzo threefold. Finally, ordinary Verra threefolds satisfy the infinitesimal Torelli theorem, while special ones have a one-dimensional kernel; in both cases the kernel agrees with that of the categorical period map of a Clifford component, and it is the tangent space to the deformations of a canonical spinor bundle, which is rigid in the ordinary case and obstructed at second order in the special case.

math.AG↗
arXiv2026

Categorical Torelli theorem for smooth Fano varieties

Let $X$ be a smooth Fano variety and $H$ an ample line bundle with $-K_X=rH$ and $r\le\dim X-2$. We prove that the appropriately defined Kuznetsov component of $X$ with respect to $H$, together with its rotation functor, determines $(X,H)$ when $H$ is very ample, and more generally when $H$ is globally generated and the image of the morphism defined by $|H|$ has a hypersurface as projective dual. As a consequence we prove Perry's conjecture, which predicts that a smooth Fano variety $X$ is determined up to isomorphism by the orthogonal complement $\mathcal{O}_X^{\perp}$ of its structure sheaf in $\mathrm{D}^b(X)$, for all smooth Fano varieties of dimension at least three with very ample anticanonical bundle, and more generally with globally generated anticanonical bundle whose image has a hypersurface as dual. We also prove it when a multiple $-qK_X$ is very ample and the corresponding embedding is cut out by equations of degree at most $(\mathrm{dim} X-1)/q$. The idea is to read off $X$ from its hyperplane sections. We show that the Kuznetsov component with its rotation functor contains the residual categories of all hyperplane sections of $X$, singular ones included. The sections whose categories are not smooth form the projective dual of $X$, and classical projective duality recovers $X$. When $H$ is not very ample, the nodes of a single tangent hyperplane section, defined over a function field and detected by its singularity category, recover $X$ as a finite cover of its image. Applications include Fano hypersurfaces, all prime Fano threefolds of index one and genus at least three, cyclic covers of quadrics, Fano complete intersections and Gushel--Mukai varieties.

math.AG↗
arXiv2026

PertMind: Eliciting Emergent Biological Reasoning in LLM via Reinforcement Learning on Cellular Perturbation Data

Large language models can describe mechanisms, yet scalable post-training still depends on costly, manually curated biological reasoning traces. Here we show that cellular perturbation atlases can instead become reinforcement-learning environments, where measured gene responses provide computable rewards for biological reasoning. We introduce PertMind, which combines trusted-trajectory supervised initialization with gene-, pathway-, and format-level reinforcement signals. Although trained only on forward perturbation-response prediction, PertMind improves response inference in unseen cellular contexts while retaining general language capabilities. It also transfers, without task-specific post-training, to reverse perturbation identification, double-perturbation reasoning, phenotypic-screen prioritization, and biological-process interpretation. PertMind further generates biological profiles that support competitive gene, cell, and donor representations across multiscale downstream tasks. These results support the hypothesis that reinforcement on experimental endpoints can concentrate reusable biological strategies already accessible to pretrained models. More broadly, perturbation-derived reinforcement learning offers a scalable route for transforming expanding experimental atlases into training environments for general-purpose biological reasoning.

cs.LG↗
arXiv2026

Categorical reconstruction of del Pezzo surfaces: Hochschild--Serre algebras and spinor modifications

We prove that, for every smooth complex del Pezzo surface of degree at most four, the enhanced right orthogonal to the structure sheaf determines the surface up to isomorphism. In degrees one, two, and three, we recover the anticanonical equation from intrinsic pieces of the Hochschild-Serre algebra via graded matrix factorizations; in degree four, the relevant Serre diagonal recovers the orbifold canonical ring associated with the pencil of quadrics. We also give an alternative proof in degrees one and two using the Bertini and Geiser involutions, equivariant topological K-theory, and classical Torelli. Then, we study the Clifford component associated with a conic bundle structure over the projective line. In every degree at most four, we construct an abstract spinor bundle whose spinor modification produces another, generally non-isomorphic, del Pezzo surface. We show via Kuznetsov's modification theorem that the relevant base-linear equivalences are precisely those induced by spinor modifications.

math.AG↗
arXiv2026

Categorical Torelli theorem for (weighted) hypersurfaces via singularity category

We prove categorical Torelli theorems for ordinary and weighted hypersurfaces using the singularity category of the completed affine cone. For Fano hypersurfaces we use the Kuznetsov component, whereas for hypersurfaces of general type we use the full category of graded matrix factorizations. When the degree is coprime to the sum of the weights, the internal grading shift can be expressed in terms of the Serre functor and the cohomological shift. Its dg orbit is therefore intrinsic and, after taking the perfect hull, agrees with the dg singularity category of the completed cone. The formal singularity is then recovered by the categorical Mather--Yau theorem. For ordinary homogeneous equations, the resulting formal equivalence induces a projective linear equivalence; in the weighted setting the dual torus action determines the grading of the Tjurina algebra and hence the weighted homogeneous equation. The argument gives a uniform proof for Fano hypersurfaces under the stated numerical assumptions and proves new categorical Torelli theorems for hypersurfaces of general type.

math.AG↗
arXiv2026

Group action of Hochschild-Serre algebra and categorical reconstruction

We study the action of the Serre functor of smooth proper dg categories at their Hochschild-Serre algebra, and the invariant sub-aglebra of the Serre functor. As applications, we prove some theorems of categorical Torelli. Namely, let $\Ku(\X)$ be the Kuznetsov component of degree $d$ smooth hypersurface in weighted projective space $\mathbb{P}(a_0, a_1, \cdots, a_n)$, where the common maximal divisor $\gcd(d, \sum^{n}_{i=0}a_{i})=1$. We show the categorical Torelli for $\Ku(\X)$. We show that the $\mathbb{C}^{\ast}$ equivariant matrix factorization category associated with a quasi-homogeneous polynomial function $f$ that has an isolated singularity together with a twisted functor $\{1\}$ reconstructs $f$ up to an isomorphism.

math.AG↗
arXiv2026

A note on the noncommutative Hodge conjecture for graded matrix factorizations

Let $m\geq 2$ and $d\geq 7$. We consider homogeneous polynomials in $2m+2$ variables of the form $f=F_0(u_0,v_0)+\cdots+F_m(u_m,v_m)$, where the $F_i$ are independently very general squarefree binary forms of degree $d$. We prove the rational noncommutative Hodge conjecture for the dg category $\mathrm{MF}^{\mathrm{gr}}(f)$ of graded matrix factorizations. Its Hochschild homology is the direct sum of the scalar-invariant Jacobian sector and $d-1$ one-dimensional point sectors. Boundary--bulk images of explicit rank-one factorizations generate a lattice of rank $(d-1)^{m+1}$ in the identity sector, while grading shifts of the stabilized residue field generate all point sectors. A reduced-Burau calculation shows that the identity-sector lattice exhausts the rational Hodge classes at a very general parameter. Consequently, $\dim_{\mathbb{Q}}\operatorname{Hdg}\bigl(\mathrm{MF}^{\mathrm{gr}}(f),\mathbb{Q}\bigr)=(d-1)^{m+1}+d-1$, and the rational topological $K$-rank is $\bigl((d-1)^{2m+2}+d-1\bigr)/d+d-1$. Finally, applying the additivity of the noncommutative Hodge conjecture for semiorthogonal decompositions together with Orlov's decompositions for Fano, Calabi--Yau, and general-type hypersurfaces proves the rational Hodge conjecture for the associated smooth projective hypersurface.

math.AG↗
arXiv2026

Semiorthogonal indecomposability for Hilbert schemes of points on integral locally planar curves

Let $C$ be an integral projective curve of arithmetic genus $g$ with locally planar singularities over an algebraically closed field. We prove that for every $1\leq n\leq g-1$, both $\mathrm{Perf}(\mathrm{Hilb}^n(C))$ and $\mathrm{D^b_{coh}}(\mathrm{Hilb}^n(C))$ are semiorthogonally indecomposable. We also establish the corresponding relative $S$-linear statement for a flat family of such curves over a connected base $S$, with admissibility required in the $\mathrm{D^b_{coh}}$ case. Our results hold in arbitrary characteristic.

math.AG↗
arXiv2026

MedGame: Storytelling Gamification Empowered by Large Language Models for Medical Education

Large Language Models (LLMs) show promise for medical education, but most existing systems focus on localized interactions such as question answering or single-turn feedback, rather than organizing an entire clinical case into a decision-centered learning trajectory. We introduce \textit{MedGame}, a framework that transforms static clinical cases into structured, executable storytelling games. MedGame uses a dual-engine design: a Medical Narrative Designer synthesizes case-grounded clinical storylines with states and decision nodes, while a Story Director converts them into dependency-aware multimodal orchestration plans rendered by our released interactive platform. We construct MedGame Bench, a 5,000-case benchmark and evaluation protocol for Medical Narrative Generation and Story Direction. Experiments show that task-specific fine-tuning substantially improves open-source LLMs on MedGame Bench and narrows the gap with commercial models. A pilot student study further shows that learners perceive MedGame as more engaging and useful than text-only alternatives.

cs.CL↗
arXiv2026

AV-Master: Dual-Path Comprehensive Perception Makes Better Audio-Visual Question Answering

Audio-Visual Question Answering (AVQA) requires models to effectively utilize both visual and auditory modalities to answer complex and diverse questions about audio-visual scenes. However, existing methods lack sufficient flexibility and dynamic adaptability in temporal sampling and modality preference awareness, making it difficult to focus on key information based on the question. This limits their reasoning capability in complex scenarios. To address these challenges, we propose a novel framework named AV-Master. It enhances the model's ability to extract key information from complex audio-visual scenes with substantial redundant content by dynamically modeling both temporal and modality dimensions. In the temporal dimension, we introduce a dynamic adaptive focus sampling mechanism that progressively focuses on audio-visual segments most relevant to the question, effectively mitigating redundancy and segment fragmentation in traditional sampling methods. In the modality dimension, we propose a preference-aware strategy that models each modality's contribution independently, enabling selective activation of critical features. Furthermore, we introduce a dual-path contrastive loss to reinforce consistency and complementarity across temporal and modality dimensions, guiding the model to learn question-specific cross-modal collaborative representations. Experiments on four large-scale benchmarks show that AV-Master significantly outperforms existing methods, especially in complex reasoning tasks.

cs.CV↗
arXiv2026

Purify then Guide: Rethinking Domain Generalization for Multimodal Face Anti-Spoofing

Face Anti-Spoofing (FAS) is essential for the security of facial recognition systems in diverse scenarios such as payment processing and surveillance. Current multimodal FAS methods often struggle with effective generalization, mainly due to modality-specific biases and domain shifts. To address these challenges, we introduce the \textbf{M}ulti\textbf{m}odal \textbf{D}enoising and \textbf{A}lignment (\textbf{MMDA}) framework. By leveraging the zero-shot generalization capability of CLIP, the MMDA framework effectively suppresses noise in multimodal data through denoising and alignment mechanisms, thereby significantly enhancing the generalization performance of cross-modal alignment. The \textbf{M}odality-\textbf{D}omain Joint \textbf{D}ifferential \textbf{A}ttention (\textbf{MD2A}) module in MMDA concurrently mitigates the impacts of domain and modality noise by refining the attention mechanism based on extracted common noise features. Furthermore, the \textbf{R}epresentation \textbf{S}pace \textbf{S}oft (\textbf{RS2}) Alignment strategy utilizes the pre-trained CLIP model to align multi-domain multimodal data into a generalized representation space in a flexible manner, preserving intricate representations and enhancing the model's adaptability to various unseen conditions. We also design a \textbf{U}-shaped \textbf{D}ual \textbf{S}pace \textbf{A}daptation (\textbf{U-DSA}) module to enhance the adaptability of representations while maintaining generalization performance. These improvements not only enhance the framework's generalization capabilities but also boost its ability to represent complex representations. Our experimental results on four benchmark datasets under different evaluation protocols demonstrate that the MMDA framework outperforms existing state-of-the-art methods in terms of cross-domain generalization and multimodal detection accuracy. The code will be released soon.

cs.CV↗
arXiv2026

VISTA: Variance-Gated Inter-Sequence Test-Time Adaptation for Multi-Sequence MRI Segmentation

Deploying multi-sequence magnetic resonance imaging (MRI) segmentation models to new clinical environments is challenging due to variations in scanners and acquisition protocols. Although existing TTA methods handle basic per-modality shifts, they often fail under a fundamental dual-shift problem, as their adaptation signals fail to capture modality-interaction shifts that disrupt inter-sequence consistency. To address this, we propose Variance-gated Inter-Sequence Test-time Adaptation (VISTA), a source-free framework that tackles modality-interaction shifts. First, we design an Inter-Sequence Intervention Generator (ISIG) that generates a set of consistency probes by swapping low-frequency spectra and entropy-localized patches across sequences, preserving anatomical semantics while challenging inter-sequence dependencies. Second, we introduce Cross-View Disagreement-Aware Pseudo Labeling (CDPL), which establishes a voxel-wise reliability metric using cross-view disagreement variance to dynamically gate self-training and enforce interventional consistency, encouraging the network to rely on robust anatomical semantics. Extensive experiments adapting from standard adult MRI (BraTS-GLI-Pre) to African low-field (BraTS-SSA) and pediatric (BraTS-PED) cohorts show improved performance over competing methods under clinical shifts, achieving absolute Dice improvements of +1.89% (SSA) and +2.82% (PED) over the source model. The code is available at https://github.com/dzp2095/VISTA.

cs.CV↗
arXiv2026

VoxShield: Protecting 3D Medical Datasets from Unauthorized Training via Frequency-Aware Inter-Slice Disruption

The release of public 3D medical image segmentation (MIS) datasets accelerates clinical research but simultaneously heightens risks of unauthorized AI model training. While Unlearnable Examples (UE) offer protection by injecting imperceptible perturbations to prevent effective model learning, existing methods primarily target 2D scenarios. They neglect the volumetric spatial correlations and inter-slice anatomical consistency inherent in 3D medical volumes, which serve as critical learning priors for 3D segmentation networks. To bridge this gap, we propose VoxShield, a UE framework that explicitly targets the volumetric inductive biases of 3D networks. Our core insight is that by systematically dismantling the cross-slice continuity that 3D architectures rely on, we can fundamentally impair their spatial aggregation process. Specifically, we introduce an Inter-Slice Frequency Consistency Disruption mechanism that maximizes the spectral divergence between adjacent slices, injecting structural incoherence along the $z$-axis. Complementing this structural attack, a Semantic Prediction Disruption module is incorporated. By maximizing the $\ell_1$ divergence between clean and perturbed logits, it forces the injected noise to penetrate the entire network and corrupt the final semantic mapping. Experiments on BraTS19 and FLARE21 demonstrate that VoxShield successfully degrades 3D segmentation performance, reducing the DSC from 80.0% to near 0.0% and from 88.6% to 6.8%, respectively. All protections are achieved with minimal perturbation ($ε=4/255$) to preserve high visual fidelity. The code is available at https://github.com/KK266299/VoxShield.

cs.CV↗
arXiv2026

SVC 2026: the Second Multimodal Deception Detection Challenge and the First Domain Generalized Remote Physiological Measurement Challenge

Subtle visual signals, although difficult to perceive with the naked eye, contain important information that can reveal hidden patterns in visual data. These signals play a key role in many applications, including biometric security, multimedia forensics, medical diagnosis, industrial inspection, and affective computing. With the rapid development of computer vision and representation learning techniques, detecting and interpreting such subtle signals has become an emerging research direction. However, existing studies often focus on specific tasks or modalities, and models still face challenges in robustness, representation ability, and generalization when handling subtle and weak signals in real-world environments. To promote research in this area, we organize the Subtle visual Challenge, which aims to learn robust representations for subtle visual signals. The challenge includes two tasks: cross-domain multimodal deception detection and remote photoplethysmography (rPPG) estimation. We hope that this challenge will encourage the development of more robust and generalizable models for subtle visual understanding, and further advance research in computer vision and multimodal learning. A total of 22 teams submitted their final results to this workshop competition, and the corresponding baseline models have been released on the \href{https://sites.google.com/view/svc-cvpr26}{MMDD2026 platform}\footnote{https://sites.google.com/view/svc-cvpr26}

cs.CV↗
arXiv2026

Multimodal Mixture-of-Experts with Retrieval Augmentation for Protein Active Site Identification

Accurate identification of protein active sites at the residue level is crucial for understanding protein function and advancing drug discovery. However, current methods face two critical challenges: vulnerability in single-instance prediction due to sparse training data, and inadequate modality reliability estimation that leads to performance degradation when unreliable modalities dominate fusion processes. To address these challenges, we introduce Multimodal Mixture-of-Experts with Retrieval Augmentation (MERA), the first retrieval-augmented framework for protein active site identification. MERA employs hierarchical multi-expert retrieval that dynamically aggregates contextual information from chain, sequence, and active-site perspectives through residue-level mixture-of-experts gating. To prevent modality degradation, we propose a reliability-aware fusion strategy based on Dempster-Shafer evidence theory that quantifies modality trustworthiness through belief mass functions and learnable discounting coefficients, enabling principled multimodal integration. Extensive experiments on ProTAD-Gen and TS125 datasets demonstrate that MERA achieves state-of-the-art performance, with 90% AUPRC on active site prediction and significant gains on peptide-binding site identification, validating the effectiveness of retrieval-augmented multi-expert modeling and reliability-guided fusion.

cs.AI↗
arXiv2026

StegaFFD: Privacy-Preserving Face Forgery Detection via Fine-Grained Steganographic Domain Lifting

Most existing Face Forgery Detection (FFD) models assume access to raw face images. In practice, under a client-server framework, private facial data may be intercepted during transmission or leaked by untrusted servers. Previous privacy protection approaches, such as anonymization, encryption, or distortion, partly mitigate leakage but often introduce severe semantic distortion, making images appear obviously protected. This alerts attackers, provoking more aggressive strategies and turning the process into a cat-and-mouse game. Moreover, these methods heavily manipulate image contents, introducing degradation or artifacts that may confuse FFD models, which rely on extremely subtle forgery traces. Inspired by advances in image steganography, which enable high-fidelity hiding and recovery, we propose a Stega}nography-based Face Forgery Detection framework (StegaFFD) to protect privacy without raising suspicion. StegaFFD hides facial images within natural cover images and directly conducts forgery detection in the steganographic domain. However, the hidden forgery-specific features are extremely subtle and interfered with by cover semantics, posing significant challenges. To address this, we propose Low-Frequency-Aware Decomposition (LFAD) and Spatial-Frequency Differential Attention (SFDA), which suppress interference from low-frequency cover semantics and enhance hidden facial feature perception. Furthermore, we introduce Steganographic Domain Alignment (SDA) to align the representations of hidden faces with those of their raw counterparts, enhancing the model's ability to perceive subtle facial cues in the steganographic domain. Extensive experiments on seven FFD datasets demonstrate that StegaFFD achieves strong imperceptibility, avoids raising attackers' suspicion, and better preserves FFD accuracy compared to existing facial privacy protection methods.

cs.CV↗