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Xun Lin

Publications and source records attributed to Xun Lin.

45 records · Page 3Linked to original sources
arXiv2024

Suppress and Rebalance: Towards Generalized Multi-Modal Face Anti-Spoofing

Face Anti-Spoofing (FAS) is crucial for securing face recognition systems against presentation attacks. With advancements in sensor manufacture and multi-modal learning techniques, many multi-modal FAS approaches have emerged. However, they face challenges in generalizing to unseen attacks and deployment conditions. These challenges arise from (1) modality unreliability, where some modality sensors like depth and infrared undergo significant domain shifts in varying environments, leading to the spread of unreliable information during cross-modal feature fusion, and (2) modality imbalance, where training overly relies on a dominant modality hinders the convergence of others, reducing effectiveness against attack types that are indistinguishable sorely using the dominant modality. To address modality unreliability, we propose the Uncertainty-Guided Cross-Adapter (U-Adapter) to recognize unreliably detected regions within each modality and suppress the impact of unreliable regions on other modalities. For modality imbalance, we propose a Rebalanced Modality Gradient Modulation (ReGrad) strategy to rebalance the convergence speed of all modalities by adaptively adjusting their gradients. Besides, we provide the first large-scale benchmark for evaluating multi-modal FAS performance under domain generalization scenarios. Extensive experiments demonstrate that our method outperforms state-of-the-art methods. Source code and protocols will be released on https://github.com/OMGGGGG/mmdg.

cs.CV↗
arXiv2024

Categorical Torelli theorems for Gushel-Mukai threefolds

We show that a general ordinary Gushel-Mukai(GM) threefold $X$ is reconstructed from the Kuznetsov component $\mathcal{K}u(X)$ together with an extra data coming from tautological sub-bundle of Grassmannian $\mathrm{Gr}(2,5)$. We also prove that $\mathcal{K}u(X)$ determines birational isomorphism class of $X$, while $\mathcal{K}u(X')$ determines the isomorphism class of a general special GM threefold $X'$. As an application, we prove a conjecture of Kuznetsov-Perry in dimension three under a mild assumption. Finally, we use $\mathcal{K}u(X)$ to restate a conjecture of Debarre-Iliev-Manivel regarding fibers of the period map for ordinary GM threefolds.

math.AG↗
arXiv2024

Fully faithful functors, skyscraper sheaves, and birational equivalence

Let $X$ and $Y$ be two smooth projective varieties such that there is a fully faithful exact functor from $D^b(\mathrm{Coh}(X))$ to $D^b(\mathrm{Coh}(Y))$. We show that $X$ and $Y$ are birational equivalent if the functor maps one skyscraper sheaf to a skyscraper sheaf. Further assuming that $X$ and $Y$ are of the same dimension, we show that if $X$ has ample canonical bundle and $H^0(X ,K_X)\neq 0$, or if $X$ is a K3 surface with Picard number one, then $Y$ is birational to a Fourier--Mukai partner of $X$.

math.AG↗
arXiv2023

Infinitesimal categorical Torelli theorems for Fano threefolds

Let $X$ be a smooth Fano variety and $\mathcal{K}u(X)$ the Kuznetsov component. Torelli theorems for $\mathcal{K}u(X)$ says that it is uniquely determined by a polarized abelian variety attached to it. An infinitesimal Torelli theorem for $X$ says that the differential of the period map is injective. A categorical variant of infinitesimal Torelli theorem for $X$ says that the morphism $H^1(X,T_X)\xrightarrowη HH^2(\mathcal{K}u(X))$ is injective. In the present article, we use the machinery of Hochschild (co)homology to relate the three Torelli-type theorems for smooth Fano varieties via a commutative diagram. As an application, we first prove infinitesimal categorical Torelli theorem for a class of prime Fano threefolds. Then we prove a restatement of the Debarre-Iliev-Manivel conjecture infinitesimally.

math.AG↗
arXiv2021

Some remarks of Hochschild homology and semi-orthogonal decompositions

Given a nontrivial semi-orthogonal decomposition $\Perf(\X)=\langle \mathcal{A},\mathcal{B}\rangle$, and assume that the base locus of $ω_{\X}$ is a proper closed subset, it was proved by Kotaro Kawatani and Shinnosuke Okawa that all skyscraper sheaves $\k(\x)$ with $\x\notin \mathsf{Bs}\vert ω_{\X}\vert$ belong to exactly one and only one of the components. It is natural to ask which one it is, and whether we can determine this by certain linear invariants. In this note we use Hochschild homology of derived category of coherent sheaves with support to provide another proof that if the $-\n^þ$ Hochschild homology of a component is nonzero, then the skyscraper sheaves we consider above belong to such component, which was originally proved by Dmitrii Pirozhkov \cite[Lemma 5.3]{pirozhkov2020admissible}. Furthermore, we prove a conjecture proposed by Kuznetsov about classifying $\n$-Calabi-Yau admissible subcategory of $\Perf(\X)$ ($\dim \X=\n$) for certain projective smooth variety $\X$ if we put more assumptions to the Calabi-Yau categories. Finally we remark that the additive invariants of derived category with support could provide more linear obstructions to semi-orthogonal decompositions.

math.AG↗
arXiv2021

On nonexistence of semi-orthogonal decompositions in algebraic geometry

The nonexistence of semi-orthogonal decompositions in algebraic geometry is known to be governed by the base locus of the canonical bundle. We study another locus, namely the intersection of the base loci of line bundles that are isomorphic to the canonical bundle in the Néron-Severi group, and show that it also governs the nonexistence of semi-orthogonal decompositions. As an application by using algebraically moving techniques, we prove that the bounded derived category of the $i$-th symmetric product of a smooth projective curve $C$ has no nontrivial semi-orthogonal decompositions when the genus $g(C)\geq 2$ and $i\leq g(C)-1$. We prove indecomposability of derived categories of some examples of elliptic surfaces with $P_{g}(X)=0$, and some natural examples of minimal surfaces of general type. Finally, an inequality involving phases of skyscraper sheaves for any Bridgeland stability condition is obtained.

math.AG↗
arXiv2021

Noncommutative Hodge conjecture

The paper provides a version of the rational Hodge conjecture for $\3\dg$ categories. The noncommutative Hodge conjecture is equivalent to the version proposed in \cite{perry2020integral} for admissible subcategories. We obtain examples of evidence of the Hodge conjecture by techniques of noncommutative geometry. Finally, we show that the noncommutative Hodge conjecture for smooth proper connective $\3\dg$ algebras is true.

math.AG↗
arXiv2019

A Distributed Approach towards Discriminative Distance Metric Learning

Distance metric learning is successful in discovering intrinsic relations in data. However, most algorithms are computationally demanding when the problem size becomes large. In this paper, we propose a discriminative metric learning algorithm, and develop a distributed scheme learning metrics on moderate-sized subsets of data, and aggregating the results into a global solution. The technique leverages the power of parallel computation. The algorithm of the aggregated distance metric learning (ADML) scales well with the data size and can be controlled by the partition. We theoretically analyse and provide bounds for the error induced by the distributed treatment. We have conducted experimental evaluation of ADML, both on specially designed tests and on practical image annotation tasks. Those tests have shown that ADML achieves the state-of-the-art performance at only a fraction of the cost incurred by most existing methods.

cs.LG↗