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Xiaojin Zhang

Xiaojin Zhang contributes to research discovery and scholarly infrastructure.

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Published work

12 published item(s)

preprint2026arXiv

ViCrop-Det: Spatial Attention Entropy Guided Cropping for Training-Free Small-Object Detection

Transformer-based architectures have established a dominant paradigm in global semantic perception; however, they remain fundamentally constrained by the profound spatial heterogeneity inherent in natural images. Specifically, the imposition of a uniform global receptive field across regions of varying information density inevitably leads to local feature degradation, particularly in dense conflict zones populated by microscopic targets. To address this mechanistic limitation, we propose ViCrop-Det, a training-free inference framework that introduces adaptive spatial trust region shrinkage. Inspired by the use of attention entropy in anomaly segmentation, ViCrop-Det leverages the detection decoder's cross-attention distribution as an endogenous probe. By utilizing Spatial Attention Entropy (SAE) to heuristically evaluate local spatial ambiguity, the framework executes dynamic spatial routing, allocating a fixed computational budget exclusively to regions exhibiting both high target saliency and high cognitive uncertainty. By shrinking the spatial trust region and injecting high-frequency localized observations, ViCrop-Det actively resolves spatial ambiguity and recovers fine-grained features without requiring architectural modifications. Extensive evaluations on VisDrone and DOTA-v1.5 demonstrate that ViCrop-Det yields competitive performance enhancements, consistently adding +1-3 mAP@50 to RT-DETR-R50 and Deformable DETR with a marginal 20-23\% latency overhead. On MS COCO, $AP_{S}$ improves while $AP_{M}/AP_{L}$ remains stable, indicating precise fine-scale refinement without compromising the global spatial prior. Under compute-matched settings, our adaptive routing strategy comprehensively surpasses uniform slicing baselines, achieving a highly optimized accuracy-speed trade-off.

preprint2023arXiv

Applications of Gorenstein projective $τ$-rigid modules

We first introduce the notion of $CM$-$τ$-tilting free algebras as the generalization of $CM$-free algebras and show the homological properties of $CM$-$τ$-tilting free algebras. Then we give a bijection between Gorenstein projective $τ$-rigid modules and certain modules by using an equivalence established by Kong and Zhang. Finally, we give a partial answer to Tachikawa's first conjecture by using Gorenstein projective $τ$-rigid modules.

preprint2023arXiv

Improved Algorithm for Permutation Testing

For a permutation $π: [K]\rightarrow [K]$, a sequence $f: \{1,2,\cdots, n\}\rightarrow \mathbb R$ contains a $π$-pattern of size $K$, if there is a sequence of indices $(i_1, i_2, \cdots, i_K)$ ($i_1<i_2<\cdots<i_K$), satisfying that $f(i_a)<f(i_b)$ if $π(a)<π(b)$, for $a,b\in [K]$. Otherwise, $f$ is referred to as $π$-free. For the special case where $π= (1,2,\cdots, K)$, it is referred to as the monotone pattern. \cite{newman2017testing} initiated the study of testing $π$-freeness with one-sided error. They focused on two specific problems, testing the monotone permutations and the $(1,3,2)$ permutation. For the problem of testing monotone permutation $(1,2,\cdots,K)$, \cite{ben2019finding} improved the $(\log n)^{O(K^2)}$ non-adaptive query complexity of \cite{newman2017testing} to $O((\log n)^{\lfloor \log_{2} K\rfloor})$. Further, \cite{ben2019optimal} proposed an adaptive algorithm with $O(\log n)$ query complexity. However, no progress has yet been made on the problem of testing $(1,3,2)$-freeness. In this work, we present an adaptive algorithm for testing $(1,3,2)$-freeness. The query complexity of our algorithm is $O(ε^{-2}\log^4 n)$, which significantly improves over the $O(ε^{-7}\log^{26}n)$-query adaptive algorithm of \cite{newman2017testing}. This improvement is mainly achieved by the proposal of a new structure embedded in the patterns.

preprint2022arXiv

A Bijection theorem for Gorenstein projective τ-tilting modules

We introduce the notions of Gorenstein projective $τ$-rigid modules, Gorenstein projective support $τ$-tilting modules and Gorenstein torsion pairs and give a Gorenstein analog to Adachi-Iyama-Reiten&#39;s bijection theorem on support $τ$-tilting modules. More precisely, for an algebra $Λ$, We prove that there is a bijection between the set of Gorenstein projective support $τ$-tilting modules and the set of functorially finite Gorenstein projective torsion classes. As an application, we introduce the notion of CM-$τ$-tilting finite algebras and show that $Λ$ is CM-$τ$-tilting finite if and only if $Λ^{\rm {op}}$ is CM-$τ$-tilting finite. Moreover, we show that the Bongartz completion of a Gorenstein projective $τ$-rigid module need not be a Gorenstein projective $τ$-tilting module.

preprint2022arXiv

A construction of Gorenstein projective tau-tilting modules

We give a construction of Gorenstein projective $τ$-tilting modules in terms of tensor products of modules. As a consequence, we give a class of non-self-injective algebras admitting non-trivial Gorenstein projective $τ$-tilting modules. Moreover, we show that a finite dimensional algebra $Λ$ over an algebraically closed field is $CM$-$τ$-tilting finite if $T_n(Λ)$ is $CM$-$τ$-tilting finite which gives a partial answer to a question on $CM$-$τ$-tilting finite algebras posed by Xie and Zhang.

preprint2022arXiv

Adaptive Double-Exploration Tradeoff for Outlier Detection

We study a variant of the thresholding bandit problem (TBP) in the context of outlier detection, where the objective is to identify the outliers whose rewards are above a threshold. Distinct from the traditional TBP, the threshold is defined as a function of the rewards of all the arms, which is motivated by the criterion for identifying outliers. The learner needs to explore the rewards of the arms as well as the threshold. We refer to this problem as &#34;double exploration for outlier detection&#34;. We construct an adaptively updated confidence interval for the threshold, based on the estimated value of the threshold in the previous rounds. Furthermore, by automatically trading off exploring the individual arms and exploring the outlier threshold, we provide an efficient algorithm in terms of the sample complexity. Experimental results on both synthetic datasets and real-world datasets demonstrate the efficiency of our algorithm.

preprint2022arXiv

Contextual Combinatorial Conservative Bandits

The problem of multi-armed bandits (MAB) asks to make sequential decisions while balancing between exploitation and exploration, and have been successfully applied to a wide range of practical scenarios. Various algorithms have been designed to achieve a high reward in a long term. However, its short-term performance might be rather low, which is injurious in risk sensitive applications. Building on previous work of conservative bandits, we bring up a framework of contextual combinatorial conservative bandits. An algorithm is presented and a regret bound of $\tilde O(d^2+d\sqrt{T})$ is proven, where $d$ is the dimension of the feature vectors, and $T$ is the total number of time steps. We further provide an algorithm as well as regret analysis for the case when the conservative reward is unknown. Experiments are conducted, and the results validate the effectiveness of our algorithm.

preprint2022arXiv

No Free Lunch Theorem for Security and Utility in Federated Learning

In a federated learning scenario where multiple parties jointly learn a model from their respective data, there exist two conflicting goals for the choice of appropriate algorithms. On one hand, private and sensitive training data must be kept secure as much as possible in the presence of \textit{semi-honest} partners, while on the other hand, a certain amount of information has to be exchanged among different parties for the sake of learning utility. Such a challenge calls for the privacy-preserving federated learning solution, which maximizes the utility of the learned model and maintains a provable privacy guarantee of participating parties&#39; private data. This article illustrates a general framework that a) formulates the trade-off between privacy loss and utility loss from a unified information-theoretic point of view, and b) delineates quantitative bounds of privacy-utility trade-off when different protection mechanisms including Randomization, Sparsity, and Homomorphic Encryption are used. It was shown that in general \textit{there is no free lunch for the privacy-utility trade-off} and one has to trade the preserving of privacy with a certain degree of degraded utility. The quantitative analysis illustrated in this article may serve as the guidance for the design of practical federated learning algorithms.

preprint2020arXiv

Classifying $τ$-tilting modules over the Auslander algebra of $K[x]/(x^n)$

We build a bijection between the set $\sttiltΛ$ of isomorphism classes of basic support $τ$-tilting modules over the Auslander algebra $Λ$ of $K[x]/(x^n)$ and the symmetric group $\mathfrak{S}_{n+1}$, which is an anti-isomorphism of partially ordered sets with respect to the generation order on $\sttiltΛ$ and the left order on $\mathfrak{S}_{n+1}$. This restricts to the bijection between the set $\tiltΛ$ of isomorphism classes of basic tilting $Λ$-modules and the symmetric group $\mathfrak{S}_n$ due to Brüstle, Hille, Ringel and Röhrle. Regarding the preprojective algebra $Γ$ of Dynkin type $A_n$ as a factor algebra of $Λ$, we show that the tensor functor $-\otimes_ΛΓ$ induces a bijection between $\sttiltΛ\to\sttiltΓ$. This recover Mizuno&#39;s bijection $\mathfrak{S}_{n+1}\to\sttiltΓ$ for type $A_n$.

preprint2020arXiv

Tilting modules over Auslander-Gorenstein Algebras

For a finite dimensional algebra $Λ$ and a non-negative integer $n$, we characterize when the set $\tilt_nΛ$ of additive equivalence classes of tilting modules with projective dimension at most $n$ has a minimal (or equivalently, minimum) element. This generalize results of Happel-Unger. Moreover, for an $n$-Gorenstein algebra $Λ$ with $n\geq 1$, we construct a minimal element in $\tilt_{n}Λ$. As a result, we give equivalent conditions for a $k$-Gorenstein algebra to be Iwanaga-Gorenstein. Moreover, for an $1$-Gorenstein algebra $Λ$ and its factor algebra $Γ=Λ/(e)$, we show that there is a bijection between $\tilt_1Λ$ and the set $\sttiltΓ$ of isomorphism classes of basic support $τ$-tilting $Γ$-modules, where $e$ is an idempotent such that $eΛ$ is the additive generator of projective-injective $Λ$-modules.