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Xiangyu Zhou

Publications and source records attributed to Xiangyu Zhou.

At least 37 records · Page 2Linked to original sources
arXiv2026

Macaulay representation of the prolongation matrix and the SOS conjecture

Let $z \in \mathbb{C}^n$, and let $A(z,\bar{z})$ be a real valued diagonal bihomogeneous Hermitian polynomial such that $A(z,\bar{z})\|z\|^2$ is a sum of squares, where $\|z\|$ denotes the Euclidean norm of $z$. In this paper, we provide an estimate for the rank of the sum of squares $A(z,\bar{z})\|z\|^2$ when $A(z,\bar{z})$ is not semipositive definite. As a consequence, we confirm the SOS conjecture proposed by Ebenfelt for $4 \leq n \leq 6$ when $A(z,\bar{z})$ is a real valued diagonal (not necessarily bihomogeneous) Hermitian polynomial, and we also give partial answers to the SOS conjecture for $n\geq 7$.

math.CV↗
arXiv2026

A Newton-Okounkov Body Viewpoint on the SOS Conjecture

Let $z\in \mathbb C^n$ be the complex coordinates on $\mathbb C^n$, and $A(z,\bar z)$ be a real-valued Hermitian polynomial. The famous Ebenfelt's SOS conjecture asks for the minimum rank of $A(z,\bar z)\|z\|^2$ under the restriction that $A(z,\bar z)\|z\|^2$ is an SOS. Assume that $A(z,\bar z)$ is bihomogeneous. In the present note, we establish a connection between Ebenfelt's (Weak) SOS Conjecture and the theory of Newton-Okounkov bodies. By reformulating the conjecture in terms of lattice semigroups and their associated Newton-Okounkov convex bodies, we transform the problem of finding the minimal rank of a prolonged sum-of-squares polynomial into an extremal problem in convex geometry. In particular, we prove that this minimal rank is attained at the extreme points of a specific Newton-Okounkov body. Furthermore, if $A(z,\bar z)$ is moreover diagonal, we demonstrate that the relevant extreme points are finitely many rational points, thereby reducing the verification of the conjecture to a computationally tractable problem. This work provides a new tool for attacking the SOS Conjecture.

math.CV↗
arXiv2026

WalkGPT: Grounded Vision-Language Conversation with Depth-Aware Segmentation for Pedestrian Navigation

Ensuring accessible pedestrian navigation requires reasoning about both semantic and spatial aspects of complex urban scenes, a challenge that existing Large Vision-Language Models (LVLMs) struggle to meet. Although these models can describe visual content, their lack of explicit grounding leads to object hallucinations and unreliable depth reasoning, limiting their usefulness for accessibility guidance. We introduce WalkGPT, a pixel-grounded LVLM for the new task of Grounded Navigation Guide, unifying language reasoning and segmentation within a single architecture for depth-aware accessibility guidance. Given a pedestrian-view image and a navigation query, WalkGPT generates a conversational response with segmentation masks that delineate accessible and harmful features, along with relative depth estimation. The model incorporates a Multi-Scale Query Projector (MSQP) that shapes the final image tokens by aggregating them along text tokens across spatial hierarchies, and a Calibrated Text Projector (CTP), guided by a proposed Region Alignment Loss, that maps language embeddings into segmentation-aware representations. These components enable fine-grained grounding and depth inference without user-provided cues or anchor points, allowing the model to generate complete and realistic navigation guidance. We also introduce PAVE, a large-scale benchmark of 41k pedestrian-view images paired with accessibility-aware questions and depth-grounded answers. Experiments show that WalkGPT achieves strong grounded reasoning and segmentation performance. The source code and dataset are available on the \href{https://sites.google.com/view/walkgpt-26/home}{project website}.

cs.CV↗
arXiv2026

Attention Smoothing Is All You Need For Unlearning

Large Language Models are prone to memorizing sensitive, copyrighted, or hazardous content, posing significant privacy and legal concerns. Retraining from scratch is computationally infeasible, whereas current unlearning methods exhibit unstable trade-offs between forgetting and utility, frequently producing incoherent outputs on forget prompts and failing to generalize due to the persistence of lexical-level and semantic-level associations in attention. We propose Attention Smoothing Unlearning (ASU), a principled framework that casts unlearning as self-distillation from a forget-teacher derived from the model's own attention. By increasing the softmax temperature, ASU flattens attention distributions and directly suppresses the lexical-level and semantic-level associations responsible for reconstructing memorized knowledge. This results in a bounded optimization objective that erases factual information yet maintains coherence in responses to forget prompts. Empirical evaluation on TOFU, MUSE, and WMDP, along with real-world and continual unlearning scenarios across question answering and text completion, demonstrates that ASU outperforms the baselines for most unlearning scenarios, delivering robust unlearning with minimal loss of model utility.

cs.LG↗
arXiv2026

Owen-based Semantics and Hierarchy-Aware Explanation (O-Shap)

Shapley value-based methods have become foundational in explainable artificial intelligence (XAI), offering theoretically grounded feature attributions through cooperative game theory. However, in practice, particularly in vision tasks, the assumption of feature independence breaks down, as features (i.e., pixels) often exhibit strong spatial and semantic dependencies. To address this, modern SHAP implementations now include the Owen value, a hierarchical generalization of the Shapley value that supports group attributions. While the Owen value preserves the foundations of Shapley values, its effectiveness critically depends on how feature groups are defined. We show that commonly used segmentations (e.g., axis-aligned or SLIC) violate key consistency properties, and propose a new segmentation approach that satisfies the $T$-property to ensure semantic alignment across hierarchy levels. This hierarchy enables computational pruning while improving attribution accuracy and interpretability. Experiments on image and tabular datasets demonstrate that O-Shap outperforms baseline SHAP variants in attribution precision, semantic coherence, and runtime efficiency, especially when structure matters.

cs.AI↗
arXiv2026

Attention Retention for Continual Learning with Vision Transformers

Continual learning (CL) empowers AI systems to progressively acquire knowledge from non-stationary data streams. However, catastrophic forgetting remains a critical challenge. In this work, we identify attention drift in Vision Transformers as a primary source of catastrophic forgetting, where the attention to previously learned visual concepts shifts significantly after learning new tasks. Inspired by neuroscientific insights into the selective attention in the human visual system, we propose a novel attention-retaining framework to mitigate forgetting in CL. Our method constrains attention drift by explicitly modifying gradients during backpropagation through a two-step process: 1) extracting attention maps of the previous task using a layer-wise rollout mechanism and generating instance-adaptive binary masks, and 2) when learning a new task, applying these masks to zero out gradients associated with previous attention regions, thereby preventing disruption of learned visual concepts. For compatibility with modern optimizers, the gradient masking process is further enhanced by scaling parameter updates proportionally to maintain their relative magnitudes. Experiments and visualizations demonstrate the effectiveness of our method in mitigating catastrophic forgetting and preserving visual concepts. It achieves state-of-the-art performance and exhibits robust generalizability across diverse CL scenarios.

cs.CV↗
arXiv2025

Not All Tokens Are Meant to Be Forgotten

Large Language Models (LLMs), pre-trained on massive text corpora, exhibit remarkable human-level language understanding, reasoning, and decision-making abilities. However, they tend to memorize unwanted information, such as private or copyrighted content, raising significant privacy and legal concerns. Unlearning has emerged as a promising solution, but existing methods face a significant challenge of over-forgetting. This issue arises because they indiscriminately suppress the generation of all the tokens in forget samples, leading to a substantial loss of model utility. To overcome this challenge, we introduce the Targeted Information Forgetting (TIF) framework, which consists of (1) a flexible targeted information identifier designed to differentiate between unwanted words (UW) and general words (GW) in the forget samples, and (2) a novel Targeted Preference Optimization approach that leverages Logit Preference Loss to unlearn unwanted information associated with UW and Preservation Loss to retain general information in GW, effectively improving the unlearning process while mitigating utility degradation. Extensive experiments on the TOFU and MUSE benchmarks demonstrate that the proposed TIF framework enhances unlearning effectiveness while preserving model utility and achieving state-of-the-art results.

cs.LG↗
arXiv2025

Degenerate Complex Hessian type equations on compact Hermitian manifolds and Applications

The aim of this paper is to further develop the theory of the degenerate complex Hessian equations on compact Hermitian manifolds. Building upon the generalization of the Bedford-Taylor pluripotential theory to complex Hessian equations by Kołodziej-Nguyen, we solve these equations in the $(ω, m)$-positive cone, $(ω, m)$-big classes and in nef classes, where $ω$ is a reference Hermitian metric. These results are also new in the Kähler case. Moreover, we adapt our techniques to solve complex Monge-Ampère equations in nef classes with mild singularities. The solutions we obtain, in the compact Kähler case, coincide with those for the complex Monge-Ampère equations in the sense of the non-pluripolar product introduced by Boucksom-Eyssidieux-Guedj-Zeriahi. One of the key ingredients in the proof is the adaption, to the Hermitian setting, of a new a priori $L^\infty$-estimate established by Guo-Phong-Tong and Guo-Phong-Tong-Wang.

math.CV↗
arXiv2025

LumiGen: An LVLM-Enhanced Iterative Framework for Fine-Grained Text-to-Image Generation

Text-to-Image (T2I) generation has made significant advancements with diffusion models, yet challenges persist in handling complex instructions, ensuring fine-grained content control, and maintaining deep semantic consistency. Existing T2I models often struggle with tasks like accurate text rendering, precise pose generation, or intricate compositional coherence. Concurrently, Vision-Language Models (LVLMs) have demonstrated powerful capabilities in cross-modal understanding and instruction following. We propose LumiGen, a novel LVLM-enhanced iterative framework designed to elevate T2I model performance, particularly in areas requiring fine-grained control, through a closed-loop, LVLM-driven feedback mechanism. LumiGen comprises an Intelligent Prompt Parsing & Augmentation (IPPA) module for proactive prompt enhancement and an Iterative Visual Feedback & Refinement (IVFR) module, which acts as a "visual critic" to iteratively correct and optimize generated images. Evaluated on the challenging LongBench-T2I Benchmark, LumiGen achieves a superior average score of 3.08, outperforming state-of-the-art baselines. Notably, our framework demonstrates significant improvements in critical dimensions such as text rendering and pose expression, validating the effectiveness of LVLM integration for more controllable and higher-quality image generation.

cs.LG↗
arXiv2025

Hijacking Large Language Models via Adversarial In-Context Learning

In-context learning (ICL) has emerged as a powerful paradigm leveraging LLMs for specific downstream tasks by utilizing labeled examples as demonstrations (demos) in the preconditioned prompts. Despite its promising performance, crafted adversarial attacks pose a notable threat to the robustness of LLMs. Existing attacks are either easy to detect, require a trigger in user input, or lack specificity towards ICL. To address these issues, this work introduces a novel transferable prompt injection attack against ICL, aiming to hijack LLMs to generate the target output or elicit harmful responses. In our threat model, the hacker acts as a model publisher who leverages a gradient-based prompt search method to learn and append imperceptible adversarial suffixes to the in-context demos via prompt injection. We also propose effective defense strategies using a few shots of clean demos, enhancing the robustness of LLMs during ICL. Extensive experimental results across various classification and jailbreak tasks demonstrate the effectiveness of the proposed attack and defense strategies. This work highlights the significant security vulnerabilities of LLMs during ICL and underscores the need for further in-depth studies.

cs.LG↗
arXiv2025

Learning to Poison Large Language Models for Downstream Manipulation

The advent of Large Language Models (LLMs) has marked significant achievements in language processing and reasoning capabilities. Despite their advancements, LLMs face vulnerabilities to data poisoning attacks, where the adversary inserts backdoor triggers into training data to manipulate outputs. This work further identifies additional security risks in LLMs by designing a new data poisoning attack tailored to exploit the supervised fine-tuning (SFT) process. We propose a novel gradient-guided backdoor trigger learning (GBTL) algorithm to identify adversarial triggers efficiently, ensuring an evasion of detection by conventional defenses while maintaining content integrity. Through experimental validation across various language model tasks, including sentiment analysis, domain generation, and question answering, our poisoning strategy demonstrates a high success rate in compromising various LLMs' outputs. We further propose two defense strategies against data poisoning attacks, including in-context learning (ICL) and continuous learning (CL), which effectively rectify the behavior of LLMs and significantly reduce the decline in performance. Our work highlights the significant security risks present during SFT of LLMs and the necessity of safeguarding LLMs against data poisoning attacks.

cs.LG↗
arXiv2025

Automatic Calibration for Membership Inference Attack on Large Language Models

Membership Inference Attacks (MIAs) have recently been employed to determine whether a specific text was part of the pre-training data of Large Language Models (LLMs). However, existing methods often misinfer non-members as members, leading to a high false positive rate, or depend on additional reference models for probability calibration, which limits their practicality. To overcome these challenges, we introduce a novel framework called Automatic Calibration Membership Inference Attack (ACMIA), which utilizes a tunable temperature to calibrate output probabilities effectively. This approach is inspired by our theoretical insights into maximum likelihood estimation during the pre-training of LLMs. We introduce ACMIA in three configurations designed to accommodate different levels of model access and increase the probability gap between members and non-members, improving the reliability and robustness of membership inference. Extensive experiments on various open-source LLMs demonstrate that our proposed attack is highly effective, robust, and generalizable, surpassing state-of-the-art baselines across three widely used benchmarks. Our code is available at: \href{https://github.com/Salehzz/ACMIA}{\textcolor{blue}{Github}}.

cs.LG↗
arXiv2025

Structure of some mapping spaces

We prove that the path space of a differentiable manifold is diffeomorphic to a Fréchet space, endowing the path space with a linear structure. Furthermore, the base point preserving mapping space consisting of maps from a cube to a differentiable manifold is also diffeomorphic to a Fréchet space. As a corollary of a more general theorem, we prove that the path fibration becomes a fibre bundle for manifolds M. Additionally, we discuss the mapping space from a compact topological space to a differentiable manifold, demonstrating that this space admits the structure of a smooth Banach manifold.

math.DG↗
arXiv2025

Log truncated threshold and zero mass conjecture

For plurisubharmonic functions $φ$ and $ψ$ lying in the Cegrell class of $\mathbb{B}^n$ and $\mathbb{B}^m$ respectively such that the Lelong number of $φ$ at the origin vanishes, we show that the mass of the origin with respect to the measure $(dd^c\max\{φ(z), ψ(Az)\})^n$ on $\mathbb{C}^n$ is zero for $A\in \mbox{Hom}(\mathbb{C}^n,\mathbb{C}^m)=\mathbb{C}^{nm}$ outside a pluripolar set. For a plurisubharmonic function $φ$ near the origin in $\mathbb{C}^n$, we introduce a new concept coined the log truncated threshold of $φ$ at $0$ which reflects a singular property of $φ$ via a log function near the origin (denoted by $lt(φ,0)$) and derive an optimal estimate of the residual Monge-Ampère mass of $φ$ at $0$ in terms of its higher order Lelong numbers $ν_j(φ)$ at $0$ for $1\leq j\leq n-1$, in the case that $lt(φ,0)<\infty$. These results provide a new approach to the zero mass conjecture of Guedj and Rashkovskii, and unify and strengthen well-known results about this conjecture.

math.CV↗
arXiv2024

Generative LLM Powered Conversational AI Application for Personalized Risk Assessment: A Case Study in COVID-19

Large language models (LLMs) have shown remarkable capabilities in various natural language tasks and are increasingly being applied in healthcare domains. This work demonstrates a new LLM-powered disease risk assessment approach via streaming human-AI conversation, eliminating the need for programming required by traditional machine learning approaches. In a COVID-19 severity risk assessment case study, we fine-tune pre-trained generative LLMs (e.g., Llama2-7b and Flan-t5-xl) using a few shots of natural language examples, comparing their performance with traditional classifiers (i.e., Logistic Regression, XGBoost, Random Forest) that are trained de novo using tabular data across various experimental settings. We develop a mobile application that uses these fine-tuned LLMs as its generative AI (GenAI) core to facilitate real-time interaction between clinicians and patients, providing no-code risk assessment through conversational interfaces. This integration not only allows for the use of streaming Questions and Answers (QA) as inputs but also offers personalized feature importance analysis derived from the LLM's attention layers, enhancing the interpretability of risk assessments. By achieving high Area Under the Curve (AUC) scores with a limited number of fine-tuning samples, our results demonstrate the potential of generative LLMs to outperform discriminative classification methods in low-data regimes, highlighting their real-world adaptability and effectiveness. This work aims to fill the existing gap in leveraging generative LLMs for interactive no-code risk assessment and to encourage further research in this emerging field.

cs.CL↗
arXiv2024

Uniqueness of irreducible desingularization of singularities associated to negative vector bundles

We prove that the irreducible desingularization of a singularity given by the Grauert blow down of a negative holomorphic vector bundle over a compact complex manifold is unique up to isomorphism, and as an application, we show that two negative line bundles over compact complex manifolds are isomorphic if and only if their Grauert blow downs have isomorphic germs near the singularities. We also show that there is a unique way to modify a submanifold of a complex manifold to a hypersurface, namely, the blow up of the ambient manifold along the submanifold.

math.AG↗
arXiv2024

Multiplicites and modifications, and singularities associated to blowing down negative vector bundles

We first present the mixed Hilbert-Samuel multiplicities of analytic local rings over \mathbb{C} as generalized Lelong numbers and further represent them as intersection numbers in the context of modifications. As applications, we give estimates or an exact formula for the multiplicities of isolated singularities that given by the Grauert blow-downs of negative holomorphic vector bundles.

math.CV↗