arXiv subjects

Wen Shen

Publications and source records attributed to Wen Shen.

At least 19 recordsLinked to original sources

arXiv2026

Nonnegative curvature on vector bundles over ${CP}^3$ and its blow-up

Every real vector bundle of rank at least seven over $CP^3$, or every real vector bundle of rank at least eight over $CP^3\#CP^3$, admits a complete metric of nonnegative sectional curvature on its total space. The corresponding unit sphere bundles also admit nonnegative sectional curvature. These are fixed-rank results: no additional trivial summand is required, and there is no restriction on any characteristic class. The proof combines low-dimensional bundle classification with the Grove--Ziller lifting theory over $S^4$ and $CP^2$.

math.DG↗

arXiv2026

Evaluating and Explaining Prompt Sensitivity of LLMs Using Interactions

The remarkable capabilities of large language models (LLMs) are often undermined by their instability. Even subtle and semantically irrelevant changes in prompts can cause dramatic fluctuations in performance, a phenomenon known as prompt sensitivity. Previous studies typically evaluate prompt sensitivity by comparing the LLM's final outputs when prompts change. However, such coarse-grained metrics fail to explain the internal reasons for prompt sensitivity. In this paper, we introduce interactions as a fine-grained tool to analyze prompt sensitivity of LLMs. Specifically, we decompose the output score of the LLM into a set of interactions. Each interaction represents a nonlinear relationship involving a set of input variables. We discover that subtle changes to prompts can trigger severe instability in interactions, even when the outputs of the LLM remain the same. To this end, we propose an Interaction-based Prompt Sensitivity (IPS) metric by quantifying changes in interactions when we introduce subtle changes to prompts. We apply the IPS metric to 50 open-source LLMs and uncover four factors that reduce the prompt sensitivity of LLMs, including supervised fine-tuning, increased model scales, dense architectures, and few-shot learning. More crucially, we discover a common mechanism by which these four factors reduce prompt sensitivity: all four factors tend to reduce the prompt sensitivity of low-order interactions (i.e., interactions involving few input variables).

cs.LG↗

arXiv2026

Loop Space Splittings for Codimensional Sphere Bundles

In this paper, we establish two loop decomposition theorems for sphere bundles of real vector bundles under appropriate connectivity and characteristic class assumptions. Specifically, we treat two families of sphere bundles: those arising from rank-$(n-1)$ vector bundles and those from rank-$(n-3)$ vector bundles over closed smooth $n$-manifolds.

math.AT↗

arXiv2026

HLL: Can Agents Cross Humanity's Last Line of Verification?

Multimodal agents are increasingly expected to operate interfaces on behalf of users, raising a central deployment question: can they truly substitute for humans in workflows that services deliberately protect against automation? CAPTCHA verification makes this question concrete. It is not merely a visual puzzle, but a human-verification boundary placed before account creation, content access, form submission, and other protected actions. We introduce \textbf{Humanity's Last Line of Verification (HLL)}, a controlled benchmark that uses interactive CAPTCHA verification to evaluate whether agents can cross this boundary through grounded, human-like interaction rather than recognition alone. HLL covers diverse CAPTCHA interactions and exposes agents to controlled realism stressors, including cluttered webpages, harder task variants, and trace-conditioned validation of the solving process. We evaluate eight frontier multimodal agents in a closed-loop GUI environment. The results show that current agents remain brittle at this human-substitution boundary: performance varies sharply across verification types, degrades under realistic interface conditions, and drops further when correct answers must be supported by valid action traces. By exposing gaps in localization, action calibration, state tracking, and process consistency, HLL provides a concrete testbed for measuring how close multimodal agents are to acting as human substitutes in protected real-world workflows. Our code is available at https://github.com/XinhaoS0101/HLL

cs.AI↗

arXiv2026

AgentDoG 1.5: A Lightweight and Scalable Alignment Framework for AI Agent Safety and Security

Modern open-world agents such as OpenClaw exhibit powerful cross-environment execution capabilities yet introduce broad new safety risk sources. Meanwhile, advanced frontier AI models drastically lower attack barriers, rendering current agent alignment frameworks inadequate for real-world deployment. To tackle these emerging threats, we propose a lightweight and scalable agent safety alignment framework. Specifically, we update the agent safety taxonomy to accommodate emergent risks from Codex and OpenClaw execution scenarios. We further build a taxonomy-guided data engine with influence-function purification to train lightweight AgentDoG 1.5 variants (0.8B, 2B, 4B, and 8B parameters) using only around 1k samples, achieving comparable performance with leading closed-source models (e.g., GPT-5.4). Based on AgentDoG 1.5, we construct a highly efficient agentic safety SFT and RL training environment, which reduces deployment overhead in Docker-level environments by two orders of magnitude. Finally, we deploy AgentDoG 1.5 as a training-free online guardrail for real-time safety moderation. Extensive experimental results indicate that AgentDoG 1.5 achieves state-of-the-art performance in diverse and complex interactive agentic scenarios. All models and datasets are openly released.

cs.AI↗

arXiv2026

Mitigating Action-Relation Hallucinations in LVLMs via Relation-aware Visual Enhancement

Large Vision-Language Models (LVLMs) have achieved remarkable performance on diverse vision-language tasks. However, LVLMs still suffer from hallucinations, generating text that contradicts the visual input. Existing research has primarily focused on mitigating object hallucinations, but often overlooks more complex relation hallucinations, particularly action relations involving interactions between objects. In this study, we empirically observe that the primary cause of action-relation hallucinations in LVLMs is the insufficient attention allocated to visual information. Thus, we propose a framework to locate action-relevant image regions and enhance the LVLM's attention to those regions. Specifically, we define the Action-Relation Sensitivity (ARS) score to identify attention heads that are most sensitive to action-relation changes, thereby localizing action-relevant image regions that contain key visual cues. Then, we propose the Relation-aware Visual Enhancement (RVE) method to enhance the LVLM's attention to these action-relevant image regions. Extensive experiments demonstrate that, compared to existing baselines, our method achieves superior performance in mitigating action-relation hallucinations with negligible additional inference cost. Furthermore, it effectively generalizes to spatial-relation hallucinations and object hallucinations.

cs.CV↗

arXiv2026

Two Regularized Determinants of Laplacian through Resurgence theory

We study two types of regularizations of the determinant of Laplacian on Riemann manifold from the viewpoint of resurgence theory. One is the formal logarithmic derivative of the determinant, and the other is its exponential deformation. Under appropriate conditions, the close formulas for both regularized determinant are established through Borel-Laplace resummation which takes into account the contribution of the singularities along the analytic continuation of Theta series $\hat{\Theta}_{D_X}$. The series resembles the trace of the heat kernel, but is defined via the spectrum of the square-root of the Laplacian. As applications, we revisit the well known formal logarithmic derivative of determinant on $S^1$ and compact Riemann surface with higher genus ($\geq2$) corresponding to the Poisson summation formula and Selberg trace formula respectively. Furthermore, the 1-Gevrey asymptotic behavior of the exponential deformation regularization at infinity is considered whose coefficients are determined by the trace of the heat kernel. In the end, we establish the relationship between the two regularized determinants. In fact, they have the same derivatives when the deformation parameter tends to $0$ in exponentially deformed regularization.

math-ph↗

arXiv2026

A Unified Approach to Interpreting Knowledge Distillation for Large Language Models via Interactions

Despite the success of knowledge distillation (KD) in Large Language Models (LLMs), the underlying mechanism behind its efficacy remains unclear. In this paper, we propose a unified approach to explore the common mechanism of various KD methods using interactions. Specifically, we decompose the output score of the LLM into the sum of numerous interactions. Each interaction represents a nonlinear relationship involving a set of input variables (e.g., words). Based on the decomposed interactions, we discover that the common mechanism underlying various KD methods is the sparsification of interactions, i.e., student models retain fewer interactions for inference while suppressing other interactions to zero effects. Furthermore, we discover that the performance variance across different KD methods arises from their capabilities in handling complex interactions. A KD method typically yields better performance if it enables the student model to achieve higher sparsity of complex interactions. Motivated by these insights, we propose a plug-and-play loss function called Complex Interaction Penalty (CIP) to explicitly enforce the sparsity of complex interactions during the distillation process. Extensive experiments demonstrate that integrating CIP consistently improves the performance of diverse KD methods on both in-domain and out-of-distribution benchmarks.

cs.LG↗

arXiv2026

Multilingual Safety Alignment via Self-Distillation

Large language models (LLMs) exhibit severe multilingual safety misalignment: they possess strong safeguards in high-resource languages but remain highly vulnerable to jailbreak attacks in low-resource languages. Current safety alignment methods generally rely on high-quality response data for each target language, which is expensive and difficult to generate. In this paper, we propose a cross-lingual safeguard transfer framework named Multilingual Self-Distillation (MSD). This framework transfers an LLM's inherent safety capabilities from high-resource (e.g., English) to low-resource (e.g., Javanese) languages, overcoming the need for response data in any language. Our framework is flexible and can be integrated with different self-distillation strategies. Specifically, we implement two concrete methods -- on-policy MSD and off-policy MSD -- both of which enable effective cross-lingual safety transfer using only multilingual queries. Furthermore, we propose Dual-Perspective Safety Weighting (DPSW), a divergence measure to optimize the distillation objective. By jointly considering the perspectives of both the teacher and the student, DPSW adaptively increases the penalty weights on safety-critical tokens while reducing the weights on non-critical tokens. Extensive experiments on representative LLMs across diverse multilingual jailbreak and utility benchmarks demonstrate that our method consistently achieves superior multilingual safety performance. Notably, it generalizes effectively to more challenging datasets and unseen languages while preserving the model's general capabilities.

cs.LG↗

arXiv2026

Local Asymptotic Patterns for Viscous Approximations of Conservation Laws

Solutions to hyperbolic conservation laws can be approximated in many different ways: by vanishing viscosity, relaxations, discrete or semi-discrete numerical schemes, approximation with a nonlocal flux, etc$\ldots$ For some of these methods, general ${\bf L}^1$ convergence results are available. Aim of this paper is to understand the local behavior of these approximations, in a neighborhood of point where the hyperbolic solution has a singularity. Specifically: a point along a shock, or where two shocks interact, or where a new shock is formed. Given a sequence of $\epsilon$-approximate solutions, a general expectation is that, by a suitable local rescaling of coordinates, as $\epsilon\to 0$ a well defined limit is obtained. This corresponds to a specific ``eternal solution" (globally defined both in space and in time) to the approximating equation. Precise results this direction are here given, in the case of vanishing viscosity.

math.AP↗

arXiv2026

TME-PSR: Time-aware, Multi-interest, and Explanation Personalization for Sequential Recommendation

In this paper, we propose a sequential recommendation model that integrates Time-aware personalization, Multi-interest personalization, and Explanation personalization for Personalized Sequential Recommendation (TME-PSR). That is, we consider the differences across different users in temporal rhythm preference, multiple fine-grained latent interests, and the personalized semantic alignment between recommendations and explanations. Specifically, the proposed TME-PSR model employs a dual-view gated time encoder to capture personalized temporal rhythms, a lightweight multihead Linear Recurrent Unit architecture that enables fine-grained sub-interest modeling with improved efficiency, and a dynamic dual-branch mutual information weighting mechanism to achieve personalized alignment between recommendations and explanations. Extensive experiments on real-world datasets demonstrate that our method consistently improves recommendation accuracy and explanation quality, at a lower computational cost.

cs.IR↗

arXiv2026

Loop Space Splittings of Sphere Bundles over Highly Connected Poincar\'e Complexes

Let $m > n \ge 2$, and let $N$ be an $(n-1)$-connected $2n$-Poincar\'e complex. In this paper, we establish sufficient conditions under which the loop space of the total space $M$ of the sphere bundle $S^{m-1} \to M \to N$ (associated to a rank-$m$ real vector bundle over $N$) splits as a product of the loop spaces of $N$ and $S^{m-1}$.

math.AT↗

arXiv2026

Understanding and Defending VLM Jailbreaks via Jailbreak-Related Representation Shift

Large vision-language models (VLMs) often exhibit weakened safety alignment with the integration of the visual modality. Even when text prompts contain explicit harmful intent, adding an image can substantially increase jailbreak success rates. In this paper, we observe that VLMs can clearly distinguish benign inputs from harmful ones in their representation space. Moreover, even among harmful inputs, jailbreak samples form a distinct internal state that is separable from refusal samples. These observations suggest that jailbreaks do not arise from a failure to recognize harmful intent. Instead, the visual modality shifts representations toward a specific jailbreak state, thereby leading to a failure to trigger refusal. To quantify this transition, we identify a jailbreak direction and define the jailbreak-related shift as the component of the image-induced representation shift along this direction. Our analysis shows that the jailbreak-related shift reliably characterizes jailbreak behavior, providing a unified explanation for diverse jailbreak scenarios. Finally, we propose a defense method that enhances VLM safety by removing the jailbreak-related shift (JRS-Rem) at inference time. Experiments show that JRS-Rem provides strong defense across multiple scenarios while preserving performance on benign tasks.

cs.CV↗

arXiv2026

A Uniqueness Condition for Conservation Laws with Discontinuous Gradient-Dependent Flux

The paper is concerned with a scalar conservation law with discontinuous gradient-dependent flux. Namely, the flux is described by two different functions $f(u)$ or $g(u)$, when the gradient $u_x$ of the solution is positive or negative, respectively. In the stable case where $f(u)<g(u)$ for all $u\in R$, it was proved in [1] that the limits of vanishing viscosity approximations form a contractive semigroup w.r.t. the $L^1$ distance. Further, they coincide with the limits of a suitable family of front tracking approximations. In the present paper we introduce a simple condition that guarantees that every weak, entropy admissible solution of a Cauchy problem coincides with the corresponding semigroup trajectory, and hence is unique.

math.AP↗

arXiv2026

AgentDoG: A Diagnostic Guardrail Framework for AI Agent Safety and Security

The rise of AI agents introduces complex safety and security challenges arising from autonomous tool use and environmental interactions. Current guardrail models lack agentic risk awareness and transparency in risk diagnosis. To introduce an agentic guardrail that covers complex and numerous risky behaviors, we first propose a unified three-dimensional taxonomy that orthogonally categorizes agentic risks by their source (where), failure mode (how), and consequence (what). Guided by this structured and hierarchical taxonomy, we introduce a new fine-grained agentic safety benchmark (ATBench) and a Diagnostic Guardrail framework for agent safety and security (AgentDoG). AgentDoG provides fine-grained and contextual monitoring across agent trajectories. More Crucially, AgentDoG can diagnose the root causes of unsafe actions and seemingly safe but unreasonable actions, offering provenance and transparency beyond binary labels to facilitate effective agent alignment. AgentDoG variants are available in three sizes (4B, 7B, and 8B parameters) across Qwen and Llama model families. Extensive experimental results demonstrate that AgentDoG achieves state-of-the-art performance in agentic safety moderation in diverse and complex interactive scenarios. All models and datasets are openly released.

cs.AI↗

arXiv2026

ReasonAny: Incorporating Reasoning Capability to Any Model via Simple and Effective Model Merging

Large Reasoning Models (LRMs) with long chain-of-thought reasoning have recently achieved remarkable success. Yet, equipping domain-specialized models with such reasoning capabilities, referred to as "Reasoning + X", remains a significant challenge. While model merging offers a promising training-free solution, existing methods often suffer from a destructive performance collapse: existing methods tend to both weaken reasoning depth and compromise domain-specific utility. Interestingly, we identify a counter-intuitive phenomenon underlying this failure: reasoning ability predominantly resides in parameter regions with low gradient sensitivity, contrary to the common assumption that domain capabilities correspond to high-magnitude parameters. Motivated by this insight, we propose ReasonAny, a novel merging framework that resolves the reasoning-domain performance collapse through Contrastive Gradient Identification. Experiments across safety, biomedicine, and finance domains show that ReasonAny effectively synthesizes "Reasoning + X" capabilities, significantly outperforming state-of-the-art baselines while retaining robust reasoning performance.

cs.CL↗

arXiv2025

The Interaction Bottleneck of Deep Neural Networks: Discovery, Proof, and Modulation

Understanding what kinds of cooperative structures deep neural networks (DNNs) can represent remains a fundamental yet insufficiently understood problem. In this work, we treat interactions as the fundamental units of such structure and investigate a largely unexplored question: how DNNs encode interactions under different levels of contextual complexity, and how these microscopic interaction patterns shape macroscopic representation capacity. To quantify this complexity, we use multi-order interactions [57], where each order reflects the amount of contextual information required to evaluate the joint interaction utility of a variable pair. This formulation enables a stratified analysis of cooperative patterns learned by DNNs. Building on this formulation, we develop a comprehensive study of interaction structure in DNNs. (i) We empirically discover a universal interaction bottleneck: across architectures and tasks, DNNs easily learn low-order and high-order interactions but consistently under-represent mid-order ones. (ii) We theoretically explain this bottleneck by proving that mid-order interactions incur the highest contextual variability, yielding large gradient variance and making them intrinsically difficult to learn. (iii) We further modulate the bottleneck by introducing losses that steer models toward emphasizing interactions of selected orders. Finally, we connect microscopic interaction structures with macroscopic representational behavior: low-order-emphasized models exhibit stronger generalization and robustness, whereas high-order-emphasized models demonstrate greater structural modeling and fitting capability. Together, these results uncover an inherent representational bias in modern DNNs and establish interaction order as a powerful lens for interpreting and guiding deep representations.

cs.LG↗

arXiv2025

Interaction-Aware 4D Gaussian Splatting for Dynamic Hand-Object Interaction Reconstruction

This paper focuses on a challenging setting of simultaneously modeling geometry and appearance of hand-object interaction scenes without any object priors. We follow the trend of dynamic 3D Gaussian Splatting based methods, and address several significant challenges. To model complex hand-object interaction with mutual occlusion and edge blur, we present interaction-aware hand-object Gaussians with newly introduced optimizable parameters aiming to adopt piecewise linear hypothesis for clearer structural representation. Moreover, considering the complementarity and tightness of hand shape and object shape during interaction dynamics, we incorporate hand information into object deformation field, constructing interaction-aware dynamic fields to model flexible motions. To further address difficulties in the optimization process, we propose a progressive strategy that handles dynamic regions and static background step by step. Correspondingly, explicit regularizations are designed to stabilize the hand-object representations for smooth motion transition, physical interaction reality, and coherent lighting. Experiments show that our approach surpasses existing dynamic 3D-GS-based methods and achieves state-of-the-art performance in reconstructing dynamic hand-object interaction.

cs.CV↗