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Fanqi Zeng

Publications and source records attributed to Fanqi Zeng.

7 recordsLinked to original sources

How User-AI Mistreatment Occurs and Matters in Conversational Systems?

Safety research often focuses on model-generated harms, but users may also direct hostility, coercion, and adversarial pressure at models. Understanding how and when that occurs is essential for accurately interpreting model behaviour, alignment drift, and real-world deployment risks. In this paper, we audit 777K English LMSYS-Chat-1M conversations with two independent detectors: an eight-category lexicon for hostility directed at the model, and the dataset's moderation signal; and show that they capture different, weakly overlapping phenomena. The lexicon identifies insults, threats, and jailbreak coercion aimed at the assistant, while moderation flags are dominated by toxic-content solicitation rather than hostility at the model. Together, they mark about 5% of user turns; adjusting the narrower lexicon-harassment union for measured precision puts mistreatment aimed at the assistant at 0.90%. These absolute rates describe arena-style evaluation traffic and should not be read as deployment-wide base rates. We find that user hostility varies 13-fold across models, driven largely by who each model attracts rather than by model behaviour: first-turn hostility spreads far wider than post-response hostility, and more than fifteenfold separates the extremes even after deduplicating opening prompts. Within conversations, assistant apologies are consistently associated with higher odds of next-turn hostility under both detectors; the effect survives restricting to non-refused prior turns and to jailbreak-free conversations, and is positive in 20 of 23 models. Yet across models, more apologetic models receive less hostility overall. Finally, hostility also shows temporal structure, with coercive openings front-loading the first turn while affective hostility accumulates over a session. We release the lexicon, the detector cross-validation pipeline, and all derived tables.

cs.AI↗

Cheng-Yau logarithmic gradient estimates for a nonlinear elliptic equation on smooth metric measure spaces

In this paper, we consider the nonlinear elliptic equation $$Δ_fv^τ+λv=0$$ on a complete smooth metric measure space with $m$-Bakry-Émery Ricci curvature bounded from below, where $τ>0$ and $λ$ are constant. We obtain some new local gradient estimates for positive solutions to the equation using the Nash-Moser iteration technique. As applications of these estimates, we obtain a Liouville type theorem and a Harnack inequality, and the global gradient estimates for such solutions. Our results generalize and improve the estimates in Wang (J. Differential Equations 260:567-585, 2016) and Zhao (Arch. Math. (Basel) 114:457-469, 2020).

math.DG↗

Sharp thresholds limit the benefit of defector avoidance in cooperation on networks

Consider a cooperation game on a spatial network of habitat patches, where players can relocate between patches if they judge the local conditions to be unfavorable. In time, the relocation events may lead to a homogeneous state where all patches harbor the same relative densities of cooperators and defectors or they may lead to self-organized patterns, where some patches become safe havens that maintain an elevated cooperator density. Here we analyze the transition between these states mathematically. We show that safe havens form once a certain threshold in connectivity is crossed. This threshold can be analytically linked to the structure of the patch network and specifically to certain network motifs. Surprisingly, a forgiving defector avoidance strategy may be most favorable for cooperators. Our results demonstrate that the analysis of cooperation games in ecological metacommunity models is mathematically tractable and has the potential to link topics such as macroecological patterns, behavioral evolution, and network topology.

q-bio.PE↗

Rigid properties of generalized $τ$-quasi Ricci-harmonic metrics

In this paper, we study compact generalized $τ$-quasi Ricci-harmonic metrics. In the first part, we explore conditions under which generalized $τ$-quasi Ricci-harmonic metrics are harmonic-Einstein and give some characterization results for it. In the second part, we obtain some rigidity results for compact $(τ, ρ)$-quasi Ricci-harmonic metrics which are special case of generalized $τ$-quasi Ricci-harmonic metrics. In the third part, we shall give two gap theorems for compact $τ$-quasi Ricci-harmonic metrics by showing some necessary and sufficient conditions for the metrics to be harmonic-Einstein.

math.DG↗

The Mean Curvature Flow in Minkowski Spaces

Studying the geometric flow plays a powerful role in mathematics and physics. In this paper, we introduce the mean curvature flow on Finsler manifolds and give a number of examples of the mean curvature flow. For Minkowski spaces, a special case of Finsler manifolds, we will prove the existence and uniqueness for solution of the mean curvature flow and prove that the flow preserves the convexity and mean convexity. We also derive some comparison principles for the mean curvature flow.

math.DG↗

Interactive Levy Flight in Interest Space

Compared to the well-studied topic of human mobility in real geographic space, very few studies focus on human mobility in virtual space, such as interests, knowledge, ideas, and so forth. However, it relates to the issues of management of public opinions, knowledge diffusion, and innovation. In this paper, we assume that the interests of a group of online users can span a Euclidean space which is called interest space, and the transfers of user interests can be modeled as the Levy Flight on the interest space. To consider the interaction between users, we assume that the random walkers are not independent but interact each other indirectly via the digital resources in the interest space. The model can successfully reproduce a set of scaling laws for describing the growth of the attention flow networks of real online communities, and the ranges of the exponents of the scaling are similar with the empirical data. Further, we can infer parameters for describing the individual behaviors of the users according to the scaling laws of the empirical attention flow network. Our model can not only provide theoretical understanding on human online behaviors, but also has wide potential applications, such as dissemination and management of public opinions, online recommendation, etc.

cs.SI↗

Monotonicity of eigenvalues of geometric operaters along the Ricci-Bourguignon flow

In this paper, we study monotonicity of eigenvalues of Laplacian-type operator $-Δ+cR$, where $c$ is a constant, along the Ricci-Bourguignon flow. For $c\neq0$, We derive monotonicity of the lowest eigenvalue of Laplacian-type operator $-Δ+cR$ which generalizes some results of Cao \cite{Cao2007}. For $c=0$, We derive monotonicity of the first eigenvalue of Laplacian which generalizes some results of Ma \cite{Ma2006}. Moreover, we prove that when $(M_{3}, g_{0})$ is a closed three manifold with positive Ricci curvature, the eigenvalue of the Laplacian diverges as $t \rightarrow T$ on a limited maximal time in terval $[0, T)$, which generalizes some results of Cerbo and Fabrizio \cite{Fabrizio2007}.

math.DG↗