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Xiaohan Jia

Publications and source records attributed to Xiaohan Jia.

12 recordsLinked to original sources
arXiv2026

R$^2$A: Learning Persona Policies Through Persona Representation Learning and Runtime Alignment

The same Persona behavior can be beneficial in one context but harmful in another, causing static Persona elicitation to perform inconsistently across tasks. We introduce the Persona Selection--Realization Framework, which models behavior generation through a latent Persona state and decomposes it into Persona Selection and Persona Realization. The discrepancies between static Persona elicitation and an ideal Persona policy in these two components define the Selection Gap and Realization Gap, respectively. Building on this framework, we propose R$^2$A, a two-stage approach for learning Persona policies. Persona Representation Learning uses structured Who--How--What presentations to encode the target Persona's objective, conditional behavioral principles, and trajectory-level manifestations. Persona Runtime Alignment then removes the explicit Persona specification and jointly calibrates behavior selection and trajectory realization using task feedback. Across 12 evaluation settings covering the four principles of the Accountable-Professional Persona studied in this work, R$^2$A overall outperforms both the base model and static Persona elicitation. Ablation results further show that Persona Representation Learning is critical for preventing Runtime Alignment from producing behaviorally imbalanced policies and for achieving more stable Persona policy learning.

cs.CL↗
arXiv2026

ASI-Bench: At the Dawn of Artificial Superintelligence

Artificial superintelligence (ASI) requires AI to move beyond mastering existing knowledge toward exploring the unknown, creating new knowledge, and turning new ideas into verifiable results. However, the capabilities of today's AI systems are still largely built on learning, compressing, and applying existing human knowledge. Accordingly, existing benchmarks primarily test whether AI can produce correct answers based on learned knowledge, or whether it can complete tasks under extensive human guidance. We therefore introduce ASI-Bench, the first benchmark to jointly evaluate AI systems' capabilities of innovative exploration and autonomous scientific execution across general research domains, and the first to progressively withdraw human methodological guidance within the same research project to test how far AI can proceed on its own. Built by over 40 experts with the cost of 31,000+ human hours, ASI-Bench contains 60 project-level research tasks across 11 scientific domains and progressively reduces methodological guidance to test whether AI can independently select methods, conduct research, and produce verifiable results. All tasks undergo expert review, AI-assisted auditing, sandbox execution, and scorer validation. Across 18 state-of-the-art agent--model configurations, the average score drops from 50.91 with full methodological guidance to 29.10 with only the method specified and 26.62 when agents must determine the method themselves. This sharp decline shows that current systems remain heavily dependent on human guidance and are still far from autonomously conducting end-to-end, project-level scientific research. ASI-Bench is open to the world. We invite researchers and builders everywhere to contribute new tasks, challenge the limits of today's AI, and help accelerate humanity's collective path toward artificial superintelligence at https://asibench.apexin.ai/submit.

cs.AI↗
arXiv2024

Willmore-type inequality in unbounded convex sets

In this paper we prove the following Willmore-type inequality: On an unbounded closed convex set $K\subset\mathbb{R}^{n+1}$ $(n\ge 2)$, for any embedded hypersurface $\Sigma\subset K$ with boundary $\partial\Sigma\subset \partial K$ satisfying a certain contact angle condition, there holds $$\frac1{n+1}\int_{\Sigma}\vert{H}\vert^n{\rm d}A\ge{\rm AVR}(K)\vert\mathbb{B}^{n+1}\vert.$$ Moreover, equality holds if and only if $\Sigma$ is a part of a sphere and $K\setminus\Omega$ is a part of the solid cone determined by $\Sigma$. Here $\Omega$ is the bounded domain enclosed by $\Sigma$ and $\partial K$, $H$ is the normalized mean curvature of $\Sigma$, and ${\rm AVR}(K)$ is the asymptotic volume ratio of $K$. We also prove an anisotropic version of this Willmore-type inequality. As a special case, we obtain a Willmore-type inequality for anisotropic capillary hypersurfaces in a half-space.

math.DG↗
arXiv2024

Quantitative Alexandrov theorem for capillary hypersurfaces in the half-space

In this paper, we prove the quantitative version of the Alexandrov theorem for capillary hypersurfaces in the half-space, which generalizes Julin-Niinikoski's result to the capillary case. The proof is based on the quantitative analysis of the Montiel-Ros-type argument carried out in our joint works with Wang-Xia.

math.DG↗
arXiv2023

Rigidity and quantitative stability for partially overdetermined problems and capillary CMC hypersurfaces

In this paper, we first prove a rigidity result for a Serrin-type partially overdetermined problem in the half-space, which gives a characterization of capillary spherical caps by the overdetermined problem. In the second part, we prove quantitative stability results for the Serrin-type partially overdetermined problem, as well as capillary almost constant mean curvature hypersurfaces in the half-space.

math.AP↗
arXiv2022

Alexandrov's theorem for anisotropic capillary hypersurfaces in the half-space

In this paper, we show that any embedded capillary hypersurface in the half-space with anisotropic constant mean curvature is a truncated Wulff shape. This extends Wente's result \cite{Wente80} to the anisotropic case and He-Li-Ma-Ge's result \cite{HLMG09} to the capillary boundary case. The main ingredients in the proof are a new Heintze-Karcher inequality and a new Minkowski formula, which have their own inetrest.

math.DG↗
arXiv2022

Heintze-Karcher inequality and capillary hypersurfaces in a wedge

In this paper, we utilize the method of Heintze-Karcher to prove a "best" version of Heintze-Karcher-type inequality for capillary hypersurfaces in the half-space or in a wedge. One of new crucial ingredients in the proof is modified parallel hypersurfaces which are very natural to be used to study capillary hypersurfaces. A more technical part is a subtle analysis along the edge of a wedge. As an application, we classify completely embedded capillary constant mean curvature hypersurfaces that hit the edge in a wedge, which is a subtler case.

math.DG↗
arXiv2022

Serrin-type overdetermined problems for Hessian quotient equations

We prove the symmetry of solutions to overdetermined problems for a class of fully nonlinear equations, namely Hessian quotient equations and Hessian quotient curvature equations. Our approach is based on establishing a Rellich-Pohozaev type identity for Hessian quotient equations and using a P function. Our result generalizes the overdetermined problems for k-Hessian equations and k-curvature equations.

math.AP↗
arXiv2022

A Heintze-Karcher type inequality for hypersurfaces with capillary boundary

In this paper, we establish a Heintze-Karcher type inequality for hypersurfaces with capillary boundary of contact angle $θ\in (0,\fracπ{2})$ in a half space or a half ball, by using solution to a mixed boundary value problem in Reilly type formula. Consequently, we give a new proof of Alexandrov type theorem for embedded capillary constant mean curvature hypersurfaces with contact angle $θ\in (0,\fracπ{2})$ in a half space or a half ball.

math.DG↗
arXiv2022

Serrin-type Overdetermined problems in $\mathbb H^n$

In this paper, we prove the symmetry of the solution to overdetermined problem for the equation $σ_k(D^2u-uI)=C_n^k$ in hyperbolic space. Our approach is based on establishing a Rellich-Pohozaev type identity and using a P function. Our result generalizes the overdetermined problem for Hessian equation in Euclidean space.

math.AP↗