arXiv subjects

Tianci Luo

Publications and source records attributed to Tianci Luo.

10 recordsLinked to original sources

arXiv2026

Positive $\tau$-bi-Ricci curvature and Mean curvature flow with surgery in hyperbolic space

Let $n\geq3$ and $0\leq\tau\leq2$. We prove that every smooth closed connected immersed hypersurface in hyperbolic space whose induced metric has positive $\tau$-bi-Ricci curvature admits a mean curvature flow with surgery which has only finitely many surgery times and terminates. In the range compatible with cylindrical necks, the key ingredients are a preserved quantitative spectral pinching condition, which converts the intrinsic hypothesis into uniform two-convexity, and cylindrical and derivative estimates that remain valid across the hyperbolic standard neck replacement. At the endpoint $n=3$, $\tau=2$, positive $\tau$-bi-Ricci curvature is positive Ricci curvature and forces strict convexity, so the ordinary mean curvature flow converges to a round point. Consequently, the underlying manifold is diffeomorphic to a sphere or to a finite connected sum of copies of $\mathbb{S}^{n-1}\times\mathbb{S}^1$. If the initial hypersurface is embedded and bounds a compact domain, that domain is a one-handlebody, namely a ball with finitely many one-handles attached.

math.DG↗

arXiv2026

Free boundary flows by powers of the Gauss curvature in the unit ball

We study smooth compact strictly convex hypersurfaces in the unit ball that meet the support sphere orthogonally and evolve by the $\alpha$-Gauss curvature flow $\partial_tX=-K^\alpha\nu$, $\alpha>0$. We prove that the solution remains strictly convex, becomes extinct in finite time and contracts to a single point on the support sphere. If $\alpha >\frac{1}{n+2}$, we apply a Cayley-type conformal map that sends the extinction point to the origin of a Euclidean half-space and then normalize the enclosed half-space volume. The resulting normalized hypersurfaces converge smoothly to the unit hemisphere. The proof combines boundary identities for the spherical free boundary, a boundary-adapted Tso estimate, an almost-monotonicity formula for a half-space entropy, and uniform curvature estimates for the normalized flow.

math.DG↗

arXiv2026

Contraction of hypersurfaces with positive sectional curvature in hyperbolic space

We study contracting curvature flows of compact hypersurfaces with positive sectional curvature in hyperbolic space $\mathbb{H}^{n+1}$. The speed is assumed to be homogeneous of degree one in the principal curvatures and to satisfy certain conditions. This class of flows includes the $k$th mean curvature flow as a special case. We show that if the initial hypersurface has positive sectional curvature, then this property is preserved along the flow, and the evolving hypersurface contracts to a round point in finite time.

math.DG↗

arXiv2026

JoyAI-RA 0.1: A Foundation Model for Robotic Autonomy

Robotic autonomy in open-world environments is fundamentally limited by insufficient data diversity and poor cross-embodiment generalization. Existing robotic datasets are often limited in scale and task coverage, while relatively large differences across robot embodiments impede effective behavior knowledge transfer. To address these challenges, we propose JoyAI-RA, a vision-language-action (VLA) embodied foundation model tailored for generalizable robotic manipulation. JoyAI-RA presents a multi-source multi-level pretraining framework that integrates web data, large-scale egocentric human manipulation videos, simulation-generated trajectories, and real-robot data. Through training on heterogeneous multi-source data with explicit action-space unification, JoyAI-RA effectively bridges embodiment gaps, particularly between human manipulation and robotic control, thereby enhancing cross-embodiment behavior learning. JoyAI-RA outperforms state-of-the-art methods in both simulation and real-world benchmarks, especially on diverse tasks with generalization demands.

cs.RO↗

arXiv2026

Love Me, Love My Label: Rethinking the Role of Labels in Prompt Retrieval for Visual In-Context Learning

Visual in-context learning (VICL) enables visual foundation models to handle multiple tasks by steering them with demonstrative prompts. The choice of such prompts largely influences VICL performance, standing out as a key challenge. Prior work has made substantial progress on prompt retrieval and reranking strategies, but mainly focuses on prompt images while overlooking labels. We reveal these approaches sometimes get visually similar but label-inconsistent prompts, which potentially degrade VICL performance. On the other hand, higher label consistency between query and prompts preferably indicates stronger VICL results. Motivated by these findings, we develop a framework named LaPR (Label-aware Prompt Retrieval), which highlights the role of labels in prompt selection. Our framework first designs an image-label joint representation for prompts to incorporate label cues explicitly. Besides, to handle unavailable query labels at test time, we introduce a mixture-of-expert mechanism to the dual encoders with query-adaptive routing. Each expert is expected to capture a specific label mode, while the router infers query-adaptive mixture weights and helps to learn label-aware representation. We carefully design alternative optimization for experts and router, with a VICL performance-guided contrastive loss and a label-guided contrastive loss, respectively. Extensive experiments show promising and consistent improvement of LaPR on in-context segmentation, detection, and colorization tasks. Moreover, LaPR generalizes well across feature extractors and cross-fold scenarios, suggesting the importance of label utilization in prompt retrieval for VICL. Code is available at https://github.com/luotc-why/CVPR26-LaPR.

cs.CV↗

arXiv2026

PromptHub: Enhancing Multi-Prompt Visual In-Context Learning with Locality-Aware Fusion, Concentration and Alignment

Visual In-Context Learning (VICL) aims to complete vision tasks by imitating pixel demonstrations. Recent work pioneered prompt fusion that combines the advantages of various demonstrations, which shows a promising way to extend VICL. Unfortunately, the patch-wise fusion framework and model-agnostic supervision hinder the exploitation of informative cues, thereby limiting performance gains. To overcome this deficiency, we introduce PromptHub, a framework that holistically strengthens multi-prompting through locality-aware fusion, concentration and alignment. PromptHub exploits spatial priors to capture richer contextual information, employs complementary concentration, alignment, and prediction objectives to mutually guide training, and incorporates data augmentation to further reinforce supervision. Extensive experiments on three fundamental vision tasks demonstrate the superiority of PromptHub. Moreover, we validate its universality, transferability, and robustness across out-of-distribution settings, and various retrieval scenarios. This work establishes a reliable locality-aware paradigm for prompt fusion, moving beyond prior patch-wise approaches. Code is available at https://github.com/luotc-why/ICLR26-PromptHub.

cs.CV↗

arXiv2025

Embracing Collaboration Over Competition: Condensing Multiple Prompts for Visual In-Context Learning

Visual In-Context Learning (VICL) enables adaptively solving vision tasks by leveraging pixel demonstrations, mimicking human-like task completion through analogy. Prompt selection is critical in VICL, but current methods assume the existence of a single "ideal" prompt in a pool of candidates, which in practice may not hold true. Multiple suitable prompts may exist, but individually they often fall short, leading to difficulties in selection and the exclusion of useful context. To address this, we propose a new perspective: prompt condensation. Rather than relying on a single prompt, candidate prompts collaborate to efficiently integrate informative contexts without sacrificing resolution. We devise Condenser, a lightweight external plugin that compresses relevant fine-grained context across multiple prompts. Optimized end-to-end with the backbone, Condenser ensures accurate integration of contextual cues. Experiments demonstrate Condenser outperforms state-of-the-arts across benchmark tasks, showing superior context compression, scalability with more prompts, and enhanced computational efficiency compared to ensemble methods, positioning it as a highly competitive solution for VICL. Code is open-sourced at https://github.com/gimpong/CVPR25-Condenser.

cs.CV↗

arXiv2024

The horospherical $p$-Christoffel-Minkowski problem in hyperbolic space

The horospherical $p$-Christoffel-Minkowski problem was posed by Li and Xu (2022) as a problem prescribing the $k$-th horospherical $p$-surface area measure of $h$-convex domains in hyperbolic space $\mathbb{H}^{n+1}$. It is a natural generalization of the classical $L^p$ Christoffel-Minkowski problem in the Euclidean space $\mathbb{R}^{n+1}$. In this paper, we consider a fully nonlinear equation associated with the horospherical $p$-Christoffel-Minkowski problem. We establish the existence of a uniformly $h$-convex solution under appropriate assumptions on the prescribed function. The key to the proof is the full rank theorem, which we will demonstrate using a viscosity approach based on the idea of Bryan-Ivaki-Scheuer (2023). When $p=0$, the horospherical $p$-Christoffel-Minkowski problem in $\mathbb{H}^{n+1}$ is equivalent to a Nirenberg-type problem on $\mathbb{S}^n$ in conformal geometry. Therefore, our result implies the existence of solutions to the Nirenberg-type problem.

math.AP↗

arXiv2024

MambaVC: Learned Visual Compression with Selective State Spaces

Learned visual compression is an important and active task in multimedia. Existing approaches have explored various CNN- and Transformer-based designs to model content distribution and eliminate redundancy, where balancing efficacy (i.e., rate-distortion trade-off) and efficiency remains a challenge. Recently, state-space models (SSMs) have shown promise due to their long-range modeling capacity and efficiency. Inspired by this, we take the first step to explore SSMs for visual compression. We introduce MambaVC, a simple, strong and efficient compression network based on SSM. MambaVC develops a visual state space (VSS) block with a 2D selective scanning (2DSS) module as the nonlinear activation function after each downsampling, which helps to capture informative global contexts and enhances compression. On compression benchmark datasets, MambaVC achieves superior rate-distortion performance with lower computational and memory overheads. Specifically, it outperforms CNN and Transformer variants by 9.3% and 15.6% on Kodak, respectively, while reducing computation by 42% and 24%, and saving 12% and 71% of memory. MambaVC shows even greater improvements with high-resolution images, highlighting its potential and scalability in real-world applications. We also provide a comprehensive comparison of different network designs, underscoring MambaVC's advantages. Code is available at https://github.com/QinSY123/2024-MambaVC.

eess.IV↗

arXiv2024

Gauss curvature type flow and Alexandrov-Fenchel inequalities in the hyperbolic space

We consider the Gauss curvature type flow for uniformly convex hypersurfaces in the hyperbolic space $\mathbb{H}^{n+1}\ (n\geqslant 2)$. We prove that if the initial closed hypersurface is smooth and uniformly convex, then the smooth solution exists for all positive time and converges smoothly and exponentially to a geodesic sphere centered at the origin. The key step is to prove the upper bound of Gauss curvature and that uniform convexity preserves along the flow. As an application, we provide a new proof for an Alexandrov-Fenchel inequality comparing $(n-2)$th quermassintegral and volume of convex domains in $\mathbb{H}^{n+1}\ (n\geqslant 2)$.

math.DG↗