arXiv subjects

Yuliang Shen

Publications and source records attributed to Yuliang Shen.

5 recordsLinked to original sources

arXiv2025

Hybrid Consistency Policy: Decoupling Multi-Modal Diversity and Real-Time Efficiency in Robotic Manipulation

In visuomotor policy learning, diffusion-based imitation learning has become widely adopted for its ability to capture diverse behaviors. However, approaches built on ordinary and stochastic denoising processes struggle to jointly achieve fast sampling and strong multi-modality. To address these challenges, we propose the Hybrid Consistency Policy (HCP). HCP runs a short stochastic prefix up to an adaptive switch time, and then applies a one-step consistency jump to produce the final action. To align this one-jump generation, HCP performs time-varying consistency distillation that combines a trajectory-consistency objective to keep neighboring predictions coherent and a denoising-matching objective to improve local fidelity. In both simulation and on a real robot, HCP with 25 SDE steps plus one jump approaches the 80-step DDPM teacher in accuracy and mode coverage while significantly reducing latency. These results show that multi-modality does not require slow inference, and a switch time decouples mode retention from speed. It yields a practical accuracy efficiency trade-off for robot policies.

cs.RO↗

arXiv2020

Weil-Petersson Teichmüller space III: dependence of Riemann mappings for Weil-Petersson curves

The primary purpose of the paper is to study how a Riemann mapping depends on the corresponding Jordan curve. We are mainly concerned with those Jordan curves in the Weil-Petersson class, namely, the corresponding Riemann mappings can be quasiconformally extended to the whole plane with Beltrami coefficients being square integrable under the Poincaré metric. We endow the space of all normalized Weil-Petersson curves with a new real Hilbert manifold structure and show that it is topologically equivalent to the standard complex Hilbert manifold structure.

math.CV↗

arXiv2019

Weil-Petersson Teichmüller space II: smoothness of flow curves of $H^{\frac 32}$-vector fields

Given a continuous vector field $λ(t, \cdot)$ of Sobolev class $H^{\frac 32}$ on the unit circle $S^1$, the flow maps $η=g(t, \cdot)$ of the differential equation $$ \cases \frac{dη}{dt}=λ(t, η)\\ η(0,ζ)=ζ\endcases $$ are known to be quasisymmetric homeomorphisms. Very recently, Gay-Balmaz-Ratiu [GR] conjectured that the flow curve $g(t, \cdot)$ is in the Weil-Petersson class WP$(S^1)$ and is continuously differentiable with respect to the Hilbert manifold structure of WP$(S^1)$ introduced by Takhtajan-Teo [TT]. The first assertion had already been demonstrated in our previous paper [Sh2]. In this sequel to [Sh2], we will continue to deal with the Weil-Petersson class WP$(S^1)$ and completely solve this conjecture in the affirmative.

math.CV↗

arXiv2017

Weil-Petersson Teichmüller space

The paper presents some recent results on the Weil-Petersson geometry theory of the universal Teichmüller space, a topic which is important in Teichmüller theory and has wide applications to various areas such as mathematical physics, differential equation and computer vision. \noindent (1) It is shown that a sense-preserving homeomorphism $h$ on the unit circle belongs to the Weil-Petersson class, namely, $h$ can be extended to a quasiconformal mapping to the unit disk whose Beltrami coefficient is squarely integrable in the Poincaré metric if and only if $h$ is absolutely continuous such that $\log h'$ belongs to the Sobolev class $H^{\frac 12}$. This solves an open problem posed by Takhtajan-Teo [TT2] in 2006 and investigated later by Figalli [Fi], Gay-Balmaz-Marsden-Ratiu ([GMR], [GR]) and others. \noindent The intrinsic characterization (1) of the Weil-Petersson class has the following applications which are also explored in this paper: \noindent (2) It is proved that there exists a quasisymmetric homeomorphism of the Weil-Petersson class which belongs neither to the Sobolev class $H^{\frac 32}$ nor to the Lipschitz class $Λ^1$, which was conjectured very recently by Gay-Balmaz-Ratiu [GR] when studying the classical Euler-Poincaré equation in the new setting that the involved sense-preserving homeomorphisms on the unit circle belong to the Weil-Petersson class. \noindent (3) It is proved that the flows of the $H^{\frac 32}$ vector fields on the unit circle are contained in the Weil-Petersson class, which was also conjectured by Gay-Balmaz-Ratiu [GR] during their above mentioned research. \noindent (4) A new metric is introduced on the Weil-Petersson Teichmüller space and is shown to be topologically equivalent to the Weil-Petersson metric.

math.CV↗

arXiv2013

On angles in Teichmüller spaces

We discuss the existence of the angle between two curves in Teichmüller spaces and show that, in any infinite dimensional Teichmüller space, there exist infinitely many geodesic triangles each of which has the same three vertices and satisfies the property that its three sides have the same and arbitrarily given length while its three angles are equal to any given three possibly different numbers from 0 to $π$. This implies that the sum of three angles of a geodesic triangle may be equal to any given number from 0 to $3π$ in an infinite dimensional Teichmüller space.

math.CV↗