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Yuyang Zhu

Publications and source records attributed to Yuyang Zhu.

6 recordsLinked to original sources

Long-VLA: Unleashing Long-Horizon Capability of Vision Language Action Model for Robot Manipulation

Vision-Language-Action (VLA) models have become a cornerstone in robotic policy learning, leveraging large-scale multimodal data for robust and scalable control. However, existing VLA frameworks primarily address short-horizon tasks, and their effectiveness on long-horizon, multi-step robotic manipulation remains limited due to challenges in skill chaining and subtask dependencies. In this work, we introduce Long-VLA, the first end-to-end VLA model specifically designed for long-horizon robotic tasks. Our approach features a novel phase-aware input masking strategy that adaptively segments each subtask into moving and interaction phases, enabling the model to focus on phase-relevant sensory cues and enhancing subtask compatibility. This unified strategy preserves the scalability and data efficiency of VLA training, and our architecture-agnostic module can be seamlessly integrated into existing VLA models. We further propose the L-CALVIN benchmark to systematically evaluate long-horizon manipulation. Extensive experiments on both simulated and real-world tasks demonstrate that Long-VLA significantly outperforms prior state-of-the-art methods, establishing a new baseline for long-horizon robotic control.

cs.RO

Several Conclusions on another site setting problem

Let $S = \{ {A_1},{A_2}, \cdots ,{A_n}\} $ be a finite point set in m-dimensional Euclidean space ${E^m}$, and$\left\| {{A_i}{A_j}} \right\|$ be the distance between $A_i$ and $A_j$. Define $σ(S) = \sum\limits_{1 \le i < j \le n} {\left\| {{A_i}{A_j}} \right\|} $, $D(S) = \mathop {\max }\limits_{1 \le i < j \le n} \left\{ {\left\| {{A_i}{A_j}} \right\|} \right\}$, $ω(m,n) = \frac{σ(S)}{D(S)}$, $\sup ω(m,n) = \max \left\{ {\left. {\frac{σ(S)}{D(S)}} \right|S \subset {E^m},\left| S \right| = n} \right\}$. This paper proves that, for any point P in an n-dimensional simplex ${A_1}{A_2} \cdots {A_{n + 1}}$ in Euclidean space, $\sum\limits_{i = 1}^{n + 1} {\left\| {P{A_i}} \right\|} $ <= $\mathop {\sup }\limits_{{i_t},{j_t} \in \{ 1,2, \cdots ,n + 1\} } \left\{ {\sum\limits_{t = 1}^n {\left\| {A_{i_t}{A_{j_t}}} \right\|} } \right\}$ By using this inequality and several results in differential geometry this paper also proves that $\sup ω(2,4) = 4 + 2\sqrt {2 - \sqrt 3 } $, $\sup ω(n,n + 2)$ >= $C_{n + 1}^2 + 1 + n\sqrt {2\left( {1 - \sqrt {{\textstyle{{n + 1} \over {2n}}}} } \right)} $.

math.GM

A Fast Algorithm to Calculate Power Sum of Natural Numbers

Permutations can be represented as linear combinations of natural numbers with different powers. In this paper, its coefficient matrix and inverse matrix is derived, and the results show the coefficient matrix is a lower triangular matrix while the inverse matrix is upper triangular. Permutations of n-th order are used to generate the inverse matrix. The generation function of natural numbers' power sum is derived to calculate the power sum.

math.GM

A few results on the infimum of regular polygons equal-size split line

If an n-side unit regular polygon is divided into m equal sized parts, then what is the minimum length of the split line ${l_{m,n}}$? This problem has its practical application in real world. This paper proved that ${l_{2,3}} = \sqrt {\frac{\sqrt 3 π}{12}} $, ${l_{3,3}} = \frac{\sqrt 3 }{2}$, and $\frac{1}{2}\sqrt {nπ{\rm{ctan}}\frac{π}{n}} \le \mathop {\lim }\limits_{m \to \infty } \frac{l_{m,n}}{\sqrt m } \le \sqrt {\frac{\sqrt 3 }{2}n{\rm{ctan}}\frac{π}{\rm{n}}} $

math.GM

The probability of Riemann's hypothesis being true is equal to 1

Let $P$ be the set of all prime numbers, ${q_1},{q_2}, \cdots ,{q_m} \in P$, $P_k$ be the k-th $(k = 1,2, \cdots m)$ element of $P$ in ascending order of size, ${α_1},{α_2}, \cdots ,{α_m}$ be positive integers, and ${β_1},{β_2}, \cdots ,{β_m}$ is a permutation of ${α_1},{α_2}, \cdots ,{α_m}$ with ${β_1} \ge {β_2} \ge \cdots \ge {β_m}$, The following results are given in this paper: (i) The following inequality is true: ${e^γ}\log \log \prod\limits_{k = 1}^m {q_k^{α_k}} - \prod\limits_{k = 1}^m {\frac{{{q_k} - {\textstyle{1 \over {q_k^{α_k}}}}}}{{{q_k} - 1}}} \ge {e^γ}\log \log \prod\limits_{k = 1}^m {p_k^{β_k}} - \prod\limits_{k = 1}^m {\frac{{{p_k} - {\textstyle{1 \over {p_k^{β_k}}}}}}{{{p_k} - 1}}}$. (ii) If $n = \prod\limits_{k = 1}^m {p_k^{β_k}}= {\left( {\prod\limits_{k = 1}^m {p_k} } \right)^{1 + {\varepsilon _m}(n)}}$, $\mathop {\lim }\limits_{m \to \infty } {\varepsilon _m}(n) > 0$ or $\mathop {\lim }\limits_{m \to \infty } {\varepsilon _m}(n) = + \infty$, then $\mathop {\lim }\limits_{m \to \infty } ({e^γ}n\log \log n - σ(n)) > 0$ . Where $\{ {β_k}\}$ is a sequence, ${β_k} \in N$, ${β_1} \ge {β_2} \ge \cdots \ge {β_m}$, $σ(n) = \sum\limits_{\left. d \right|n} d$, and $γ$ is the Euler constant. (iii) The probability of Riemann's hypothesis being true is equal to 1. In addition, two results are given when $\mathop {\lim }\limits_{m \to \infty } {\varepsilon _m}(n) = 0$.

math.GM

An asymptotic Robin inequality

The conjectured Robin inequality for an integer $n>7!$ is $σ(n)<e^γn \log \log n,$ where $γ$ denotes Euler constant, and $σ(n)=\sum_{d | n} d $. Robin proved that this conjecture is equivalent to Riemann hypothesis (RH). Writing $D(n)=e^γn \log \log n-σ(n),$ and $d(n)=\frac{D(n)}{n},$ we prove unconditionally that $\liminf_{n \rightarrow \infty} d(n)=0.$ The main ingredients of the proof are an estimate for Chebyshev summatory function, and an effective version of Mertens third theorem due to Rosser and Schoenfeld. A new criterion for RH depending solely on $\liminf_{n \rightarrow \infty}D(n)$ is derived.

math.NT