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Zhiying Wen

Publications and source records attributed to Zhiying Wen.

10 recordsLinked to original sources
arXiv2026

FVAttn: Adaptive Sparse Attention with Runtime Load Balancing for Video Generation

Video Diffusion Transformers process long spatio-temporal sequences, making self-attention the main bottleneck in high-resolution video generation. Training-free sparse attention reduces this cost, but adaptive Top-$p$ routing creates uneven per-head workloads under multi-GPU sequence parallelism. The resulting workload heterogeneity turns sparse attention into a rank-level straggler problem. We present \method{}, a training-free sparse-attention system that improves the distributed execution efficiency of adaptive sparse attention under multi-GPU sequence parallelism. \method{} uses Top-$p$ routing, a Top-$k$ safety floor, and video-aware block organization as the sparse-routing frontend, then repairs the materialized mask at runtime. Runtime Load Balancing migrates a small number of heavy heads via P2P communication to shorten the current critical path. Slack-Aware Sparse Augmentation fills residual non-critical-rank slack with additional high-value blocks, while overlap hides scheduling and migration overhead behind existing computation. On step-distilled Wan2.2 I2V, \method{} reduces average load imbalance from 1.34 to 1.08 and delivers a $4.41\times$ attention speedup over FlashAttention, while achieving a $2.02$--$2.11\times$ DiT inference speedup with competitive video quality.

cs.CV↗
arXiv2022

Box-counting measure of metric spaces

In this paper, we introduce a new notion called the \emph{box-counting measure} of a metric space. We show that for a doubling metric space, an Ahlfors regular measure is always a box-counting measure; consequently, if $E$ is a self-similar set satisfying the open set condition, then the Hausdorff measure restricted to $E$ is a box-counting measure. We show two classes of self-affine sets, the generalized Lalley-Gatzouras type self-affine sponges and Barański carpets, always admit box-counting measures; this also provides a very simple method to calculate the box-dimension of these fractals. Moreover, among others, we show that if two doubling metric spaces admit box-counting measures, then the multi-fractal spectra of the box-counting measures coincide provided the two spaces are Lipschitz equivalent.

math.MG↗
arXiv2021

Finite state automata and homeomorphism of self-similar sets

The topological and metrical equivalence of fractals is an important topic in analysis. In this paper, we use a class of finite state automata, called $Σ$-automaton, to construct psuedo-metric spaces, and then apply them to the study of classification of self-similar sets. We first introduce a notion of topology automaton of a fractal gasket, which is a simplified version of neighbor automaton; we show that a fractal gasket is homeomorphic to the psuedo-metric space induced by the topology automaton. Then we construct a universal map to show that psuedo-metric spaces induced by different automata can be bi-Lipschitz equivalent. As an application, we obtain a rather general sufficient condition for two fractal gaskets to be homeomorphic or Lipschitz equivalent.

math.GN↗
arXiv2017

On strict Whitney arcs and $t$-quasi self-similar arcs

A connected compact subset $E$ of $\mathbb{R}^N$ is said to be a strict Whitney set if there exists a real-valued $C^1$ function $f$ on $\mathbb{R}^N$ with $\nabla f|_E\equiv 0$ such that $f$ is constant on no non-empty relatively open subsets of $E$. We prove that each self-similar arc of Hausdorff dimension $s>1$ in $\mathbb{R}^N$ is a strict Whitney set with criticality $s$. We also study a special kind of self-similar arcs, which we call "regular" self-similar arcs. We obtain necessary and sufficient conditions for a regular self-similar arc $Λ$ to be a $t$-quasi-arc, and for the Hausdorff measure function on $Λ$ to be a strict Whitney function. We prove that if a regular self-similar arc has "minimal corner angle" $θ_{\min}>0$, then it is a 1-quasi-arc and hence its Hausdorff measure function is a strict Whitney function. We provide an example of a one-parameter family of regular self-similar arcs with various features. For some value of the parameter $τ$, the Hausdorff measure function of the self-similar arc is a strict Whitney function on the arc, and hence the self-similar arc is an $s$-quasi-arc, where $s$ is the Hausdorff dimension of the arc. For each $t_0\ge 1$, there is a value of $τ$ such that the corresponding self-similar arc is a $t$-quasi-arc for each $t>t_0$, but it is not a $t_0$-quasi-arc. For each $t_0>1$, there is a value of $τ$ such that the corresponding self-similar arc is a $t_0$-quasi-arc, but it is a $t$-quasi-arc for no $t\in [1, t_0)$.

math.MG↗
arXiv2016

The Square Trees in the Tribonacci Sequence

The Tribonacci sequence $\mathbb{T}$ is the fixed point of the substitution $σ(a,b,c)=(ab,ac,a)$. In this note, we get the explicit expressions of all squares, and then establish the tree structure of the positions of repeated squares in $\mathbb{T}$, called square trees. Using the square trees, we give a fast algorithm for counting the number of repeated squares in $\mathbb{T}[1,n]$ for all $n$, where $\mathbb{T}[1,n]$ is the prefix of $\mathbb{T}$ of length $n$. Moreover we get explicit expressions for some special $n$ such as $n=t_m$ (the Tribonacci number) etc.

math.DS↗
arXiv2016

The number of distinct and repeated squares and cubes in the Fibonacci sequence

The Fibonacci sequence $\mathbb{F}$ is the fixed point beginning with $a$ of morphism $σ(a,b)=(ab,a)$. In this paper, we get the explicit expressions of all squares and cubes, then we determine the number of distinct squares and cubes in $\mathbb{F}[1,n]$ for all $n$, where $\mathbb{F}[1,n]$ is the prefix of $\mathbb{F}$ of length $n$. By establishing and discussing the recursive structure of squares and cubes, we give algorithms for counting the number of repeated squares and cubes in $\mathbb{F}[1,n]$ for all $n$, and get explicit expressions for some special $n$ such as $n=f_m$ (the Fibonacci number) etc., which including some known results such as in A.S.Fraenkel and J.Simpson, J.Shallit et al.

math.DS↗
arXiv2016

The structure of palindromes in the Fibonacci sequence and some applications

Let ${\cal P}$ be the set of palindromes occurring in the Fibonacci sequence. In this note, we establish three structures of $\mathcal{P}$ and and discuss their properties: cylinder structure, chain structure and recursive structure. Using these structures, we determine that the number of distinct palindrome occurrences in $\mathbb{F}[1,n]$ is exactly $n$, where $\mathbb{F}[1,n]$ is the prefix of the Fibonacci sequence of length $n$. Then we give an algorithm for counting the number of repeated palindrome occurrences in $\mathbb{F}[1,n]$, and get explicit expressions for some special $n$, which include the known results. We also give simpler proofs of some classical properties, such as in X.Droubay, W.F.Chuan and J.Shallit et al.

math.DS↗
arXiv2014

Gap Sequence of Factors of Fibonacci Sequence

Let w be a factor of Fibonacci sequence F=x_1x_2..., then it appears in the sequence infinitely many times. Let w_p be the p-th appearance of w and v_{w,p} be the gap between w_p and w_{p+1}. In this paper, we discuss the structure of the gap sequence {v_{w,p}}, we first introduce the singular kernel word sk(w) for any factor w of F and give a decomposition of w with respect to sk(w). Using the singular kernel and the decomposition, we prove the gap sequence {v_{w,p}} has exactly two different elements {v_{w,1},v_{w,2}} and determine the expressions of gaps completely, then we prove that the gap sequence over the alphabet {v_{w,1},v_{w,2}} is still a Fibonacci sequence. Finally, we introduce the spectrum for studying some typical combinatorial, using the results above, we determine completely the spectrums.

math.DS↗
arXiv2013

The fractal dimensions of the spectrum of Sturm Hamiltonian

Let $α\in(0,1)$ be irrational and $[0;a_1,a_2,\cdots]$ be the continued fraction expansion of $α$. Let $H_{α,V}$ be the Sturm Hamiltonian with frequency $α$ and coupling $V$, $Σ_{α,V}$ be the spectrum of $H_{α,V}$. The fractal dimensions of the spectrum have been determined by Fan, Liu and Wen (Erg. Th. Dyn. Sys.,2011) when $\{a_n\}_{n\ge1}$ is bounded. The present paper will treat the most difficult case, i.e, $\{a_n\}_{n\ge1}$ is unbounded. We prove that for $V\ge24$, $$ \dim_H\ Σ_{α,V}=s_*(V)\ \ \ \text{and}\ \ \ \bar{\dim}_B\ Σ_{α,V}=s^*(V), $$ where $s_*(V)$ and $s^*(V)$ are lower and upper pre-dimensions respectively. By this result, we determine the fractal dimensions of the spectrums for all Sturm Hamiltonians. We also show the following results: $s_*(V)$ and $s^*(V)$ are Lipschitz continuous on any bounded interval of $[24,\infty)$; the limits $s_*(V)\ln V$ and $s^*(V)\ln V$ exist as $V$ tend to infinity, and the limits are constants only depending on $α$; $s^\ast(V)=1$ if and only if $\limsup_{n\to\infty}(a_1\cdots a_n)^{1/n}=\infty,$ which can be compared with the fact: $s_\ast(V)=1$ if and only if $\liminf_{n\to\infty}(a_1\cdots a_n)^{1/n}=\infty$(Liu and Wen, Potential anal. 2004).

math-ph↗