arXiv subjects

Xiangzhou Liu

Publications and source records attributed to Xiangzhou Liu.

7 recordsLinked to original sources

arXiv2026

Quasi-kernels in Hereditary Classes and Applications to Break

Recently, Nguyen, Seymour and Scott verified the small quasi-kernel conjecture for split digraphs, and initiated the study of quasi-kernels in break digraphs. Following their research, we introduce a weighted half-neighborhood property for hereditary classes of oriented graphs and show that it gives a $2n/3$ bound of small quasi-kernel for break digraphs. We also record two stronger $n/2$ results for special classes of break digraphs. Finally, using the same framework we also prove that every digraph on $n$ vertices has a quasi-kernel $Q$ with $|N_D^+[Q]|\ge \sqrt n$.

math.CO↗

arXiv2025

Analyzing Communication Predictability in LLM Training

Effective communication is essential in distributed training, with predictability being one of its most significant characteristics. However, existing studies primarily focus on exploiting predictability through online profiling for runtime optimization, without a systematic understanding of it. In this work, we aim to systematically formulate communication predictability in distributed training, particularly in Large Language Models (LLMs) that utilize hybrid parallelism. Our analysis focuses on both traffic patterns and communication overhead. Specifically, we investigate predictable traffic patterns in typical LLMs and evaluate how various factors influence GPU utilization and effective bandwidth (two critical variables affecting communication overhead). Furthermore, we develop an analytical formulation to estimate communication overhead in LLM training, which is validated with high accuracy against empirical data. Leveraging this formulation, we propose a configuration tuning tool, ConfigTuner, to optimize training performance. Compared to Megatron-LM, the training configurations optimized by ConfigTuner demonstrate up to a 1.36$\times$ increase in throughput. Compared to Alpa, ConfigTuner generates the same configuration suggestion while significantly reducing the search complexity.

cs.NI↗

arXiv2025

Feedback vertex sets of digraphs with bounded maximum degree

A digraph $D$ is an oriented graph if $D$ does not have a pair of opposite arcs. The degree of a vertex $v$ of $D$ is the sum of the in-degree and out-degree of $v.$ Let $fvs(D)$ be the minimum number of vertices whose deletion from $D$ makes it acyclic. Let $D$ be a digraph with $n$ vertices and maximum degree $Δ$. We prove the following bounds. If $D$ is an oriented graph, then $fvs(D)\leq \frac{3n}{7}$ when $Δ\le 4$ and $fvs(D)\leq \frac{n}{2}$ when $Δ\le 5$. If $D$ is a connected digraph, $Δ\le 4$ and $D$ is not obtained from an odd undirected cycle by replacing every edge with the pair of opposite arcs with the same endvertices, then $fvs(D)\leq \frac{n}{2}$. If $D$ is an arbitrary digraph with $Δ\le 5$ then $fvs(D)\leq \frac{2n}{3}.$ Note that all the above bounds are tight.

math.CO↗

arXiv2024

Spanning weakly even trees of graphs

Let $G$ be a graph (with multiple edges allowed) and let $T$ be a tree in $G$. We say that $T$ is $\textit{even}$ if every leaf of $T$ belongs to the same part of the bipartition of $T$, and that $T$ is $\textit{weakly even}$ if every leaf of $T$ that has maximum degree in $G$ belongs to the same part of the bipartition of $T$. We confirm two recent conjectures of Jackson and Yoshimoto by showing that every connected graph that is not a regular bipartite graph has a spanning weakly even tree.

math.CO↗

arXiv2024

A short note on spanning even trees

We call a tree $T$ is \emph{even} if every pair of its leaves is joined by a path of even length. Jackson and Yoshimoto~[J. Graph Theory, 2024] conjectured that every $r$-regular nonbipartite connected graph $G$ has a spanning even tree. They verified this conjecture for the case when $G$ has a $2$-factor. In this paper, we prove that the conjecture holds when $r$ is odd, thereby resolving the only remaining unsolved case for this conjecture.

math.CO↗

arXiv2024

A variable version of the quasi-kernel conjecture

A quasi-kernel of a digraph $D$ is an independent set $Q$ such that every vertex can reach $Q$ in at most two steps. A 48-year conjecture made by P.L. Erdős and Székely, denoted the small QK conjecture, says that every sink-free digraph contains a quasi-kernel of size at most $n/2$. Recently, Spiro posed the large QK conjecture, that every sink-free digraph contains a quasi-kernel $Q$ such that $|N^-[Q]|\geq n/2$, and showed that it follows from the small QK conjecture. In this paper, we establish that the large QK conjecture implies the small QK conjecture with a weaker constant. We also show that the large QK conjecture is equivalent to a sharp version of it, answering affirmatively a question of Spiro. We formulate variable versions of these conjectures, which are still open in general. Not many digraphs are known to have quasi-kernels of size $(1-α)n$ or less. We show this for digraphs with bounded dichromatic number, by proving the stronger statement that every sink-free digraph contains a quasi-kernel of size at most $(1-1/k)n$, where $k$ is the digraph's kernel-perfect number.

math.CO↗

arXiv2023

General-Purpose Multi-Modal OOD Detection Framework

Out-of-distribution (OOD) detection identifies test samples that differ from the training data, which is critical to ensuring the safety and reliability of machine learning (ML) systems. While a plethora of methods have been developed to detect uni-modal OOD samples, only a few have focused on multi-modal OOD detection. Current contrastive learning-based methods primarily study multi-modal OOD detection in a scenario where both a given image and its corresponding textual description come from a new domain. However, real-world deployments of ML systems may face more anomaly scenarios caused by multiple factors like sensor faults, bad weather, and environmental changes. Hence, the goal of this work is to simultaneously detect from multiple different OOD scenarios in a fine-grained manner. To reach this goal, we propose a general-purpose weakly-supervised OOD detection framework, called WOOD, that combines a binary classifier and a contrastive learning component to reap the benefits of both. In order to better distinguish the latent representations of in-distribution (ID) and OOD samples, we adopt the Hinge loss to constrain their similarity. Furthermore, we develop a new scoring metric to integrate the prediction results from both the binary classifier and contrastive learning for identifying OOD samples. We evaluate the proposed WOOD model on multiple real-world datasets, and the experimental results demonstrate that the WOOD model outperforms the state-of-the-art methods for multi-modal OOD detection. Importantly, our approach is able to achieve high accuracy in OOD detection in three different OOD scenarios simultaneously. The source code will be made publicly available upon publication.

cs.CV↗