Searcharxiv⌕ Search

arXiv subjects

Qirui Li

Publications and source records attributed to Qirui Li.

22 records · Page 2Linked to original sources

Learning by Sampling and Compressing: Efficient Graph Representation Learning with Extremely Limited Annotations

Graph convolution network (GCN) attracts intensive research interest with broad applications. While existing work mainly focused on designing novel GCN architectures for better performance, few of them studied a practical yet challenging problem: How to learn GCNs from data with extremely limited annotation? In this paper, we propose a new learning method by sampling strategy and model compression to overcome this challenge. Our approach has multifold advantages: 1) the adaptive sampling strategy largely suppresses the GCN training deviation over uniform sampling; 2) compressed GCN-based methods with a smaller scale of parameters need fewer labeled data to train; 3) the smaller scale of training data is beneficial to reduce the human resource cost to label them. We choose six popular GCN baselines and conduct extensive experiments on three real-world datasets. The results show that by applying our method, all GCN baselines cut down the annotation requirement by as much as 90$\%$ and compress the scale of parameters more than 6$\times$ without sacrificing their strong performance. It verifies that the training method could extend the existing semi-supervised GCN-based methods to the scenarios with the extremely small scale of labeled data.

cs.LG↗

Implications of Stahl's Theorems to Holomorphic Embedding Pt. 2: Numerical Convergence

What has become known as Stahl's Theorem in power-engineering circles has been used to justify a convergence guarantee of the Holomorphic Embedding Method (HEM) as it applies to the power-flow problem. In this, the second part of a two-part paper, we examine implications to numerical convergence of HEM and the numerical properties of a Padé approximant algorithm. We show that even if the convergence domain is identical to the function's domain, numerical convergence of the sequence of Padé approximants computed with finite precision is not guaranteed. We also show that the study of convergence properties of the Padé approximant is the study of the location of branch-points of the function, which dictate branch-cut topology and capacity and, therefore, convergence rate. We show how poorly chosen embeddings can prevent numerical convergence.

eess.SY↗

On Gross-Keating's result of lifting endomorphisms for formal modules

$\newcommand{\OO}[1]{\mathcal{O}_{#1}}\newcommand{\GG}{\mathcal{G}}\newcommand{\End}{\mathrm{End}}\newcommandØ{\mathcal{O}}$Let $K/F$ be a quadratic extension of non-Archimedean local fields of characteristic not equal to 2, with rings of integers denoted by $\OO K$ and $\OO F$. We consider a formal $\OO F$-module $\GG$, over a discrete valuation ring $\OO W$ with an uniformizer $\varpi$, with extra endomorphisms by a subring $Ø$ of $\OO K$, and the height of its reduction $\GG_0=\GG\otimes \OO W/\varpi$ is 2. The endomorphism ring of $\GG_n=\GG\otimes \OO W/\varpi^{n+1}$ is a subring between $\OO s$ and $\OO D=\End(\GG_0)$. We will determine them explicitly. This result was previously proved by Gross and Keating. Their treatment is the formal cohomology theory. We will give another proof using the intersection formula of CM cycles in Lubin-Tate deformation spaces.

math.NT↗

Extensions of Vector Bundles on the Fargues-Fontaine Curve

We completely classify the possible extensions between semistable vector bundles on the Fargues-Fontaine curve (over an algebraically closed perfectoid field), in terms of a simple condition on Harder-Narasimhan polygons. Our arguments rely on a careful study of various moduli spaces of bundle maps, which we define and analyze using Scholze's language of diamonds. This analysis reduces our main results to a somewhat involved combinatorial problem, which we then solve via a reinterpretation in terms of the euclidean geometry of Harder-Narasimhan polygons.

math.NT↗