Graph Neural Networks (GNNs) have garnered significant attention for their
success in learning the representation of homophilic or heterophilic graphs.
However, they cannot generalize well to real-world graphs with different levels
of homophily. In response, the Possion-Charlier Network (PCNet)
\cite{li2024pc}, the previous work, allows graph representation to be learned
from heterophily to homophily. Although PCNet alleviates the heterophily issue,
there remain some challenges in further improving the efficacy and efficiency.
In this paper, we simplify PCNet and enhance its robustness. We first extend
the filter order to continuous values and reduce its parameters. Two variants
with adaptive neighborhood sizes are implemented. Theoretical analysis shows
our model's robustness to graph structure perturbations or adversarial attacks.
We validate our approach through semi-supervised learning tasks on various
datasets representing both homophilic and heterophilic graphs.

本文研究了图神经网络在学习同质或异质图代表性表示方面的成功，介绍了 Possion-Charlier Network (PCNet) 的先前工作，并通过简化和增强 PCNet，提出了两种适应性邻域大小的变体，以应对异质性问题，并通过半监督学习任务在各种代表同质和异质图的数据集上验证了模型的鲁棒性.

简化的 PCNet 与鲁棒性

Simplified PCNet with Robustness

Recently, many carefully crafted graph representation learning methods have
achieved impressive performance on either strong heterophilic or homophilic
graphs, but not both. Therefore, they are incapable of generalizing well across
real-world graphs with different levels of homophily. This is attributed to
their neglect of homophily in heterophilic graphs, and vice versa. In this
paper, we propose a two-fold filtering mechanism to extract homophily in
heterophilic graphs and vice versa. In particular, we extend the graph heat
equation to perform heterophilic aggregation of global information from a long
distance. The resultant filter can be exactly approximated by the
Possion-Charlier (PC) polynomials. To further exploit information at multiple
orders, we introduce a powerful graph convolution PC-Conv and its instantiation
PCNet for the node classification task. Compared with state-of-the-art GNNs,
PCNet shows competitive performance on well-known homophilic and heterophilic
graphs. Our implementation is available at this https URL

提出了一种两重过滤机制来提取异态图里的同质性和同态图里的不同质性，其中使用了扩展图热方程来进行异态聚合，并介绍了一个强大的 PCNet 图卷积方法，通过该方法在节点分类任务上展现出了有竞争力的性能。

PC-Conv：融合同质性与异质性的双重过滤

PC-Conv: Unifying Homophily and Heterophily with Two-fold Filtering

Knowing when an output can be trusted is critical for reliably using face
recognition systems. While there has been enormous effort in recent research on
improving face verification performance, understanding when a model's
predictions should or should not be trusted has received far less attention.
Our goal is to assign a confidence score for a face image that reflects its
quality in terms of recognizable information. To this end, we propose a method
for generating image quality training data automatically from 'mated-pairs' of
face images, and use the generated data to train a lightweight Predictive
Confidence Network, termed as PCNet, for estimating the confidence score of a
face image. We systematically evaluate the usefulness of PCNet with its error
versus reject performance, and demonstrate that it can be universally paired
with and improve the robustness of any verification model. We describe three
use cases on the public IJB-C face verification benchmark: (i) to improve 1:1
image-based verification error rates by rejecting low-quality face images; (ii)
to improve quality score based fusion performance on the 1:1 set-based
verification benchmark; and (iii) its use as a quality measure for selecting
high quality (unblurred, good lighting, more frontal) faces from a collection,
e.g. for automatic enrolment or display.

本研究旨在提出一种基于 PCNet 的人脸图像质量评估方法，通过自动生成图像质量训练数据，实现生成可靠的人脸图像的置信度得分，进而提高任何人脸验证模型的识别准确度，以达到三个应用目的：筛选高质量人脸进行自动注册或显示；通过拒绝低质量人脸提高 1:1 基于图像的验证错误率；在 1:1 集合验证基准测试中，提高基于质量分数的融合效果。