The nature of heterophilous graphs is significantly different with that of
homophilous graphs, which suggests aggregations beyond 1-hop neighborhood and
causes difficulties in early graph neural network models. In this paper, we
develop a new way to implement multi-scale extraction via constructing
Haar-type graph framelets with desired properties of permutation equivariance,
efficiency, and sparsity, for deep learning tasks on graphs. We further deisgn
a graph framelet neural network model PEGFAN using our constructed graph
framelets. The experiments are conducted on a synthetic dataset and 9 benchmark
datasets to compare performance with other state-of-the-art models. The result
shows that our model can achieve best performance on certain datasets of
heterophilous graphs (including the majority of heterophilous datasets with
relatively larger sizes and denser connections) and competitive performance on
the remaining.

本文提出了 Haar-type graph framelets 及其相关的神经网络模型 PEGFAN，适用于在异质图上进行多尺度特征提取与深度学习任务，并通过实验验证其在大多数异质图数据集上表现良好。

异质半监督学习的置换等变图框架

Permutaion Equivariant Graph Framelets for Heterophilous Semi-supervised  Learning

Rain streaks bring serious blurring and visual quality degradation, which
often vary in size, direction and density. Current CNN-based methods achieve
encouraging performance, while are limited to depict rain characteristics and
recover image details in the poor visibility environment. To address these
issues, we present a Multi-scale Hourglass Hierarchical Fusion Network
(MH2F-Net) in end-to-end manner, to exactly captures rain streak features with
multi-scale extraction, hierarchical distillation and information aggregation.
For better extracting the features, a novel Multi-scale Hourglass Extraction
Block (MHEB) is proposed to get local and global features across different
scales through down- and up-sample process. Besides, a Hierarchical Attentive
Distillation Block (HADB) then employs the dual attention feature responses to
adaptively recalibrate the hierarchical features and eliminate the redundant
ones. Further, we introduce a Residual Projected Feature Fusion (RPFF) strategy
to progressively discriminate feature learning and aggregate different features
instead of directly concatenating or adding. Extensive experiments on both
synthetic and real rainy datasets demonstrate the effectiveness of the designed
MH2F-Net by comparing with recent state-of-the-art deraining algorithms. Our
source code will be available on the GitHub:
this https URL

提出了一种多尺度 Hourglass 分层融合网络 (MH2F-Net)，通过多尺度提取、分层蒸馏和信息聚合来准确捕捉雨滴特征，采用残差投影特征融合策略逐步区分特征学习和聚合不同特征，与最新的去雨算法相比在合成和真实的数据集上展示了其有效性。