Revealing Decurve Flows for Generalized Graph Propagation
CoRR(2024)
摘要
This study addresses the limitations of the traditional analysis of
message-passing, central to graph learning, by defining generalized propagation with directed and weighted graphs. The
significance manifest in two ways. Firstly, we propose Generalized Propagation Neural Networks (GPNNs), a framework that
unifies most propagation-based graph neural networks. By generating
directed-weighted propagation graphs with adjacency function and connectivity
function, GPNNs offer enhanced insights into attention mechanisms across
various graph models. We delve into the trade-offs within the design space with
empirical experiments and emphasize the crucial role of the adjacency function
for model expressivity via theoretical analysis. Secondly, we propose
the Continuous Unified Ricci Curvature (CURC), an extension of
celebrated Ollivier-Ricci Curvature for directed and weighted graphs.
Theoretically, we demonstrate that CURC possesses continuity, scale invariance,
and a lower bound connection with the Dirichlet isoperimetric constant
validating bottleneck analysis for GPNNs. We include a preliminary exploration
of learned propagation patterns in datasets, a first in the field. We observe
an intriguing “decurve flow” - a curvature reduction during
training for models with learnable propagation, revealing the evolution of
propagation over time and a deeper connection to over-smoothing and bottleneck
trade-off.
更多查看译文
AI 理解论文
溯源树
样例
生成溯源树,研究论文发展脉络
Chat Paper
正在生成论文摘要