Graphs are ubiquitous in social networks and biochemistry, where Graph Neural
Networks (GNN) are the state-of-the-art models for prediction. Graphs can be
evolving and it is vital to formally model and understand how a trained GNN
responds to graph evolution. We propose a smooth parameterization of the GNN
predicted distributions using axiomatic attribution, where the distributions
are on a low-dimensional manifold within a high-dimensional embedding space. We
exploit the differential geometric viewpoint to model distributional evolution
as smooth curves on the manifold. We reparameterize families of curves on the
manifold and design a convex optimization problem to find a unique curve that
concisely approximates the distributional evolution for human interpretation.
Extensive experiments on node classification, link prediction, and graph
classification tasks with evolving graphs demonstrate the better sparsity,
faithfulness, and intuitiveness of the proposed method over the
state-of-the-art methods.

通过使用公理化归因，我们提出了一种平滑参数化的图神经网络（GNN）预测分布，在一个高维嵌入空间中的低维流形上进行。我们利用微分几何观点在流形上建模分布演化，通过重新参数化流形上的曲线族并设计一个凸优化问题，找到一个独特的曲线，以简洁地近似分布演化，以供人类解释。对于具有演化图的节点分类、链路预测和图分类任务的大量实验证明了所提方法相对于现有技术方法的更好的稀疏性、忠实性和直观性。

演化图上 GNN 的微分几何视角与可解释性

A Differential Geometric View and Explainability of GNN on Evolving  Graphs

Reasoning about graphs evolving over time is a challenging concept in many
domains, such as bioinformatics, physics, and social networks. We consider a
common case in which edges can be short term interactions (e.g., messaging) or
long term structural connections (e.g., friendship). In practice, long term
edges are often specified by humans. Human-specified edges can be both
expensive to produce and suboptimal for the downstream task. To alleviate these
issues, we propose a model based on temporal point processes and variational
autoencoders that learns to infer temporal attention between nodes by observing
node communication. As temporal attention drives between-node feature
propagation, using the dynamics of node interactions to learn this key
component provides more flexibility while simultaneously avoiding issues
associated with human-specified edges. We also propose a bilinear
transformation layer for pairs of node features instead of concatenation,
typically used in prior work, and demonstrate its superior performance in all
cases. In experiments on two datasets in the dynamic link prediction task, our
model often outperforms the baseline model that requires a human-specified
graph. Moreover, our learned attention is semantically interpretable and infers
connections similar to actual graphs.

该论文通过使用时态点过程和变分自编码器提出了一种无需人工边缘指定的模型，学习推断节点间的时间关注力，从而具有更大的灵活性和更好的性能，用于动态链接预测任务。

动态图中的双线性交互学习时间注意力

Learning Temporal Attention in Dynamic Graphs with Bilinear Interactions

How do real graphs evolve over time? What are ``normal'' growth patterns in
social, technological, and information networks? Many studies have discovered
patterns in static graphs, identifying properties in a single snapshot of a
large network, or in a very small number of snapshots; these include heavy
tails for in- and out-degree distributions, communities, small-world phenomena,
and others. However, given the lack of information about network evolution over
long periods, it has been hard to convert these findings into statements about
trends over time.
Here we study a wide range of real graphs, and we observe some surprising
phenomena. First, most of these graphs densify over time, with the number of
edges growing super-linearly in the number of nodes. Second, the average
distance between nodes often shrinks over time, in contrast to the conventional
wisdom that such distance parameters should increase slowly as a function of
the number of nodes (like O(log n) or O(log(log n)).
Existing graph generation models do not exhibit these types of behavior, even
at a qualitative level. We provide a new graph generator, based on a ``forest
fire'' spreading process, that has a simple, intuitive justification, requires
very few parameters (like the ``flammability'' of nodes), and produces graphs
exhibiting the full range of properties observed both in prior work and in the
present study.
We also notice that the ``forest fire'' model exhibits a sharp transition
between sparse graphs and graphs that are densifying. Graphs with decreasing
distance between the nodes are generated around this transition point.

研究实际图随时间如何演变并发现大多数图在时间上会加密，同时节点间平均距离缩短，提出森林火灾模型可生成具有相同属性的图。