Due to their ability to model meaningful higher order relations among a set
of entities, higher order network models have emerged recently as a powerful
alternative for graph-based network models which are only capable of modeling
binary relationships. Message passing paradigm is still dominantly used to
learn representations even for higher order network models. While powerful,
message passing can have disadvantages during inference, particularly when the
higher order connectivity information is missing or corrupted. To overcome such
limitations, we propose Topo-MLP, a purely MLP-based simplicial neural network
algorithm to learn the representation of elements in a simplicial complex
without explicitly relying on message passing. Our framework utilizes a novel
Higher Order Neighborhood Contrastive (HONC) loss which implicitly incorporates
the simplicial structure into representation learning. Our proposed model's
simplicity makes it faster during inference. Moreover, we show that our model
is robust when faced with missing or corrupted connectivity structure.

通过提出一种仅基于 MLP 的简化神经网络算法 Topo-MLP，可以学习简单复合物中元素的表示，而不需要明确依赖消息传递方法。该模型的简洁性使其在推理过程中更快速，并且在面对缺失或损坏的连接结构时仍然表现出鲁棒性。

Topo-MLP：一种无需消息传递机制的单纯网络

Topo-MLP : A Simplicial Network Without Message Passing

Most graph neural networks (GNNs) use the message passing paradigm, in which
node features are propagated on the input graph. Recent works pointed to the
distortion of information flowing from distant nodes as a factor limiting the
efficiency of message passing for tasks relying on long-distance interactions.
This phenomenon, referred to as 'over-squashing', has been heuristically
attributed to graph bottlenecks where the number of $k$-hop neighbors grows
rapidly with $k$. We provide a precise description of the over-squashing
phenomenon in GNNs and analyze how it arises from bottlenecks in the graph. For
this purpose, we introduce a new edge-based combinatorial curvature and prove
that negatively curved edges are responsible for the over-squashing issue. We
also propose and experimentally test a curvature-based graph rewiring method to
alleviate the over-squashing.

本文研究图神经网络中信息传递中的 over-squashing 问题，通过引入基于曲率的重连方法以减轻该问题，同时探究其根源为图中负曲率边所导致的瓶颈现象。

通过曲率理解图形上的压缩和瓶颈

Understanding over-squashing and bottlenecks on graphs via curvature

Nowadays, Graph Neural Networks (GNNs) following the Message Passing paradigm
become the dominant way to learn on graphic data. Models in this paradigm have
to spend extra space to look up adjacent nodes with adjacency matrices and
extra time to aggregate multiple messages from adjacent nodes. To address this
issue, we develop a method called LinkDist that distils self-knowledge from
connected node pairs into a Multi-Layer Perceptron (MLP) without the need to
aggregate messages. Experiment with 8 real-world datasets shows the MLP derived
from LinkDist can predict the label of a node without knowing its adjacencies
but achieve comparable accuracy against GNNs in the contexts of semi- and
full-supervised node classification. Moreover, LinkDist benefits from its
Non-Message Passing paradigm that we can also distil self-knowledge from
arbitrarily sampled node pairs in a contrastive way to further boost the
performance of LinkDist.

本研究发展出一种名为 LinkDist 的方法，它利用连接节点对的自身知识来提取无需聚合消息的多层感知机 (MLP)，并在半监督和全监督节点分类方面表现出与 GNNs 相对可比的准确性。此外，LinkDist 从其非消息传递范式中受益，我们可以用对比的方式从任意抽样的节点对中提取自知识，从而进一步提高 LinkDist 的性能。