The Snowflake Hypothesis: Training Deep GNN with One Node One Receptive field

• URL: http://arxiv.org/abs/2308.10051v1
• Date: Sat, 19 Aug 2023 15:21:12 GMT
• Title: The Snowflake Hypothesis: Training Deep GNN with One Node One Receptive field
• Authors: Kun Wang, Guohao Li, Shilong Wang, Guibin Zhang, Kai Wang, Yang You, Xiaojiang Peng, Yuxuan Liang, Yang Wang
• Abstract summary: We introduce the Snowflake Hypothesis -- a novel paradigm underpinning the concept of one node, one receptive field'' We employ the simplest gradient and node-level cosine distance as guiding principles to regulate the aggregation depth for each node. The observational results demonstrate that our hypothesis can serve as a universal operator for a range of tasks.
• Score: 39.679151680622375
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Despite Graph Neural Networks demonstrating considerable promise in graph representation learning tasks, GNNs predominantly face significant issues with over-fitting and over-smoothing as they go deeper as models of computer vision realm. In this work, we conduct a systematic study of deeper GNN research trajectories. Our findings indicate that the current success of deep GNNs primarily stems from (I) the adoption of innovations from CNNs, such as residual/skip connections, or (II) the tailor-made aggregation algorithms like DropEdge. However, these algorithms often lack intrinsic interpretability and indiscriminately treat all nodes within a given layer in a similar manner, thereby failing to capture the nuanced differences among various nodes. To this end, we introduce the Snowflake Hypothesis -- a novel paradigm underpinning the concept of ``one node, one receptive field''. The hypothesis draws inspiration from the unique and individualistic patterns of each snowflake, proposing a corresponding uniqueness in the receptive fields of nodes in the GNNs. We employ the simplest gradient and node-level cosine distance as guiding principles to regulate the aggregation depth for each node, and conduct comprehensive experiments including: (1) different training schemes; (2) various shallow and deep GNN backbones, and (3) various numbers of layers (8, 16, 32, 64) on multiple benchmarks (six graphs including dense graphs with millions of nodes); (4) compare with different aggregation strategies. The observational results demonstrate that our hypothesis can serve as a universal operator for a range of tasks, and it displays tremendous potential on deep GNNs. It can be applied to various GNN frameworks, enhancing its effectiveness when operating in-depth, and guiding the selection of the optimal network depth in an explainable and generalizable way.

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