The Snowflake Hypothesis: Training and Powering GNN with One Node One Receptive Field

Despite Graph Neural Networks (GNNs) demonstrating considerable promise in graph representation learning tasks, GNNs predominantly face significant issues with overfitting and over-smoothing as they go deeper as models of computer vision (CV) realm. The success of artificial intelligence in computer vision and natural language processing largely stems from its ability to train deep models effectively. We have thus conducted a systematic study on deep GNN models. 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. In this paper, 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 scheme; (2) various shallow and deep GNN backbones; (3) various numbers of layers (8, 16, 32, 64) on multiple benchmarks; (4) compare with different aggregation strategies. The observational results demonstrate that our framework can serve as a universal operator for a range of tasks, and it displays tremendous potential on deep GNNs. Code is available at: https://github.com/CunWang520/Snowhypothe.