Notably, most real-world homophilic and heterophilic graphs are comprised of a mixture of nodes in both homophilic and heterophilic structural patterns, exhibiting a structural disparity.

Recent studies on Graph Neural Networks(GNNs) provide both empirical and theoretical evidence supporting their effectiveness in capturing structural patterns on both homophilic and certain heterophilic graphs. Notably, most real-world homophilic and heterophilic graphs are comprised of a mixture of nodes in both homophilic and heterophilic structural patterns, exhibiting a structural disparity. However, the analysis of GNN performance with respect to nodes exhibiting different structural patterns, e.g., homophilic nodes in heterophilic graphs, remains rather limited. In the present study, we provide evidence that Graph Neural Networks(GNNs) on node classification typically perform admirably on homophilic nodes within homophilic graphs and heterophilic nodes within heterophilic graphs while struggling on the opposite node set, exhibiting a performance disparity. We theoretically and empirically identify effects of GNNs on testing nodes exhibiting distinct structural patterns. We then propose a rigorous, non-i.i.d PAC-Bayesian generalization bound for GNNs, revealing reasons for the performance disparity, namely the aggregated feature distance and homophily ratio difference between training and testing nodes. Furthermore, we demonstrate the practical implications of our new findings via (1) elucidating the effectiveness of deeper GNNs; and (2) revealing an over-looked distribution shift factor on graph out-of-distribution problem and proposing a new scenario accordingly.

Current large language models, such as OpenAI's ChatGPT, have captured the public's attention because how remarkable they are in the use of language. Here, I demonstrate that ChatGPT displays phonological biases that are a hallmark of human language processing. More concretely, just like humans, ChatGPT has a consonant bias. That is, the chatbot has a tendency to use consonants over vowels to identify words. This is observed across languages that differ in their relative distribution of consonants and vowels such as English and Spanish.

Graph neural networks (GNNs) have gained traction over the past few years for their superior performance in numerous machine learning tasks. Graph Convolutional Neural Networks (GCN) are a common variant of GNNs that are known to have high performance in semi-supervised node classification (SSNC), and work well under the assumption of homophily. Recent literature has highlighted that GCNs can achieve strong performance on heterophilous graphs under certain "special conditions". These arguments motivate us to understand why, and how, GCNs learn to perform SSNC. We find a positive correlation between similarity of latent node embeddings of nodes within a class and the performance of a GCN. Our investigation on underlying graph structures of a dataset finds that a GCN's SSNC performance is significantly influenced by the consistency and uniqueness in neighborhood structure of nodes within a class.