Graph-based neural network models are producing strong results in a number of domains, in part because graphs provide flexibility to encode domain knowledge in the form of relational structure (edges) between nodes in the graph. In practice, edges are used both to represent intrinsic structure (e.g., abstract syntax trees of programs) and more abstract relations that aid reasoning for a downstream task (e.g., results of relevant program analyses). In this work, we study the problem of learning to derive abstract relations from the intrinsic graph structure. Motivated by their power in program analyses, we consider relations defined by paths on the base graph accepted by a finite-state automaton. We show how to learn these relations end-to-end by relaxing the problem into learning finite-state automata policies on a graph-based POMDP and then training these policies using implicit differentiation. The result is a differentiable Graph Finite-State Automaton (GFSA) layer that adds a new edge type (expressed as a weighted adjacency matrix) to a base graph. We demonstrate that this layer can find shortcuts in grid-world graphs and reproduce simple static analyses on Python programs. Additionally, we combine the GFSA layer with a larger graph-based model trained end-to-end on the variable misuse program understanding task, and find that using the GFSA layer leads to better performance than using hand-engineered semantic edges or other baseline methods for adding learned edge types.

As a motivating example, consider a dataset of source code samples.

The development of artificial intelligence systems capable of understanding and reasoning about complex real-world scenarios is a significant challenge. In this work we present a novel approach to enhance and exploit LLM reactive capability to address complex problems and interpret deeply contextual real-world meaning. We introduce a method and a tool for creating a multimodal, knowledge-augmented formal representation of meaning that combines the strengths of large language models with structured semantic representations. Our method begins with an image input, utilizing state-of-the-art large language models to generate a natural language description. This description is then transformed into an Abstract Meaning Representation (AMR) graph, which is formalized and enriched with logical design patterns, and layered semantics derived from linguistic and factual knowledge bases. The resulting graph is then fed back into the LLM to be extended with implicit knowledge activated by complex heuristic learning, including semantic implicatures, moral values, embodied cognition, and metaphorical representations. By bridging the gap between unstructured language models and formal semantic structures, our method opens new avenues for tackling intricate problems in natural language understanding and reasoning.

Graph-based neural network models are producing strong results in a number of domains, in part because graphs provide flexibility to encode domain knowledge in the form of relational structure (edges) between nodes in the graph. In practice, edges are used both to represent intrinsic structure (e.g., abstract syntax trees of programs) and more abstract relations that aid reasoning for a downstream task (e.g., results of relevant program analyses). In this work, we study the problem of learning to derive abstract relations from the intrinsic graph structure. Motivated by their power in program analyses, we consider relations defined by paths on the base graph accepted by a finite-state automaton. We show how to learn these relations end-to-end by relaxing the problem into learning finite-state automata policies on a graph-based POMDP and then training these policies using implicit differentiation.

We explore graph rewiring methods that optimise commute time. Recent graph rewiring approaches facilitate long-range interactions in sparse graphs, making such rewirings commute-time-optimal $\textit{on average}$. However, when an expert prior exists on which node pairs should or should not interact, a superior rewiring would favour short commute times between these privileged node pairs. We construct two synthetic datasets with known priors reflecting realistic settings, and use these to motivate two bespoke rewiring methods that incorporate the known prior. We investigate the regimes where our rewiring improves test performance on the synthetic datasets. Finally, we perform a case study on a real-world citation graph to investigate the practical implications of our work.

Recent advancements in graph learning contributed to explaining predictions generated by Graph Neural Networks. However, existing methodologies often fall short when applied to real-world datasets. We introduce HOGE, a framework to capture higher-order structures using cell complexes, which excel at modeling higher-order relationships. In the real world, higher-order structures are ubiquitous like in molecules or social networks, thus our work significantly enhances the practical applicability of graph explanations. HOGE produces clearer and more accurate explanations compared to prior methods. Our method can be integrated with all existing graph explainers, ensuring seamless integration into current frameworks. We evaluate on GraphXAI benchmark datasets, HOGE achieves improved or comparable performance with minimal computational overhead. Ablation studies show that the performance gain observed can be attributed to the higher-order structures that come from introducing cell complexes.

Graph structure expression plays a vital role in distinguishing various graphs. In this work, we propose a Structure-Sensitive Graph Dictionary Embedding (SS-GDE) framework to transform input graphs into the embedding space of a graph dictionary for the graph classification task. Instead of a plain use of a base graph dictionary, we propose the variational graph dictionary adaptation (VGDA) to generate a personalized dictionary (named adapted graph dictionary) for catering to each input graph. In particular, for the adaptation, the Bernoulli sampling is introduced to adjust substructures of base graph keys according to each input, which increases the expression capacity of the base dictionary tremendously. To make cross-graph measurement sensitive as well as stable, multi-sensitivity Wasserstein encoding is proposed to produce the embeddings by designing multi-scale attention on optimal transport. To optimize the framework, we introduce mutual information as the objective, which further deduces to variational inference of the adapted graph dictionary. We perform our SS-GDE on multiple datasets of graph classification, and the experimental results demonstrate the effectiveness and superiority over the state-of-the-art methods.

Subgraph classification is an emerging field in graph representation learning where the task is to classify a group of nodes (i.e., a subgraph) within a graph. Subgraph classification has applications such as predicting the cellular function of a group of proteins or identifying rare diseases given a collection of phenotypes. Graph neural networks (GNNs) are the de facto solution for node, link, and graph-level tasks but fail to perform well on subgraph classification tasks. Even GNNs tailored for graph classification are not directly transferable to subgraph classification as they ignore the external topology of the subgraph, thus failing to capture how the subgraph is located within the larger graph. The current state-of-the-art models for subgraph classification address this shortcoming through either labeling tricks or multiple message-passing channels, both of which impose a computation burden and are not scalable to large graphs. To address the scalability issue while maintaining generalization, we propose Stochastic Subgraph Neighborhood Pooling (SSNP), which jointly aggregates the subgraph and its neighborhood (i.e., external topology) information without any computationally expensive operations such as labeling tricks. To improve scalability and generalization further, we also propose a simple data augmentation pre-processing step for SSNP that creates multiple sparse views of the subgraph neighborhood. We show that our model is more expressive than GNNs without labeling tricks. Our extensive experiments demonstrate that our models outperform current state-of-the-art methods (with a margin of up to 2%) while being up to 3X faster in training.