Shalima Binta Manir

Shalima Binta Manir, Tim Oates

Standard message-passing graph neural networks (GNNs) often struggle on graphs with low homophily, yet homophily alone does not explain this behavior, as graphs with similar homophily levels can exhibit markedly different performance and some heterophilous graphs remain easy for vanilla GCNs. Recent work suggests that label informativeness (LI), the mutual information between labels of adjacent nodes, provides a more faithful characterization of when graph structure is useful. In this work, we develop a unified theoretical framework that connects curvature-guided rewiring and positional geometry through the lens of label informativeness, and instantiate it in a practical geometry-aware architecture, ASEHybrid. Our analysis provides a necessary-and-sufficient characterization of when geometry-aware GNNs can improve over feature-only baselines: such gains are possible if and only if graph structure carries label-relevant information beyond node features. Theoretically, we relate adjusted homophily and label informativeness to the spectral behavior of label signals under Laplacian smoothing, show that degree-based Forman curvature does not increase expressivity beyond the one-dimensional Weisfeiler--Lehman test but instead reshapes information flow, and establish convergence and Lipschitz stability guarantees for a curvature-guided rewiring process. Empirically, we instantiate ASEHybrid using Forman curvature and Laplacian positional encodings and conduct controlled ablations on Chameleon, Squirrel, Texas, Tolokers, and Minesweeper, observing gains precisely on label-informative heterophilous benchmarks where graph structure provides label-relevant information beyond node features, and no meaningful improvement in high-baseline regimes.

Shalima Binta Manir, Tim Oates

We introduce a novel Theory of Mind (ToM) framework inspired by dual-process theories from cognitive science, integrating a fast, habitual graph-based reasoning system (System 1), implemented via graph convolutional networks (GCNs), and a slower, context-sensitive meta-adaptive learning system (System 2), driven by meta-learning techniques. Our model dynamically balances intuitive and deliberative reasoning through a learned context gate mechanism. We validate our architecture on canonical false-belief tasks and systematically explore its capacity to replicate hallmark cognitive biases associated with dual-process theory, including anchoring, cognitive-load fatigue, framing effects, and priming effects. Experimental results demonstrate that our dual-process approach closely mirrors human adaptive behavior, achieves robust generalization to unseen contexts, and elucidates cognitive mechanisms underlying reasoning biases. This work bridges artificial intelligence and cognitive theory, paving the way for AI systems exhibiting nuanced, human-like social cognition and adaptive decision-making capabilities.

Shalima Binta Manir, Tim Oates

A common observation in the Graph Convolutional Network (GCN) literature is that stacking GCN layers may or may not result in better performance on tasks like node classification and edge prediction. We have found empirically that a graph's algebraic connectivity, which is known as the Fiedler value, is a good predictor of GCN performance. Intuitively, graphs with similar Fiedler values have analogous structural properties, suggesting that the same filters and hyperparameters may yield similar results when used with GCNs, and that transfer learning may be more effective between graphs with similar algebraic connectivity. We explore this theoretically and empirically with experiments on synthetic and real graph data, including the Cora, CiteSeer and Polblogs datasets. We explore multiple ways of aggregating the Fiedler value for connected components in the graphs to arrive at a value for the entire graph, and show that it can be used to predict GCN performance. We also present theoretical arguments as to why the Fiedler value is a good predictor.