ASEHybrid: When Geometry Matters Beyond Homophily in Graph Neural Networks

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.

Hierarchical Learning for Maze Navigation: Emergence of Mental Representations via Second-Order Learning

Mental representation, characterized by structured internal models mirroring external environments, is fundamental to advanced cognition but remains challenging to investigate empirically. Existing theory hypothesizes that second-order learning -- learning mechanisms that adapt first-order learning (i.e., learning about the task/domain) -- promotes the emergence of such environment-cognition isomorphism. In this paper, we empirically validate this hypothesis by proposing a hierarchical architecture comprising a Graph Convolutional Network (GCN) as a first-order learner and an MLP controller as a second-order learner. The GCN directly maps node-level features to predictions of optimal navigation paths, while the MLP dynamically adapts the GCN's parameters when confronting structurally novel maze environments. We demonstrate that second-order learning is particularly effective when the cognitive system develops an internal mental map structurally isomorphic to the environment. Quantitative and qualitative results highlight significant performance improvements and robust generalization on unseen maze tasks, providing empirical support for the pivotal role of structured mental representations in maximizing the effectiveness of second-order learning.

One Model, Two Minds: A Context-Gated Graph Learner that Recreates Human Biases

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.