The Hidden Fragility of GNNs: How Graph Structure Amplifies Numerical Errors

Disentangling Homophily and Rarity: Explaining Failure in Graph Neural Networks

Are heterophilic nodes in a graph harder to classify because they are heterophilic or because they are rare? Some existing work frames classification of such nodes as a subgroup generalisation problem, where a model performs well on the majority group at the expense of the rare group. Others explain this as a problem of neighbourhood aggregation in graph neural networks (GNNs). We assess these two viewpoints through a detailed evaluation of six GNNs on five datasets of varying homophily, and find that homophilic nodes tend to be easier to classify, even when they are rare---challenging the subgroup framing. However, our findings also nuance existing beliefs about how GNNs misrepresent heterophilic nodes. We demonstrate that the information needed to classify heterophilic nodes correctly is often recoverable by retraining the classification head of a model, or even just the final linear classification layer.

H4G: Unlocking Faithful Inference for Zero-Shot Graph Learning in Hyperbolic Space

Text-attributed graphs are widely used across domains, offering rich opportunities for zero-shot learning via graph-text alignment. However, existing methods struggle with tasks requiring fine-grained pattern recognition, particularly on heterophilic graphs. Through empirical and theoretical analysis, we identify an over-abstraction problem: current approaches operate at excessively large hyperbolic radii, compressing multi-scale structural information into uniform high-level abstractions. This abstraction-induced information loss obscures critical local patterns essential for accurate predictions. By analyzing embeddings in hyperbolic space, we demonstrate that optimal graph learning requires faithful preservation of fine-grained structural details, better retained by representations positioned closer to the origin. To address this, we propose H4G, a framework that systematically reduces embedding radii using learnable block-diagonal scaling matrices and Möbius matrix multiplication. This approach restores access to fine-grained patterns while maintaining global receptive ability with minimal computational overhead. Experiments show H4G achieves state-of-the-art zero-shot performance with 12.8% improvement on heterophilic graphs and 8.4% on homophilic graphs, confirming that radius reduction enables faithful multi-scale representation for advancing zero-shot graph learning.

Local Geometry Improves Explanation Robustness for Graph Neural Networks

Controlling representation evolution in deep graph neural networks.

Deep Graph Neural Networks (GNNs) often degrade when many propagation layers are stacked. Although this phenomenon is commonly associated with over-smoothing, node-wise similarity alone does not fully describe deep representation failure. During propagation, node representations form a layer-wise trajectory that may become unstable, lose traceability to input information, or collapse into a low-dimensional subspace. Motivated by this view, we formulate deep GNN degradation as a problem of representation trajectory control. The framework integrates three complementary controls along a shared representation trajectory. The Stable Reaction-Diffusion encoder (SRD) provides a trajectory-stabilizing forward evolution mechanism that explicitly controls propagation drift and finite-depth sensitivity, rather than simply stacking additional message-passing layers. A deterministic depth-normalized traceability constraint (RDC) encourages intermediate input-space targets to remain traceable to the original features through graph-aware residual consistency. A Rank-Rate Constraint (RRC) penalizes excessive inter-layer decay of logarithmic numerical rank to slow premature subspace degeneration. We position the method as an integration and diagnostic framework rather than a new propagation operator. Theoretical analysis and experiments demonstrate the effectiveness, robustness, and stability of the proposed trajectory-control framework.

Topological Simplification in Predictive Coding Networks

We study the topology of learned representations in predictive coding networks (PCNs), a neuro-inspired bidirectional architecture, using a quantitative layer-wise persistent homology analysis. We train well-performing PCNs on a synthetic classification dataset ($\geq 99.9\%$ test accuracy) and on MNIST ($\geq 95\%$ test accuracy), and measure how topological features change across layers for different architectures and activation functions. We find that smaller PCNs collapse connected components across layers earlier than larger models (Spearman $\unicode{x1D70C} \in [0.72, 0.79]$ across activations), with model size measured as the sum of hidden-layer widths. We also observe a strong negative correlation ($\unicode{x1D70C} = -0.58$) between the depth at which simplification occurs and reconstruction error; i.e., architectures that simplify later reconstruct better. Finally, a seed-level bootstrap comparison across architectures and activations shows that PCNs consistently collapse connected components later than matched MLPs, with an average difference of $3.6$ layers. These results suggest that persistent homology offers a useful quantitative lens on the compression--reconstruction tradeoff in PCNs, and that both model capacity and the recurrent, bidirectional dynamics of predictive coding inference shape when this tradeoff is resolved across layers.

Faithful, Sufficient and Understandable: Rethinking Graph Counterfactual Explanations via Discrete Diffusion Inversion

This work proposes Graph Diffusion Counterfactual Explanation via Inversion (GDCE-I), a discrete denoising diffusion model with a novel discrete inversion scheme that enables distribution-aware edits leveraging the whole domain edit space and qualitatively shows that GDCE-I attains interpretable in-distribution solutions.