Diagnosing GNN Failure Modes with Layer-Wise Probe Entropy

Graph Neural Networks (GNNs) have proven effective for graph analytical tasks, yet their "black-box" nature complicates the understanding of their layer-wise behavior and hinders their application to large graphs. We demonstrate SliceGXQ, an end-to-end declarative and interactive system for querying and exploring layer-wise explanations for GNNs over large-scale graphs. In particular, SliceGXQ provides (1) an interactive graphical user interface for dataset, model, and explanation configuration; (2) a lightweight SPARQL-like parser that allows users to specify target nodes, layers, explanation modes, and constraints; and (3) an integrated execution and visualization workflow that invokes SliceGX as its underlying explanation engine. We demonstrate how users can diagnose a misclassified node, identify problematic layers and influential messages, and perform targeted model debugging, together with large-scale graph interpretation and fraud-detection analysis. Our demonstration video and source code are available at https://github.com/jinzhaoqet/SliceGXQ.

Graph Neural Networks (GNNs) learn node representations through iterative network-based message-passing. While powerful, deep GNNs suffer from oversmoothing, where node features converge to a homogeneous, non-informative state. We re-frame this problem of representational collapse from a bifurcation theory perspective, characterizing oversmoothing as convergence to a stable ``homogeneous fixed point.'' Our central contribution is the theoretical discovery that this undesired stability can be broken by replacing standard monotone activations (e.g., ReLU) with a class of functions. Using Lyapunov-Schmidt reduction, we analytically prove that this substitution induces a bifurcation that destabilizes the homogeneous state and creates a new pair of stable, non-homogeneous patterns that provably resist oversmoothing. Our theory predicts a precise, nontrivial scaling law for the amplitude of these emergent patterns, which we quantitatively validate in experiments. Finally, we demonstrate the practical utility of our theory by deriving a closed-form, bifurcation-aware initialization and showing its utility in real benchmark experiments.

Curvature notions on graphs, particularly Ollivier-Ricci and Forman, have emerged as powerful tools for addressing fundamental issues in Graph Neural Networks (GNNs) such as oversmoothing and oversquashing, but rely almost exclusively on local edge-level comparisons and therefore fail to certify how information actually propagates over long distances. We introduce Entropic Curvature, a global, transport-based curvature obtained by extending the Lott-Sturm-Villani framework to graphs through the displacement convexity of entropy along Wasserstein geodesics. We define a tractable Weak Entropic Curvature proxy that lower-bounds the global entropic curvature, and from it derive (i) a Poincare-type inequality controlling oversmoothing, (ii) a transport-entropy generalization bound, and (iii) an expansion paradox proving that sparsity, strong spectral expansion, and positive entropic curvature cannot coexist in large graphs, unifying oversmoothing and oversquashing as opposite ends of a single curvature spectrum. We translate the theory into three practical mechanisms, the E-Gate aggregator, the ENT structural encoding, and Midpoint-Completion Rewiring (MCR), and benchmark them against SDRF, FoSR, BORF, LCP, and Graph Ricci Flow on six node-classification benchmarks, and graph-classification.