Differentiable Higher-Order Graph Learning via Sheaf-Inspired Local Inconsistency

Topological neural networks (TNNs) extend graph neural networks by modeling higher-order interactions beyond pairwise relations, but their effectiveness critically depends on how higher-order structures are constructed. Existing graph lifting methods typically rely on connectivity or feature similarity, which often fail to capture meaningful relationships, particularly in heterophilous graphs where connected nodes exhibit dissimilar features or labels. To address this issue, we propose a graph lifting framework based on local inconsistency, inspired by cellular sheaf theory, where edge-dependent transformations compare node representations in shared spaces to capture relational patterns beyond similarity. We further introduce a differentiable framework that aggregates edge-level inconsistencies over cycles and employs a soft gating mechanism to construct weighted higher-order structures in an end-to-end manner. The proposed framework is applicable across various topological domains, e.g., simplicial and cellular complexes, and can be integrated with diverse TNN architectures. Extensive experiments demonstrate consistent performance improvements across diverse TNN backbones and a wide range of graph lifting baselines, with particularly strong gains on heterophilous graph datasets. Code will be released upon acceptance.