2026/02/25 by Emilio Ferrara · 1 voice
Computer Science · Mathematics · #Computability, Logic, AI Algorithms #Logic, programming, and type systems #Algebraic and Geometric Analysis
paper · pdf · doi:10.1016/j.mlwa.2026.100930
Community detection in attributed networks faces a fundamental divide: topological algorithms ignore semantic features, while Graph Neural Networks (GNNs) encounter significant computational bottlenecks. Specifically, GNNs suffer from a “Semantic Wall” of feature over-smoothing in dense or heterophilic networks, and a “Systems Wall” driven by the O ( N 2 ) memory constraints of pairwise clustering. To address these barriers, we introduce ECHO (Encoding Communities via High-order Operators), a scalable, self-supervised architecture that reframes community detection as an adaptive, multi-scale diffusion process. ECHO features a Topology-Aware Router that automatically analyzes structural heuristics (sparsity, density, and assortativity) to route graphs through the optimal inductive bias, preventing over-smoothing from neighborhood aggregation in heterophilic settings while ensuring semantic densification. Coupled with a memory-sharded full-batch contrastive objective and a chunked O ( N ⋅ k m a x ) similarity extraction method, ECHO bypasses traditional O ( N 2 ) memory bottlenecks without sacrificing the mathematical precision of global gradients. Extensive evaluations demonstrate that this topology-feature synergy consistently overcomes the classical resolution limit. On synthetic LFR benchmarks scaled up to 1 million nodes, ECHO achieves scale-invariant accuracy despite severe topological noise. Furthermore, on massive real-world social networks with over 1.6 million nodes and 30 million edges, it completes clustering in mere minutes with throughput exceeding 2800 nodes per second, matching the speed of highly optimized purely topological baselines.