Not Just Oversmoothing: Detecting the Echo Chamber Effect in Graph Neural Networks

Community detection in attributed networks faces a fundamental divide: topological algorithms ignore semantic features, while Graph Neural Networks (GNNs) encounter devastating 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 dismantle 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 heterophilic poisoning while ensuring semantic densification. Coupled with a memory sharded full batch contrastive objective and a novel chunked O(N \cdot K) similarity extraction method, ECHO completely 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 throughputs exceeding 2,800 nodes per second matching the speed of highly optimized purely topological baselines. The implementation utilizes a unified framework that automatically engages memory sharded optimization to support adoption across varying hardware constraints. GitHub Repository: https://github.com/emilioferrara/ECHO-GNN

We define an information-complexity property for aggregation functions, capturing a vast range of practical aggregations, and prove that any Message-Passing Graph Neural Network (MP-GNN) model with such aggregations induces only a polynomial number of equivalence classes on all graphs - while the number of non-isomorphic graphs is super-exponential (in number of vertices). Adding a familiar perspective, we observe that merely 2 iterations of Color Refinement (CR) induce at least an exponential number of equivalence classes, making the aforementioned MP-GNNs relatively infinitely weaker. Previous studies state that sum-aggregation MP-GNNs match full CR however they consider a weak, 'non-uniform', notion of distinguishing-power where each graph size may require a different MP-GNN to distinguish graphs up to that size. Our results concern both distinguishing between non-equivariant vertices and distinguishing between non-isomorphic graphs.

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.