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ECHO: Encoding Communities via High-order Operators

Emilio Ferrara

TL;DR

ECHO (Encoding Communities via High order Operators), a scalable, self supervised architecture that reframes community detection as an adaptive, multi scale diffusion process, and achieves scale invariant accuracy despite severe topological noise.

Abstract

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

ECHO: Encoding Communities via High-order Operators

TL;DR

ECHO (Encoding Communities via High order Operators), a scalable, self supervised architecture that reframes community detection as an adaptive, multi scale diffusion process, and achieves scale invariant accuracy despite severe topological noise.

Abstract

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
Paper Structure (32 sections, 9 equations, 3 figures, 6 tables, 1 algorithm)

This paper contains 32 sections, 9 equations, 3 figures, 6 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Topological Community Detection and Higher-Order Structures
  4. Graph Representation Learning
  5. Attributed Graph Clustering and GNNs
  6. Methodology
  7. Topology-Aware Semantic Routing
  8. Adaptive Semantic Encoding
  9. Pathway A: The Isolating Encoder (MLP)
  10. Pathway B: The Densifying Encoder (GraphSAGE)
  11. Attention-Guided Multi-Scale Diffusion
  12. Memory-Sharded Contrastive Learning
  13. Scalable $O(N \cdot K)$ Clustering Extraction
  14. Experimental Setup
  15. Synthetic Networks (LFR Benchmarks)
  16. ...and 17 more sections

Figures (3)

  • Figure 1: The ECHO architecture pipeline. Phase 1 actively prevents heterophilic poisoning and semantic starvation by routing the graph based on structural heuristics. Phase 2 extracts multi-scale representations and bypasses training memory limits via tensor sharding, while Phase 3 extracts communities via chunked topological filtering.
  • Figure 2: Evolution of Cluster Geometry on Cora. Left: Raw bag-of-words features exhibit significant overlap, explaining the poor performance of feature-only methods. Right: ECHO embeddings demonstrate clear manifold separation, where the academic disciplines are pulled into distinct, cohesive islands with minimal inter-class noise.
  • Figure 3: High-Density Manifold Separation on Amazon Computers. Despite an average degree of 36, ECHO identifies distinct product categories. The use of a topology-constrained MLP ($K=0$) prevents feature collapse, maintaining sharp boundaries between disparate product clusters (e.g., Laptops vs. Desktops).