Extremely Fast and Compact Binary Graph Representations via Randomized Operator Sketching

2026-09-26

AI Summary

This study addresses the high computational overhead of dense floating-point representations in graph neural networks and the limitations of existing binary hashing methods that either sacrifice topological information or incur prohibitive generation costs. To overcome these bottlenecks, this work proposes an ultrafast, feature-free, and training-free algebraic graph hashing framework. The method approximates the structural transition matrix via Nyström-inspired randomized column sampling, combined with label-safe semantic propagation and threshold-based discretization, yielding the first fully algebraic, gradient-free binary encoding mechanism. Evaluated across ten node classification datasets, the proposed approach consistently outperforms existing feature-free baselines in accuracy while achieving sub-second code generation. Furthermore, its compatibility with neuromorphic spiking networks is demonstrated, validating the efficacy of simple algebraic approximations in preserving global topology for highly efficient graph representation learning.

Abstract

Graph neural networks typically rely on dense, floating-point node representations, which can impose substantial memory and computational costs. Binary graph hashing offers an alternative by encoding node information as compact bit strings. However, existing approaches either sacrifice global topological information for computational efficiency or incur substantial generation costs. We introduce an ultra-fast, entirely algebraic hashing method that constructs binary node representations directly from graph structure, without requiring node features or gradient-based training. Our method approximates a high-order structural transition matrix using randomized column sampling inspired by the Nystr\"om method and combines it with an efficient label-safe semantic propagation mechanism. The resulting continuous representations are discretized through column-wise thresholding to obtain compact binary codes. Experiments on ten node classification datasets show that the proposed method consistently improves classification accuracy over existing feature-free binary baselines while requiring sub-second code generation on many datasets. The resulting binary representations are also naturally suited to event-driven computation, making them compatible with neuromorphic spiking neural networks and gradient-free learning rules. These results demonstrate that simple algebraic approximations can provide an efficient alternative to learned pipelines for discrete graph representation learning.

Problem

• Binary Graph Hashing
• Graph Neural Networks
• Compact Node Representations
• Discrete Graph Representation Learning
• Computational Efficiency

Innovation

• Binary Graph Hashing
• Randomized Operator Sketching
• Nystrom Approximation
• Graph Neural Networks
• Neuromorphic Computing