Memory Is No Longer a Bottleneck: Memory-Efficient Graph Filtering for Scalable Collaborative Filtering

2026-06-19

AI Summary

This work addresses the excessive memory overhead of existing graph filtering–based collaborative filtering methods, which require explicit storage of a full item similarity graph, rendering them impractical for large-scale scenarios. To overcome this limitation, we propose Mem-GF, the first approach to integrate Krylov subspace techniques into graph filtering for collaborative filtering. By leveraging a matrix-free polynomial filtering approximation, Mem-GF enables efficient signal smoothing without storing the similarity graph, while theoretically guaranteeing near-lossless approximation. Our method drastically alleviates the memory bottleneck—reducing memory consumption to 1/5.74 of baseline methods and accelerating runtime by 4.38×—while achieving superior recommendation accuracy over state-of-the-art graph filtering and graph convolutional network approaches. Notably, Mem-GF scales effectively to datasets with tens of millions of interactions.

Abstract

Graph convolutional networks (GCNs) have demonstrated significant success in capturing complex user-item relationships for collaborative filtering (CF). However, due to their reliance on extensive model training, training-free graph filtering (GF)-based CF methods have emerged as a promising alternative, offering computational efficiency by smoothing graph signals via matrix operations. In particular, polynomial GF-based approaches demonstrate improved accuracy through their ability to design more expressive and flexible filtering functions. Despite these advantages, existing GF methods suffer from a critical memory bottleneck: they necessitate storing the full item similarity graph, incurring prohibitive memory costs for large-scale datasets, which limits their practical applicability. To tackle this challenge, we propose Mem-GF (Memory-efficient GF), a new GF-based CF method that departs from conventional designs by principally leveraging the structure of Krylov subspaces as a core mechanism for approximating polynomial graph filters without explicitly storing the item similarity graph. We theoretically analyze the minimum Krylov subspace size that guarantees lossless approximation. Through extensive experiments, we demonstrate that Mem-GF achieves up to 5.74$\times$ lower memory usage and 4.38$\times$ speedup in runtime, while consistently exceeding the recommendation accuracy of state-of-the-art GF and GCN-based methods. Mem-GF robustly scales to datasets with tens of millions of interactions, establishing itself as a practically viable and theoretically grounded solution for efficient CF.

Problem

• graph filtering
• collaborative filtering
• memory bottleneck
• item similarity graph
• scalability

Innovation

• Memory-efficient
• Graph Filtering
• Krylov Subspace
• Collaborative Filtering
• Scalable Recommendation