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

arXiv: https://arxiv.org/abs/2606.21540 · HTML: https://mlsanity.com/paper/2606.21540/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 41 of its 69 references that are in the map.
- First posted on arXiv 19 Jun 2026.

## Builds on (most cited first, 30 of 41)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [LightGCN: Simplifying and Powering Graph Convolution Network for Recommendation](https://mlsanity.com/paper/2002.02126/) (2020)
- [Graph Convolutional Neural Networks for Web-Scale Recommender Systems](https://mlsanity.com/paper/1806.01973/) (2018)
- [Neural Collaborative Filtering](https://mlsanity.com/paper/1708.05031/) (2017)
- [Neural Graph Collaborative Filtering](https://mlsanity.com/paper/1905.08108/) (2019)
- [Ups and Downs: Modeling the Visual Evolution of Fashion Trends with One-Class Collaborative Filtering](https://mlsanity.com/paper/1602.01585/) (2016)
- [Graph Signal Processing: Overview, Challenges and Applications](https://mlsanity.com/paper/1712.00468/) (2017)
- [Session-based Recommendation with Graph Neural Networks](https://mlsanity.com/paper/1811.00855/) (2018)
- [Variational Autoencoders for Collaborative Filtering](https://mlsanity.com/paper/1802.05814/) (2018)
- [Self-supervised Graph Learning for Recommendation](https://mlsanity.com/paper/2010.10783/) (2020)
- [Graph-less Neural Networks: Teaching Old MLPs New Tricks via Distillation](https://mlsanity.com/paper/2110.08727/) (2021)
- [VBPR: Visual Bayesian Personalized Ranking from Implicit Feedback](https://mlsanity.com/paper/1510.01784/) (2015)
- [Disentangled Graph Collaborative Filtering](https://mlsanity.com/paper/2007.01764/) (2020)
- [Embarrassingly Shallow Autoencoders for Sparse Data](https://mlsanity.com/paper/1905.03375/) (2019)
- [Diffusion Recommender Model](https://mlsanity.com/paper/2304.04971/) (2023)
- [LanczosNet: Multi-Scale Deep Graph Convolutional Networks](https://mlsanity.com/paper/1901.01484/) (2019)
- [SimpleX: A Simple and Strong Baseline for Collaborative Filtering](https://mlsanity.com/paper/2109.12613/) (2021)
- [RecVAE: a New Variational Autoencoder for Top-N Recommendations with Implicit Feedback](https://mlsanity.com/paper/1912.11160/) (2019)
- [How Powerful is Graph Convolution for Recommendation?](https://mlsanity.com/paper/2108.07567/) (2021)
- [Spectral Collaborative Filtering](https://mlsanity.com/paper/1808.10523/) (2018)
- [LiGNN: Graph Neural Networks at LinkedIn](https://mlsanity.com/paper/2402.11139/) (2024)
- [EdgeRec: Recommender System on Edge in Mobile Taobao](https://mlsanity.com/paper/2005.08416/) (2020)
- [Personalized Graph Signal Processing for Collaborative Filtering](https://mlsanity.com/paper/2302.02113/) (2023)
- [A User Guide to Low-Pass Graph Signal Processing and its Applications](https://mlsanity.com/paper/2008.01305/) (2020)
- [Revisiting Neighborhood-based Link Prediction for Collaborative Filtering](https://mlsanity.com/paper/2203.15789/) (2022)
- [Graph-less Collaborative Filtering](https://mlsanity.com/paper/2303.08537/) (2023)
- [Blind Community Detection from Low-rank Excitations of a Graph Filter](https://mlsanity.com/paper/1809.01485/) (2018)
- [Mutually-Regularized Dual Collaborative Variational Auto-encoder for Recommendation Systems](https://mlsanity.com/paper/2211.11662/) (2022)

## Built on by (most cited first, 1 of 1)

- [Advancing Model Research in AgentX: Long-Horizon Autonomy for Industrial Recommender Systems](https://mlsanity.com/paper/2609.30001/) (2026)

## Abstract (arXiv)

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× lower memory usage and 4.38× 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.