# SVD-AE: Simple Autoencoders for Collaborative Filtering

arXiv: https://arxiv.org/abs/2405.04746 · HTML: https://mlsanity.com/paper/2405.04746/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 73 references that are in the map.
- First posted on arXiv 8 May 2024.

## Builds on (most cited first, 30 of 31)

- [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)
- [Graph Signal Processing: Overview, Challenges and Applications](https://mlsanity.com/paper/1712.00468/) (2017)
- [Revisiting Graph based Collaborative Filtering: A Linear Residual Graph Convolutional Network Approach](https://mlsanity.com/paper/2001.10167/) (2020)
- [Disentangled Graph Collaborative Filtering](https://mlsanity.com/paper/2007.01764/) (2020)
- [Learning Disentangled Representations for Recommendation](https://mlsanity.com/paper/1910.14238/) (2019)
- [Collaborative Deep Learning for Recommender Systems](https://mlsanity.com/paper/1409.2944/) (2014)
- [UltraGCN: Ultra Simplification of Graph Convolutional Networks for Recommendation](https://mlsanity.com/paper/2110.15114/) (2021)
- [A Survey of Graph Neural Networks for Social Recommender Systems](https://mlsanity.com/paper/2212.04481/) (2022)
- [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)
- [Blurring-Sharpening Process Models for Collaborative Filtering](https://mlsanity.com/paper/2211.09324/) (2022)
- [Sequential Variational Autoencoders for Collaborative Filtering](https://mlsanity.com/paper/1811.09975/) (2018)
- [An Attentive Inductive Bias for Sequential Recommendation beyond the Self-Attention](https://mlsanity.com/paper/2312.10325/) (2023)
- [Bootstrapping User and Item Representations for One-Class Collaborative Filtering](https://mlsanity.com/paper/2105.06323/) (2021)
- [LT-OCF: Learnable-Time ODE-based Collaborative Filtering](https://mlsanity.com/paper/2108.06208/) (2021)
- [AutoSVD++: An Efficient Hybrid Collaborative Filtering Model via Contractive Auto-encoders](https://mlsanity.com/paper/1704.00551/) (2017)
- [Infinite Recommendation Networks: A Data-Centric Approach](https://mlsanity.com/paper/2206.02626/) (2022)
- [Linear, or Non-Linear, That is the Question!](https://mlsanity.com/paper/2111.07265/) (2021)
- [SVD-GCN: A Simplified Graph Convolution Paradigm for Recommendation](https://mlsanity.com/paper/2208.12689/) (2022)
- [Mutually-Regularized Dual Collaborative Variational Auto-encoder for Recommendation Systems](https://mlsanity.com/paper/2211.11662/) (2022)
- [TimeKit: A Time-series Forecasting-based Upgrade Kit for Collaborative Filtering](https://mlsanity.com/paper/2211.04266/) (2022)
- [It's Enough: Relaxing Diagonal Constraints in Linear Autoencoders for Recommendation](https://mlsanity.com/paper/2305.12922/) (2023)
- [Turbo-CF: Matrix Decomposition-Free Graph Filtering for Fast Recommendation](https://mlsanity.com/paper/2404.14243/) (2024)
- [Faster Matrix Completion Using Randomized SVD](https://mlsanity.com/paper/1810.06860/) (2018)
- [SCONE: A Novel Stochastic Sampling to Generate Contrastive Views and Hard Negative Samples for Recommendation](https://mlsanity.com/paper/2405.00287/) (2024)
- [RDGCL: Reaction-Diffusion Graph Contrastive Learning for Recommendation](https://mlsanity.com/paper/2312.16563/) (2023)

## Built on by (most cited first, 4 of 4)

- [Towards Unified and Adaptive Cross-Domain Collaborative Filtering via Graph Signal Processing](https://mlsanity.com/paper/2407.12374/) (2024)
- [LLM-Enhanced Linear Autoencoders for Recommendation](https://mlsanity.com/paper/2508.13500/) (2025)
- [Memory Is No Longer a Bottleneck: Memory-Efficient Graph Filtering for Scalable Collaborative Filtering](https://mlsanity.com/paper/2606.21540/) (2026)
- [TV-Rec: Time-Variant Convolutional Filter for Sequential Recommendation](https://mlsanity.com/paper/2510.25259/) (2025)

## Abstract (arXiv)

Collaborative filtering (CF) methods for recommendation systems have been extensively researched, ranging from matrix factorization and autoencoder-based to graph filtering-based methods. Recently, lightweight methods that require almost no training have been recently proposed to reduce overall computation. However, existing methods still have room to improve the trade-offs among accuracy, efficiency, and robustness. In particular, there are no well-designed closed-form studies for balanced CF in terms of the aforementioned trade-offs. In this paper, we design SVD-AE, a simple yet effective singular vector decomposition (SVD)-based linear autoencoder, whose closed-form solution can be defined based on SVD for CF. SVD-AE does not require iterative training processes as its closed-form solution can be calculated at once. Furthermore, given the noisy nature of the rating matrix, we explore the robustness against such noisy interactions of existing CF methods and our SVD-AE. As a result, we demonstrate that our simple design choice based on truncated SVD can be used to strengthen the noise robustness of the recommendation while improving efficiency. Code is available at https://github.com/seoyoungh/svd-ae.