# Rethinking Collaborative Metric Learning: Toward an Efficient Alternative without Negative Sampling

arXiv: https://arxiv.org/abs/2206.11549 · HTML: https://mlsanity.com/paper/2206.11549/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 94 references that are in the map.
- First posted on arXiv 23 Jun 2022.

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

- [Neural Collaborative Filtering](https://mlsanity.com/paper/1708.05031/) (2017)
- [SphereFace: Deep Hypersphere Embedding for Face Recognition](https://mlsanity.com/paper/1704.08063/) (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)
- [KGAT: Knowledge Graph Attention Network for Recommendation](https://mlsanity.com/paper/1905.07854/) (2019)
- [Neural Factorization Machines for Sparse Predictive Analytics](https://mlsanity.com/paper/1708.05027/) (2017)
- [A Survey on Network Embedding](https://mlsanity.com/paper/1711.08752/) (2017)
- [Neural Collaborative Filtering vs. Matrix Factorization Revisited](https://mlsanity.com/paper/2005.09683/) (2020)
- [Learning Disentangled Representations for Recommendation](https://mlsanity.com/paper/1910.14238/) (2019)
- [Fast Matrix Factorization for Online Recommendation with Implicit Feedback](https://mlsanity.com/paper/1708.05024/) (2017)
- [Collaborative Deep Learning for Recommender Systems](https://mlsanity.com/paper/1409.2944/) (2014)
- [Unifying Knowledge Graph Learning and Recommendation: Towards a Better Understanding of User Preferences](https://mlsanity.com/paper/1902.06236/) (2019)
- [Personalizing Session-based Recommendations with Hierarchical Recurrent Neural Networks](https://mlsanity.com/paper/1706.04148/) (2017)
- [Denoising Implicit Feedback for Recommendation](https://mlsanity.com/paper/2006.04153/) (2020)
- [IRGAN: A Minimax Game for Unifying Generative and Discriminative Information Retrieval Models](https://mlsanity.com/paper/1705.10513/) (2017)
- [On Sampling Strategies for Neural Network-based Collaborative Filtering](https://mlsanity.com/paper/1706.07881/) (2017)
- [Understanding Negative Sampling in Graph Representation Learning](https://mlsanity.com/paper/2005.09863/) (2020)
- [One-Pass AUC Optimization](https://mlsanity.com/paper/1305.1363/) (2013)
- [Outer Product-based Neural Collaborative Filtering](https://mlsanity.com/paper/1808.03912/) (2018)
- [Reinforced Negative Sampling over Knowledge Graph for Recommendation](https://mlsanity.com/paper/2003.05753/) (2020)
- [Latent Relational Metric Learning via Memory-based Attention for Collaborative Ranking](https://mlsanity.com/paper/1707.05176/) (2017)
- [Adversarial Sampling and Training for Semi-Supervised Information Retrieval](https://mlsanity.com/paper/1811.04155/) (2018)
- [Relational Collaborative Filtering:Modeling Multiple Item Relations for Recommendation](https://mlsanity.com/paper/1904.12796/) (2019)
- [Collaborative Translational Metric Learning](https://mlsanity.com/paper/1906.01637/) (2019)
- [Fast Matrix Factorization with Non-Uniform Weights on Missing Data](https://mlsanity.com/paper/1811.04411/) (2018)
- [Item Silk Road: Recommending Items from Information Domains to Social Users](https://mlsanity.com/paper/1706.03205/) (2017)
- [Improving Collaborative Metric Learning with Efficient Negative Sampling](https://mlsanity.com/paper/1909.10912/) (2019)
- [User Diverse Preference Modeling by Multimodal Attentive Metric Learning](https://mlsanity.com/paper/1908.07738/) (2019)
- [The Sample Complexity of Online One-Class Collaborative Filtering](https://mlsanity.com/paper/1706.00061/) (2017)
- [A Univariate Bound of Area Under ROC](https://mlsanity.com/paper/1804.05981/) (2018)

## Built on by (most cited first, 14 of 14)

- [Uni-MoE: Scaling Unified Multimodal LLMs with Mixture of Experts](https://mlsanity.com/paper/2405.11273/) (2024)
- [AUCSeg: AUC-oriented Pixel-level Long-tail Semantic Segmentation](https://mlsanity.com/paper/2409.20398/) (2024)
- [Improved Diversity-Promoting Collaborative Metric Learning for Recommendation](https://mlsanity.com/paper/2409.01012/) (2024)
- [Exploring the Algorithm-Dependent Generalization of AUPRC Optimization with List Stability](https://mlsanity.com/paper/2209.13262/) (2022)
- [The Achilles' Heel of LLMs: How Altering a Handful of Neurons Can Cripple Language Abilities](https://mlsanity.com/paper/2510.10238/) (2025)
- [Survey of Computerized Adaptive Testing: A Machine Learning Perspective](https://mlsanity.com/paper/2404.00712/) (2024)
- [Dynamic Worlds, Dynamic Humans: Generating Virtual Human-Scene Interaction Motion in Dynamic Scenes](https://mlsanity.com/paper/2601.19484/) (2026)
- [Geometric Collaborative Filtering with Convergence](https://mlsanity.com/paper/2410.03064/) (2024)
- [UniTraffic-Agent: Unified Traffic Video Reasoning for AI City Challenge 2026 Track 3 with Two Out-of-Domain Evaluations](https://mlsanity.com/paper/2608.13031/) (2026)
- [Extremely Fine-Grained Visual Classification over Resembling Glyphs in the Wild](https://mlsanity.com/paper/2408.13774/) (2024)
- [Towards Size-invariant Salient Object Detection: A Generic Evaluation and Optimization Approach](https://mlsanity.com/paper/2509.15573/) (2025)
- [Cross-Temporal 3D Gaussian Splatting for Sparse-View Guided Scene Update](https://mlsanity.com/paper/2512.00534/) (2025)
- [Closing the Approximation Gap of Partial AUC Optimization: A Tale of Two Formulations](https://mlsanity.com/paper/2512.01213/) (2025)
- [OSCS-SupCon: Orthogonal Sigmoid-based Common and Style Supervised Contrastive Learning for Robust Feature Disentanglement](https://mlsanity.com/paper/2606.11233/) (2026)

## Abstract (arXiv)

The recently proposed Collaborative Metric Learning (CML) paradigm has aroused wide interest in the area of recommendation systems (RS) owing to its simplicity and effectiveness. Typically, the existing literature of CML depends largely on the textitnegative sampling strategy to alleviate the time-consuming burden of pairwise computation. However, in this work, by taking a theoretical analysis, we find that negative sampling would lead to a biased estimation of the generalization error. Specifically, we show that the sampling-based CML would introduce a bias term in the generalization bound, which is quantified by the per-user textitTotal Variance (TV) between the distribution induced by negative sampling and the ground truth distribution. This suggests that optimizing the sampling-based CML loss function does not ensure a small generalization error even with sufficiently large training data. Moreover, we show that the bias term will vanish without the negative sampling strategy. Motivated by this, we propose an efficient alternative without negative sampling for CML named textitSampling-Free Collaborative Metric Learning (SFCML), to get rid of the sampling bias in a practical sense. Finally, comprehensive experiments over seven benchmark datasets speak to the superiority of the proposed algorithm.