# Multi-Sample based Contrastive Loss for Top-k Recommendation

arXiv: https://arxiv.org/abs/2109.00217 · HTML: https://mlsanity.com/paper/2109.00217/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 33 of its 66 references that are in the map.
- First posted on arXiv 1 Sep 2021.

## Builds on (most cited first, 30 of 33)

- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Representation Learning with Contrastive Predictive Coding](https://mlsanity.com/paper/1807.03748/) (2018)
- [Momentum Contrast for Unsupervised Visual Representation Learning](https://mlsanity.com/paper/1911.05722/) (2019)
- [Bootstrap your own latent: A new approach to self-supervised Learning](https://mlsanity.com/paper/2006.07733/) (2020)
- [FaceNet: A Unified Embedding for Face Recognition and Clustering](https://mlsanity.com/paper/1503.03832/) (2015)
- [Supervised Contrastive Learning](https://mlsanity.com/paper/2004.11362/) (2020)
- [Unsupervised Feature Learning via Non-Parametric Instance-level Discrimination](https://mlsanity.com/paper/1805.01978/) (2018)
- [Learning deep representations by mutual information estimation and maximization](https://mlsanity.com/paper/1808.06670/) (2018)
- [Graph Contrastive Learning with Augmentations](https://mlsanity.com/paper/2010.13902/) (2020)
- [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)
- [Learning Representations by Maximizing Mutual Information Across Views](https://mlsanity.com/paper/1906.00910/) (2019)
- [Neural Graph Collaborative Filtering](https://mlsanity.com/paper/1905.08108/) (2019)
- [Contrastive Multi-View Representation Learning on Graphs](https://mlsanity.com/paper/2006.05582/) (2020)
- [Prototypical Contrastive Learning of Unsupervised Representations](https://mlsanity.com/paper/2005.04966/) (2020)
- [Graph Contrastive Learning with Adaptive Augmentation](https://mlsanity.com/paper/2010.14945/) (2020)
- [GCC: Graph Contrastive Coding for Graph Neural Network Pre-Training](https://mlsanity.com/paper/2006.09963/) (2020)
- [Debiased Contrastive Learning](https://mlsanity.com/paper/2007.00224/) (2020)
- [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)
- [Data Augmentation for Graph Neural Networks](https://mlsanity.com/paper/2006.06830/) (2020)
- [Attentional Factorization Machines: Learning the Weight of Feature Interactions via Attention Networks](https://mlsanity.com/paper/1708.04617/) (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)
- [Contrastive Learning for Cold-Start Recommendation](https://mlsanity.com/paper/2107.05315/) (2021)
- [Graph-MLP: Node Classification without Message Passing in Graph](https://mlsanity.com/paper/2106.04051/) (2021)
- [On Sampling Strategies for Neural Network-based Collaborative Filtering](https://mlsanity.com/paper/1706.07881/) (2017)
- [POG: Personalized Outfit Generation for Fashion Recommendation at Alibaba iFashion](https://mlsanity.com/paper/1905.01866/) (2019)
- [Outer Product-based Neural Collaborative Filtering](https://mlsanity.com/paper/1808.03912/) (2018)

## Built on by (most cited first, 7 of 7)

- [Improving Graph Collaborative Filtering with Neighborhood-enriched Contrastive Learning](https://mlsanity.com/paper/2202.06200/) (2022)
- [Adap-τ: Adaptively Modulating Embedding Magnitude for Recommendation](https://mlsanity.com/paper/2302.04775/) (2023)
- [A Survey on Self-Supervised Graph Foundation Models: Knowledge-Based Perspective](https://mlsanity.com/paper/2403.16137/) (2024)
- [Guidelines for Augmentation Selection in Contrastive Learning for Time Series Classification](https://mlsanity.com/paper/2407.09336/) (2024)
- [Graph-based Alignment and Uniformity for Recommendation](https://mlsanity.com/paper/2308.09292/) (2023)
- [A Comparative Analysis of Bias Amplification in Graph Neural Network Approaches for Recommender Systems](https://mlsanity.com/paper/2301.07639/) (2023)
- [Context-Enriched Contrastive Loss: Enhancing Presentation of Inherent Sample Connections in Contrastive Learning Framework](https://mlsanity.com/paper/2512.02152/) (2025)

## Abstract (arXiv)

The top-k recommendation is a fundamental task in recommendation systems which is generally learned by comparing positive and negative pairs. The Contrastive Loss (CL) is the key in contrastive learning that has received more attention recently and we find it is well suited for top-k recommendations. However, it is a problem that CL treats the importance of the positive and negative samples as the same. On the one hand, CL faces the imbalance problem of one positive sample and many negative samples. On the other hand, positive items are so few in sparser datasets that their importance should be emphasized. Moreover, the other important issue is that the sparse positive items are still not sufficiently utilized in recommendations. So we propose a new data augmentation method by using multiple positive items (or samples) simultaneously with the CL loss function. Therefore, we propose a Multi-Sample based Contrastive Loss (MSCL) function which solves the two problems by balancing the importance of positive and negative samples and data augmentation. And based on the graph convolution network (GCN) method, experimental results demonstrate the state-of-the-art performance of MSCL. The proposed MSCL is simple and can be applied in many methods. We will release our code on GitHub upon the acceptance.