# Toward a Better Understanding of Loss Functions for Collaborative Filtering

arXiv: https://arxiv.org/abs/2308.06091 · HTML: https://mlsanity.com/paper/2308.06091/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 36 of its 63 references that are in the map.
- First posted on arXiv 11 Aug 2023.

## Builds on (most cited first, 30 of 36)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [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)
- [SimCSE: Simple Contrastive Learning of Sentence Embeddings](https://mlsanity.com/paper/2104.08821/) (2021)
- [Understanding Contrastive Representation Learning through Alignment and Uniformity on the Hypersphere](https://mlsanity.com/paper/2005.10242/) (2020)
- [LightGCN: Simplifying and Powering Graph Convolution Network for Recommendation](https://mlsanity.com/paper/2002.02126/) (2020)
- [Neural Collaborative Filtering](https://mlsanity.com/paper/1708.05031/) (2017)
- [Session-based Recommendations with Recurrent Neural Networks](https://mlsanity.com/paper/1511.06939/) (2015)
- [Neural Graph Collaborative Filtering](https://mlsanity.com/paper/1905.08108/) (2019)
- [Understanding the Behaviour of Contrastive Loss](https://mlsanity.com/paper/2012.09740/) (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)
- [Are We Really Making Much Progress? A Worrying Analysis of Recent Neural Recommendation Approaches](https://mlsanity.com/paper/1907.06902/) (2019)
- [Are Graph Augmentations Necessary? Simple Graph Contrastive Learning for Recommendation](https://mlsanity.com/paper/2112.08679/) (2021)
- [RecBole: Towards a Unified, Comprehensive and Efficient Framework for Recommendation Algorithms](https://mlsanity.com/paper/2011.01731/) (2020)
- [Collaborative Deep Learning for Recommender Systems](https://mlsanity.com/paper/1409.2944/) (2014)
- [Embarrassingly Shallow Autoencoders for Sparse Data](https://mlsanity.com/paper/1905.03375/) (2019)
- [LightGCL: Simple Yet Effective Graph Contrastive Learning for Recommendation](https://mlsanity.com/paper/2302.08191/) (2023)
- [On Sampling Strategies for Neural Network-based Collaborative Filtering](https://mlsanity.com/paper/1706.07881/) (2017)
- [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)
- [Towards Representation Alignment and Uniformity in Collaborative Filtering](https://mlsanity.com/paper/2206.12811/) (2022)
- [On the Effectiveness of Sampled Softmax Loss for Item Recommendation](https://mlsanity.com/paper/2201.02327/) (2022)
- [Contrastive Learning for Debiased Candidate Generation in Large-Scale Recommender Systems](https://mlsanity.com/paper/2005.12964/) (2020)
- [Simplify and Robustify Negative Sampling for Implicit Collaborative Filtering](https://mlsanity.com/paper/2009.03376/) (2020)
- [HRCF: Enhancing Collaborative Filtering via Hyperbolic Geometric Regularization](https://mlsanity.com/paper/2204.08176/) (2022)
- [AutoLoss: Automated Loss Function Search in Recommendations](https://mlsanity.com/paper/2106.06713/) (2021)
- [AM-LFS: AutoML for Loss Function Search](https://mlsanity.com/paper/1905.07375/) (2019)
- [Incorporating Bias-aware Margins into Contrastive Loss for Collaborative Filtering](https://mlsanity.com/paper/2210.11054/) (2022)
- [Heterogeneous Graph Contrastive Learning for Recommendation](https://mlsanity.com/paper/2303.00995/) (2023)

## Built on by (most cited first, 8 of 8)

- [Popularity-Aware Alignment and Contrast for Mitigating Popularity Bias](https://mlsanity.com/paper/2405.20718/) (2024)
- [SimCE: Simplifying Cross-Entropy Loss for Collaborative Filtering](https://mlsanity.com/paper/2406.16170/) (2024)
- [On the Role of Weight Decay in Collaborative Filtering: A Popularity Perspective](https://mlsanity.com/paper/2505.11318/) (2025)
- [Advancing Loss Functions in Recommender Systems: A Comparative Study with a R'enyi Divergence-Based Solution](https://mlsanity.com/paper/2506.15120/) (2025)
- [Understanding and Scaling Collaborative Filtering Optimization from the Perspective of Matrix Rank](https://mlsanity.com/paper/2410.23300/) (2024)
- [LLM-Enhanced Linear Autoencoders for Recommendation](https://mlsanity.com/paper/2508.13500/) (2025)
- [Multi-Margin Cosine Loss: Proposal and Application in Recommender Systems](https://mlsanity.com/paper/2405.04614/) (2024)
- [MergeRec: Model Merging for Data-Isolated Cross-Domain Sequential Recommendation](https://mlsanity.com/paper/2601.01753/) (2026)

## Abstract (arXiv)

Collaborative filtering (CF) is a pivotal technique in modern recommender systems. The learning process of CF models typically consists of three components: interaction encoder, loss function, and negative sampling. Although many existing studies have proposed various CF models to design sophisticated interaction encoders, recent work shows that simply reformulating the loss functions can achieve significant performance gains. This paper delves into analyzing the relationship among existing loss functions. Our mathematical analysis reveals that the previous loss functions can be interpreted as alignment and uniformity functions: (i) the alignment matches user and item representations, and (ii) the uniformity disperses user and item distributions. Inspired by this analysis, we propose a novel loss function that improves the design of alignment and uniformity considering the unique patterns of datasets called Margin-aware Alignment and Weighted Uniformity (MAWU). The key novelty of MAWU is two-fold: (i) margin-aware alignment (MA) mitigates user/item-specific popularity biases, and (ii) weighted uniformity (WU) adjusts the significance between user and item uniformities to reflect the inherent characteristics of datasets. Extensive experimental results show that MF and LightGCN equipped with MAWU are comparable or superior to state-of-the-art CF models with various loss functions on three public datasets.