# Rethinking Popularity Bias in Collaborative Filtering via Analytical Vector Decomposition

arXiv: https://arxiv.org/abs/2512.10688 · HTML: https://mlsanity.com/paper/2512.10688/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 45 references that are in the map.
- First posted on arXiv 11 Dec 2025.

## Builds on (most cited first, 28 of 28)

- [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)
- [Graph Neural Networks in Recommender Systems: A Survey](https://mlsanity.com/paper/2011.02260/) (2020)
- [Self-supervised Graph Learning for Recommendation](https://mlsanity.com/paper/2010.10783/) (2020)
- [Recommendations as Treatments: Debiasing Learning and Evaluation](https://mlsanity.com/paper/1602.05352/) (2016)
- [Bias and Debias in Recommender System: A Survey and Future Directions](https://mlsanity.com/paper/2010.03240/) (2020)
- [Are Graph Augmentations Necessary? Simple Graph Contrastive Learning for Recommendation](https://mlsanity.com/paper/2112.08679/) (2021)
- [Unbiased Learning-to-Rank with Biased Feedback](https://mlsanity.com/paper/1608.04468/) (2016)
- [RecBole: Towards a Unified, Comprehensive and Efficient Framework for Recommendation Algorithms](https://mlsanity.com/paper/2011.01731/) (2020)
- [Disentangled Graph Collaborative Filtering](https://mlsanity.com/paper/2007.01764/) (2020)
- [Causal Intervention for Leveraging Popularity Bias in Recommendation](https://mlsanity.com/paper/2105.06067/) (2021)
- [A Survey on the Fairness of Recommender Systems](https://mlsanity.com/paper/2206.03761/) (2022)
- [Model-Agnostic Counterfactual Reasoning for Eliminating Popularity Bias in Recommender System](https://mlsanity.com/paper/2010.15363/) (2020)
- [Improving Graph Collaborative Filtering with Neighborhood-enriched Contrastive Learning](https://mlsanity.com/paper/2202.06200/) (2022)
- [Causal Embeddings for Recommendation](https://mlsanity.com/paper/1706.07639/) (2017)
- [AutoDebias: Learning to Debias for Recommendation](https://mlsanity.com/paper/2105.04170/) (2021)
- [A Survey on Accuracy-oriented Neural Recommendation: From Collaborative Filtering to Information-rich Recommendation](https://mlsanity.com/paper/2104.13030/) (2021)
- [Towards Representation Alignment and Uniformity in Collaborative Filtering](https://mlsanity.com/paper/2206.12811/) (2022)
- [Deconfounded Recommendation for Alleviating Bias Amplification](https://mlsanity.com/paper/2105.10648/) (2021)
- [RecBole 2.0: Towards a More Up-to-Date Recommendation Library](https://mlsanity.com/paper/2206.07351/) (2022)
- [Graph Signal Diffusion Model for Collaborative Filtering](https://mlsanity.com/paper/2311.08744/) (2023)
- [Item-side Fairness of Large Language Model-based Recommendation System](https://mlsanity.com/paper/2402.15215/) (2024)
- [Improving Recommendation Fairness via Data Augmentation](https://mlsanity.com/paper/2302.06333/) (2023)
- [SetRank: A Setwise Bayesian Approach for Collaborative Ranking from Implicit Feedback](https://mlsanity.com/paper/2002.09841/) (2020)
- [Disentangled Causal Embedding With Contrastive Learning For Recommender System](https://mlsanity.com/paper/2302.03248/) (2023)
- [Popularity-Aware Alignment and Contrast for Mitigating Popularity Bias](https://mlsanity.com/paper/2405.20718/) (2024)
- [Unveiling Contrastive Learning's Capability of Neighborhood Aggregation for Collaborative Filtering](https://mlsanity.com/paper/2504.10113/) (2025)
- [On the Role of Weight Decay in Collaborative Filtering: A Popularity Perspective](https://mlsanity.com/paper/2505.11318/) (2025)

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

- [CEDAR: Controlled and Event-Driven Demand Forecasting via Residual Decomposition](https://mlsanity.com/paper/2608.25871/) (2026)

## Abstract (arXiv)

Popularity bias fundamentally undermines the personalization capabilities of collaborative filtering (CF) models, causing them to disproportionately recommend popular items while neglecting users' genuine preferences for niche content. While existing approaches treat this as an external confounding factor, we reveal that popularity bias is an intrinsic geometric artifact of Bayesian Pairwise Ranking (BPR) optimization in CF models. Through rigorous mathematical analysis, we prove that BPR systematically organizes item embeddings along a dominant "popularity direction" where embedding magnitudes directly correlate with interaction frequency. This geometric distortion forces user embeddings to simultaneously handle two conflicting tasks-expressing genuine preference and calibrating against global popularity-trapping them in suboptimal configurations that favor popular items regardless of individual tastes. We propose Directional Decomposition and Correction (DDC), a universally applicable framework that surgically corrects this embedding geometry through asymmetric directional updates. DDC guides positive interactions along personalized preference directions while steering negative interactions away from the global popularity direction, disentangling preference from popularity at the geometric source. Extensive experiments across multiple BPR-based architectures demonstrate that DDC significantly outperforms state-of-the-art debiasing methods, reducing training loss to less than 5% of heavily-tuned baselines while achieving superior recommendation quality and fairness. Code is available in https://github.com/LingFeng-Liu-AI/DDC.