# Towards Representation Alignment and Uniformity in Collaborative Filtering

arXiv: https://arxiv.org/abs/2206.12811 · HTML: https://mlsanity.com/paper/2206.12811/

## Key facts

- Cited by 57 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Jun 2022.

## Built on by (most cited first, 30 of 57)

- [Rethinking Graph Masked Autoencoders through Alignment and Uniformity](https://mlsanity.com/paper/2402.07225/) (2024)
- [How Do Recommendation Models Amplify Popularity Bias? An Analysis from the Spectral Perspective](https://mlsanity.com/paper/2404.12008/) (2024)
- [Efficient Bi-Level Optimization for Recommendation Denoising](https://mlsanity.com/paper/2210.10321/) (2022)
- [SSLRec: A Self-Supervised Learning Framework for Recommendation](https://mlsanity.com/paper/2308.05697/) (2023)
- [Multi-task Item-attribute Graph Pre-training for Strict Cold-start Item Recommendation](https://mlsanity.com/paper/2306.14462/) (2023)
- [STERLING: Synergistic Representation Learning on Bipartite Graphs](https://mlsanity.com/paper/2302.05428/) (2023)
- [Unveiling Vulnerabilities of Contrastive Recommender Systems to Poisoning Attacks](https://mlsanity.com/paper/2311.18244/) (2023)
- [RecDCL: Dual Contrastive Learning for Recommendation](https://mlsanity.com/paper/2401.15635/) (2024)
- [Neighborhood-Enhanced Supervised Contrastive Learning for Collaborative Filtering](https://mlsanity.com/paper/2402.11523/) (2024)
- [On Manipulating Signals of User-Item Graph: A Jacobi Polynomial-based Graph Collaborative Filtering](https://mlsanity.com/paper/2306.03624/) (2023)
- [Popularity-Aware Alignment and Contrast for Mitigating Popularity Bias](https://mlsanity.com/paper/2405.20718/) (2024)
- [Toward a Better Understanding of Loss Functions for Collaborative Filtering](https://mlsanity.com/paper/2308.06091/) (2023)
- [GUME: Graphs and User Modalities Enhancement for Long-Tail Multimodal Recommendation](https://mlsanity.com/paper/2407.12338/) (2024)
- [Enhancing High-order Interaction Awareness in LLM-based Recommender Model](https://mlsanity.com/paper/2409.19979/) (2024)
- [Mitigating Propensity Bias of Large Language Models for Recommender Systems](https://mlsanity.com/paper/2409.20052/) (2024)
- [Lost in Sequence: Do Large Language Models Understand Sequential Recommendation?](https://mlsanity.com/paper/2502.13909/) (2025)
- [Graph Spectral Filtering with Chebyshev Interpolation for Recommendation](https://mlsanity.com/paper/2505.00552/) (2025)
- [KuaiLive: A Real-time Interactive Dataset for Live Streaming Recommendation](https://mlsanity.com/paper/2508.05633/) (2025)
- [A Comprehensive Survey on Self-Supervised Learning for Recommendation](https://mlsanity.com/paper/2404.03354/) (2024)
- [uCTRL: Unbiased Contrastive Representation Learning via Alignment and Uniformity for Collaborative Filtering](https://mlsanity.com/paper/2305.12768/) (2023)
- [Revisiting Recommendation Loss Functions through Contrastive Learning (Technical Report)](https://mlsanity.com/paper/2312.08520/) (2023)
- [Synergistic Anchored Contrastive Pre-training for Few-Shot Relation Extraction](https://mlsanity.com/paper/2312.12021/) (2023)
- [How Does Message Passing Improve Collaborative Filtering?](https://mlsanity.com/paper/2404.08660/) (2024)
- [GraphCL-DTA: a graph contrastive learning with molecular semantics for drug-target binding affinity prediction](https://mlsanity.com/paper/2307.08989/) (2023)
- [Graph-based Alignment and Uniformity for Recommendation](https://mlsanity.com/paper/2308.09292/) (2023)
- [Cold-start Bundle Recommendation via Popularity-based Coalescence and Curriculum Heating](https://mlsanity.com/paper/2310.03813/) (2023)
- [Unified Pretraining for Recommendation via Task Hypergraphs](https://mlsanity.com/paper/2310.13286/) (2023)
- [SimCE: Simplifying Cross-Entropy Loss for Collaborative Filtering](https://mlsanity.com/paper/2406.16170/) (2024)
- [Temporal Linear Item-Item Model for Sequential Recommendation](https://mlsanity.com/paper/2412.07382/) (2024)
- [LightGNN: Simple Graph Neural Network for Recommendation](https://mlsanity.com/paper/2501.03228/) (2025)

## Abstract (arXiv)

Collaborative filtering (CF) plays a critical role in the development of recommender systems. Most CF methods utilize an encoder to embed users and items into the same representation space, and the Bayesian personalized ranking (BPR) loss is usually adopted as the objective function to learn informative encoders. Existing studies mainly focus on designing more powerful encoders (e.g., graph neural network) to learn better representations. However, few efforts have been devoted to investigating the desired properties of representations in CF, which is important to understand the rationale of existing CF methods and design new learning objectives. In this paper, we measure the representation quality in CF from the perspective of alignment and uniformity on the hypersphere. We first theoretically reveal the connection between the BPR loss and these two properties. Then, we empirically analyze the learning dynamics of typical CF methods in terms of quantified alignment and uniformity, which shows that better alignment or uniformity both contribute to higher recommendation performance. Based on the analyses results, a learning objective that directly optimizes these two properties is proposed, named DirectAU. We conduct extensive experiments on three public datasets, and the proposed learning framework with a simple matrix factorization model leads to significant performance improvements compared to state-of-the-art CF methods. Our implementations are publicly available at https://github.com/THUwangcy/DirectAU.