Towards Representation Alignment and Uniformity in Collaborative Filtering

TL;DR

This paper investigates the properties of representation alignment and uniformity in collaborative filtering, revealing their importance for recommendation quality and proposing a new objective, DirectAU, to optimize these properties for improved performance.

Contribution

It introduces a theoretical and empirical analysis of alignment and uniformity in CF representations and proposes a novel learning objective, DirectAU, to enhance these properties.

Findings

Better alignment or uniformity improves recommendation performance.

DirectAU outperforms state-of-the-art CF methods on public datasets.

Theoretical connection between BPR loss and representation properties.

Abstract

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.