Towards Representation Alignment and Uniformity in Collaborative Filtering (2206.12811v1)

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.

Overview of Representation Alignment and Uniformity in Collaborative Filtering

The research paper titled "Towards Representation Alignment and Uniformity in Collaborative Filtering" explores the integral aspects of embedding representation in collaborative filtering (CF) for recommender systems. The authors introduce a novel perspective to evaluate the representation quality via two pivotal properties: alignment and uniformity.

Collaborative filtering is a predominant technique in recommender systems, renowned for its efficacy in predicting user preferences based solely on the historical interaction data. Traditionally, CF methods rely on encoders that embed users and items into a latent space, typically optimized using the Bayesian personalized ranking (BPR) loss function. While previous studies have predominantly focused on enhancing encoder architecture—such as employing graph neural networks—to learn superior representations, the intrinsic properties of these representations have seldom been explored.

Theoretical Insights

The paper initiates by providing a theoretical analysis that ties the commonly used BPR loss to the properties of alignment and uniformity. Alignment is characterized by closely embedded representations for user-item pairs with positive interactions, while uniformity ensures that these embeddings scatter uniformly across the hypersphere, preserving diversity and preventing them from collapsing into trivial constant vectors. The authors analytically show that optimally aligned and uniformly distributed representations are the minimizers of the BPR loss, framing it as conducive to these properties.

Empirical Analysis

Following the theoretical discussion, empirical analyses are presented exploring how these properties evolve during training with various CF methods on public datasets. It's observed that while traditional BPR approaches favor uniformity primarily through discriminative ranking, methods like BPR with dynamic sampling (BPR-DS) improve uniformity but at the cost of alignment. In contrast, graph-based models like LightGCN offer improved initial alignment that benefits training dynamics. Efficient Neural Matrix Factorization (ENMF), which uses all interactions, shows a balanced enhancement of both alignment and uniformity, yielding superior results.

DirectAU Framework

Based on the insights garnered from the analyses, the paper introduces a new learning objective termed DirectAU that directly optimizes alignment and uniformity. The framework leverages empirical metrics from contrastive learning literature, quantifying alignment as the expected distance between normalized embeddings of positive pairs, and uniformity with respects to the average pairwise Gaussian potential among embeddings. This approach eschews traditional negative sampling, simplifying the optimization process. Implemented with a straightforward matrix factorization encoder, DirectAU manifests significant empirical gains across various benchmark datasets.

Implications and Future Directions

The proposed DirectAU framework highlights the pivotal role alignment and uniformity play in refining representation learning within collaborative filtering. By focusing on these properties, the method achieves state-of-the-art performance, underscoring the necessity of revisiting how objectives are formulated over the complexity of encoder architectures. Moving forward, this research opens avenues for exploring alternative loss functions that inherently bolster these properties, potentially enhancing the robustness of recommendations across diverse domains.

In summary, this paper offers a compelling narrative on the utility of alignment and uniformity as desirable representation properties in CF, advocating for a shift in focus towards optimizing these intrinsic qualities for improving recommender system performance.