Toward a Better Understanding of Loss Functions for Collaborative Filtering

TL;DR

This paper analyzes existing loss functions in collaborative filtering, revealing their roles as alignment and uniformity measures, and introduces MAWU, a novel loss function that improves recommendation performance by addressing dataset-specific biases.

Contribution

The paper provides a mathematical interpretation of loss functions as alignment and uniformity, and proposes MAWU, a new loss that enhances CF models by mitigating biases and adjusting for dataset characteristics.

Findings

MAWU improves CF model performance on public datasets.

MAWU achieves comparable or superior results to state-of-the-art loss functions.

The analysis unifies loss functions under a common framework of alignment and uniformity.

Abstract

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.