$FM^2$: Field-matrixed Factorization Machines for Recommender Systems

TL;DR

This paper introduces Field-matrixed Factorization Machines ($FM^2$), a novel model for CTR prediction that effectively models field information, improves efficiency, and outperforms more complex models like FFM and DNNs.

Contribution

The paper proposes $FM^2$, a new field-aware factorization machine that supports field-specific embedding dimensions and efficient optimization, improving over existing models.

Findings

$FM^2$ outperforms FFM in accuracy.

$FM^2$ achieves comparable performance to DNNs.

$FM^2$ requires fewer FLOPs for prediction.

Abstract

Click-through rate (CTR) prediction plays a critical role in recommender systems and online advertising. The data used in these applications are multi-field categorical data, where each feature belongs to one field. Field information is proved to be important and there are several works considering fields in their models. In this paper, we proposed a novel approach to model the field information effectively and efficiently. The proposed approach is a direct improvement of FwFM, and is named as Field-matrixed Factorization Machines (FmFM, or $FM^2$). We also proposed a new explanation of FM and FwFM within the FmFM framework, and compared it with the FFM. Besides pruning the cross terms, our model supports field-specific variable dimensions of embedding vectors, which acts as soft pruning. We also proposed an efficient way to minimize the dimension while keeping the model performance. The FmFM model can also be optimized further by caching the intermediate vectors, and it only takes thousands of floating-point operations (FLOPs) to make a prediction. Our experiment results show that it can out-perform the FFM, which is more complex. The FmFM model's performance is also comparable to DNN models which require much more FLOPs in runtime.