Balancing Embedding Spectrum for Recommendation

Modern recommender systems heavily rely on high-quality representations learned from high-dimensional sparse data. While significant efforts have been invested in designing powerful algorithms for extracting user preferences, the factors contributing to good representations have remained relatively unexplored. In this work, we shed light on an issue in the existing pairwise learning paradigm (i.e., embedding collapse), that the representations tend to span a subspace of the whole embedding space, leading to a suboptimal solution and reducing the model capacity. Specifically, we show that alignment of positive pairs is equivalent to a low-pass filter causing users and items to collapse to a constant vector. While negative sampling can partially mitigate this issue by acting as a high-pass filter to balance the spectrum, leading to an incomplete collapse. To tackle this issue, we present a novel learning paradigm DirectSpec, which directly optimizes the spectrum distribution to ensure that users and items effectively span the entire embedding space. We demonstrate that many self-supervised learning algorithms without explicit negative sampling can be considered as special cases of DirectSpec. Furthermore, we show that optimizing the spectrum inappropriately could also be detrimental to data representation, where the key lies in a dynamic balance between alignment of positive pairs and spectrum balancing. Finally, we propose an enhanced and practical implementation DirectSpec + to balance the embedding spectrum more adaptively and effectively. We implement DirectSpec + on two popular recommender models: matrix factorization and LightGCN. Our experimental results demonstrate its effectiveness and efficiency over competitive baselines.

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