Sequential recommendation (SR) investigates the dynamic user preferences modeling and generates the next-item prediction. The next item preference is typically generated by the affinity between the sequence and item representations. However, both sequence and item representations suffer from the rank degeneration issue due to the data sparsity problem. The rank degeneration issue significantly impairs the representations for SR. This motivates us to measure how severe is the rank degeneration issue and alleviate the sequence and item representation rank degeneration issues simultaneously for SR. In this work, we theoretically connect the sequence representation degeneration issue with the item rank degeneration, particularly for short sequences and cold items. We also identify the connection between the fast singular value decay phenomenon and the rank collapse issue in transformer sequence output and item embeddings. We propose the area under the singular value curve metric to evaluate the severity of the singular value decay phenomenon and use it as an indicator of rank degeneration. We further introduce a novel singular spectrum smoothing regularization to alleviate the rank degeneration on both sequence and item sides, which is the Singular sPectrum sMoothing for sequential Recommendation (SPMRec). We also establish a correlation between the ranks of sequence and item embeddings and the rank of the user-item preference prediction matrix, which can affect recommendation diversity. We conduct experiments on four benchmark datasets to demonstrate the superiority of SPMRec over the state-of-the-art recommendation methods, especially in short sequences. The experiments also demonstrate a strong connection between our proposed singular spectrum smoothing and recommendation diversity.

本文研究了顺序推荐中的排名降级问题，并提出了基于奇异值曲线下面积度量和奇异值平滑正则化方法的顺序推荐算法SPMRec来解决此问题，该方法在四个基准数据集上的实验结果表明其优于其他推荐算法，尤其在短序列中表现出更好的推荐效果，并可提高推荐的多样性。

通过奇异谱平滑处理解决序列推荐中的排名退化问题