User cold-start problem is a long-standing challenge in recommendation systems. Fortunately, cross-domain recommendation (CDR) has emerged as a highly effective remedy for the user cold-start challenge, with recently developed diffusion models (DMs) demonstrating exceptional performance. However, these DMs-based CDR methods focus on dealing with user-item interactions, overlooking correlations between items across the source and target domains. Meanwhile, the Gaussian noise added in the forward process of diffusion models would hurt user's personalized preference, leading to the difficulty in transferring user preference across domains. To this end, we propose a novel paradigm of Smoothing-Sharpening Process Model for CDR to cold-start users, termed as S2CDR which features a corruption-recovery architecture and is solved with respect to ordinary differential equations (ODEs). Specifically, the smoothing process gradually corrupts the original user-item/item-item interaction matrices derived from both domains into smoothed preference signals in a noise-free manner, and the sharpening process iteratively sharpens the preference signals to recover the unknown interactions for cold-start users. Wherein, for the smoothing process, we introduce the heat equation on the item-item similarity graph to better capture the correlations between items across domains, and further build the tailor-designed low-pass filter to filter out the high-frequency noise information for capturing user's intrinsic preference, in accordance with the graph signal processing (GSP) theory. Extensive experiments on three real-world CDR scenarios confirm that our S2CDR significantly outperforms previous SOTA methods in a training-free manner.

翻译：用户冷启动问题是推荐系统中长期存在的挑战。幸运的是，跨域推荐已成为应对用户冷启动挑战的一种高效解决方案，而近期发展的扩散模型在其中展现出卓越性能。然而，这些基于扩散模型的跨域推荐方法主要关注处理用户-物品交互，忽略了源域与目标域之间物品的关联性。同时，扩散模型前向过程中添加的高斯噪声会损害用户的个性化偏好，导致跨域用户偏好迁移困难。为此，我们提出一种面向冷启动用户的跨域推荐平滑-锐化过程模型新范式，称为S2CDR。该模型采用“破坏-恢复”架构，并基于常微分方程进行求解。具体而言，平滑过程以无噪声方式将来自双域的原始用户-物品/物品-物品交互矩阵逐步退化为平滑的偏好信号；锐化过程则通过迭代锐化偏好信号来恢复冷启动用户的未知交互。其中，在平滑过程中，我们基于物品-物品相似图引入热传导方程以更好地捕捉跨域物品关联，并依据图信号处理理论构建定制化低通滤波器来滤除高频噪声信息，从而捕获用户内在偏好。在三个真实跨域推荐场景上的大量实验证实，我们的S2CDR在无需训练的情况下显著优于现有最优方法。