Adaptive Rich-kernelized Contrastive Learning for Capacity Enhancement in Collaborative Filtering

Recent research has shown that single-vector embedding retrieval models face a fundamental bottleneck: the finite dimensionality of single-vector representations limits their capacity to represent arbitrary top-k relevant item combinations, even with perfect training. This inherent bottleneck substantially limits the expressive capacity of such models and reduces their ability to capture complex user-item interaction patterns. To overcome this bottleneck, we propose Adaptive Rich-kernelized Contrastive Learning (ARC), which enhances model expressiveness while maintaining the computational efficiency of single-vector retrieval. ARC replaces the fixed inner product with a learnable spherical kernel family parameterized by a truncated Gegenbauer expansion, thereby increasing the model's effective dimensionality while preserving single-vector efficiency and low-pass inductive bias for generalization. Specifically, we construct a positive-definite kernel on the unit sphere using a positive combination of Gegenbauer polynomials, and adopt a contrastive learning objective to jointly learn the polynomials weights and user–item embeddings. Through data-driven optimization, the adaptive kernel induces a more expressive representation space, enabling the model to better capture complex preferences. From a theoretical perspective, the learned kernel implicitly maps embeddings into a higher-dimensional Reproducing Kernel Hilbert Space, allowing the model to capture a broader range of top-k item combinations before reaching the geometric limit imposed by the embedding dimensionality. Consequently, the proposed ARC framework effectively alleviates the inherent representational bottleneck in traditional single-vector embedding models. Extensive experiments on four real-world datasets demonstrate the effectiveness of our method, showing consistent improvements over strong baselines and state-of-the-art models.