CUBER: KEEP DEPENDENCY IN PARALLEL SID FOR GENERATIVE RECOMMENDATION

Semantic IDs (SIDs) play a critical role in generative recommendation (GR), with early approaches capturing hierarchical item information through progressively refined code sequences. To improve efficiency, more recent approaches based on product quantization (PQ) decompose item representations into multiple subspaces and quantize them independently, enabling parallel SID construction and single-forward code prediction. However, such methods do not explicitly encode structured dependencies among SID codes. To address this limitation, we present Cuber, which captures structured dependencies among SID codes while retaining parallel code prediction. Specifically, Cuber integrates three key techniques: (1) RPQ-Tree, a unified SID construction framework that recursively composes residual and product quantization, introducing dependencies across quantization components while supporting single-forward prediction; (2) a geometry-aware embedding initialization scheme that transfers the structural relationships learned during quantization into the code-token embeddings; and (3) a progressive training mechanism that exploits partial-tree predictions to mine increasingly challenging hard negatives, strengthening both code-level discrimination and catalog-level ranking. Extensive experiments demonstrate that Cuber consistently outperforms competitive baselines across multiple recommendation metrics, achieving 25.2% improvement in Recall and 23.6% in NDCG.