Order-Marginalized Generation of Semantic and Collaborative IDs for Generative Recommendation

Generative Recommendation (GR) increasingly incorporates collaborative signals into item tokenization to complement content semantics. When semantic and collaborative representations are separately quantized into two identifier chains, however, their cross-chain generation order is inherently unspecified. Their combination therefore forms a partially ordered target, whereas autoregressive generation requires a total order. Existing methods consequently rely on a prescribed cross-identifier serialization, an arbitrary choice that can materially affect recommendation performance. We propose LatticeRec, an order-marginalized framework that treats cross-identifier serialization as a latent variable rather than a prescribed generation target. The key idea is to represent partial generations by canonical states determined only by the revealed prefixes of the two identifiers, allowing different interleavings with equivalent revealed information to share the same predictive state. This organizes all valid interleavings into a compact lattice and enables exact marginalization over generation orders via dynamic programming, without explicit path enumeration. We further introduce coverage-aware training to prevent supervision from concentrating on only a few generation paths. Experiments on three benchmarks demonstrate the effectiveness of LatticeRec and its key components.