History-Conditioned Joint-Prefix Alignment for Generative Recommendation

Generative recommendation retrieves items by autoregressively generating semantic identifiers, but beam search may discard a target before its complete identifier is generated. Our preliminary analysis across three benchmarks shows that most missed targets are pruned within the first two decoding steps, highlighting the importance of early prefix retention. However, retaining a target's first-token branch alone is insufficient if its continuation is pruned at the next step: aligning only the first-token distribution improves first-token survival but yields little gain in complete-path retention. This observation motivates joint supervision of early branches and their continuations. We propose Prefix Alignment with Temporal History (PATH), which aggregates transition statistics from the training corpus over recent interactions with exponential decay to construct history-conditioned two-token prefix targets. PATH aligns the model's joint predictions with these targets through forward KL divergence, using a chain-rule decomposition that enables unbiased Monte Carlo estimation. At inference time, PATH reuses the transition statistics for pointwise mutual information (PMI) calibration, reranking completed candidates relative to global prefix frequency. Experiments on Beauty, Instruments, and Yelp demonstrate the effectiveness of PATH, showing consistent improvements in recommendation performance and higher full-SID survival rates.