# History-Conditioned Joint-Prefix Alignment for Generative Recommendation

arXiv: https://arxiv.org/abs/2608.29179 · HTML: https://mlsanity.com/paper/2608.29179/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 31 references that are in the map.
- First posted on arXiv 29 Aug 2026.

## Builds on (most cited first, 27 of 27)

- [Self-Attentive Sequential Recommendation](https://mlsanity.com/paper/1808.09781/) (2018)
- [LightGCN: Simplifying and Powering Graph Convolution Network for Recommendation](https://mlsanity.com/paper/2002.02126/) (2020)
- [BERT4Rec: Sequential Recommendation with Bidirectional Encoder Representations from Transformer](https://mlsanity.com/paper/1904.06690/) (2019)
- [Session-based Recommendations with Recurrent Neural Networks](https://mlsanity.com/paper/1511.06939/) (2015)
- [Personalized Top-N Sequential Recommendation via Convolutional Sequence Embedding](https://mlsanity.com/paper/1809.07426/) (2018)
- [Recommendation as Language Processing (RLP): A Unified Pretrain, Personalized Prompt & Predict Paradigm (P5)](https://mlsanity.com/paper/2203.13366/) (2022)
- [Autoregressive Entity Retrieval](https://mlsanity.com/paper/2010.00904/) (2020)
- [Transformer Memory as a Differentiable Search Index](https://mlsanity.com/paper/2202.06991/) (2022)
- [Recommender Systems with Generative Retrieval](https://mlsanity.com/paper/2305.05065/) (2023)
- [Adapting Large Language Models by Integrating Collaborative Semantics for Recommendation](https://mlsanity.com/paper/2311.09049/) (2023)
- [M6-Rec: Generative Pretrained Language Models are Open-Ended Recommender Systems](https://mlsanity.com/paper/2205.08084/) (2022)
- [Autoregressive Search Engines: Generating Substrings as Document Identifiers](https://mlsanity.com/paper/2204.10628/) (2022)
- [Learnable Item Tokenization for Generative Recommendation](https://mlsanity.com/paper/2405.07314/) (2024)
- [Hierarchical Gating Networks for Sequential Recommendation](https://mlsanity.com/paper/1906.09217/) (2019)
- [Straightening Out the Straight-Through Estimator: Overcoming Optimization Challenges in Vector Quantized Networks](https://mlsanity.com/paper/2305.08842/) (2023)
- [A Bi-Step Grounding Paradigm for Large Language Models in Recommendation Systems](https://mlsanity.com/paper/2308.08434/) (2023)
- [Inference-Time Text-to-Video Alignment with Diffusion Latent Beam Search](https://mlsanity.com/paper/2501.19252/) (2025)
- [Debiased Contrastive Learning for Sequential Recommendation](https://mlsanity.com/paper/2303.11780/) (2023)
- [Generative Recommender with End-to-End Learnable Item Tokenization](https://mlsanity.com/paper/2409.05546/) (2024)
- [Generating Long Semantic IDs in Parallel for Recommendation](https://mlsanity.com/paper/2506.05781/) (2025)
- [PropRAG: Guiding Retrieval with Beam Search over Proposition Paths](https://mlsanity.com/paper/2504.18070/) (2025)
- [Differentiable Semantic ID for Generative Recommendation](https://mlsanity.com/paper/2601.19711/) (2026)
- [Generative Large Recommendation Models: Emerging Trends in LLMs for Recommendation](https://mlsanity.com/paper/2502.13783/) (2025)
- [Vectorizing the Trie: Efficient Constrained Decoding for LLM-based Generative Retrieval on Accelerators](https://mlsanity.com/paper/2602.22647/) (2026)
- [APAO: Bridging the Training-Inference Gap in Generative Recommendation via Adaptive Prefix-Aware Optimization](https://mlsanity.com/paper/2603.02730/) (2026)
- [BEAR: Towards Beam-Search-Aware Optimization for Recommendation with Large Language Models](https://mlsanity.com/paper/2601.22925/) (2026)
- [Restoring Collaborative Signals in Semantic-ID Generative Recommendation via Personalized Natural Language](https://mlsanity.com/paper/2607.27682/) (2026)

## Built on by (most cited first, 1 of 1)

- [Training with Missed Targets in Generative Recommendation: Separating Supervision from Probability Competition](https://mlsanity.com/paper/2610.10124/) (2026)

## Abstract (arXiv)

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.