证明了自回归预测与完整物品词表最大似然等价，为推荐系统提供理论基础。
On the Equivalence Between Auto-Regressive Next Token Prediction and Full-Item-Vocabulary Maximum Likelihood Estimation in Generative Recommendation--A Short Note
- 在物品与令牌序列一一对应前提下，自回归预测等价于全词汇最大似然估计。
- 该等价性在串行和并行两种令牌化方案中均成立。
- 为工业级生成式推荐系统设计提供理论指导，适合算法研究者阅读。
生成式推荐（GR）已成为工业界序列推荐的主流范式。当前GR系统普遍采用：物品索引分词、以自回归下一令牌预测为训练目标、自回归解码生成下一个物品的流程。然而，现有研究多集中于架构设计与性能优化，缺乏对自回归下一令牌预测在推荐场景下工作机制的严格理论解释。本文正式证明，在物品与其对应k令牌序列存在双射映射的核心假设下，k令牌自回归下一令牌预测（AR-NTP）范式严格等价于全物品词表最大似然估计（FV-MLE）。我们进一步表明，该等价性在工业中广泛应用的级联与并行令牌化方案中均成立。本研究首次为占主导地位的工业级生成式推荐范式提供了形式化理论基础，并为未来系统优化提供原则性指导。
原文摘要 · Abstract (English)
Generative recommendation (GR) has emerged as a widely adopted paradigm in industrial sequential recommendation. Current GR systems follow a similar pipeline: tokenization for item indexing, next-token prediction as the training objective and auto-regressive decoding for next-item generation. However, existing GR research mainly focuses on architecture design and empirical performance optimization, with few rigorous theoretical explanations for the working mechanism of auto-regressive next-token prediction in recommendation scenarios. In this work, we formally prove that \textbf{the k-token auto-regressive next-token prediction (AR-NTP) paradigm is strictly mathematically equivalent to full-item-vocabulary maximum likelihood estimation (FV-MLE)}, under the core premise of a bijective mapping between items and their corresponding k-token sequences. We further show that this equivalence holds for both cascaded and parallel tokenizations, the two most widely used schemes in industrial GR systems. Our result provides the first formal theoretical foundation for the dominant industrial GR paradigm, and offers principled guidance for future GR system optimization.
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