On the Equivalence Between Auto-Regressive Next Token Prediction and Full-Item-Vocabulary Maximum Likelihood Estimation in Generative Recommendation--A Short Note

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.