Multi-Token Prediction (MTP): Mathematical Foundations, Shared Trunk Architectures, Sequential Future Verification, and Speculative Decoding Dynamics
The standard training objective for autoregressive large language models is next-token prediction (NTP), where model parameters $\theta$ are trained via maximum likelihood estimation to forecast a single subsequent token given all previous context. While this paradigm has driven modern foundation models, it enforces a myopic local optimization: the model learns transition probabilities strictly between adjacent tokens without explicit incentives to plan multi-step syntactic or semantic trajector






