Autoregressive Decoding as a Martingale: Characterizing the Stochastic Dynamics of LLM Generation
Large language models (LLMs) have achieved remarkable success across a wide range of language tasks. At their core, autoregressive LLMs are conditional probability models that learn to approximate the next-token distribution given the preceding context. Despite this probabilistic nature, the stochastic dynamics of autoregressive decoding have rarely been investigated from a rigorous probabilistic perspective. In this work, we define the per-step prediction error as the difference between the sampled token indicator and the model's conditional predictive distribution, and prove that the cumulative error process is a martingale with respect to the decoding filtration, implying that its cond...
| Authors | Xiahui Zhu, Zhenyi Qi, Wanwei Liu et al. |
|---|---|
| Primary category | cs.LG |
| Published | 12 October 2026 |
| Last updated at source | 12 October 2026 |
Silytics shows public metadata from arXiv and links to the original. Information may be incomplete or out of date. Last refreshed 14 October 2026. Licenses and terms of the original apply to the work itself. Not financial, legal or professional advice.