Autoregressive Decoding as a Martingale: Characterizing the Stochastic Dynamics of LLM Generation

Key points

• Large language models (LLMs) have achieved remarkable success across a wide range of language tasks.1
• 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 conditional first-order moment is identically zero.1
• This identity establishes a direct theoretical connection between sequence fluctuations and predictive uncertainty during autoregressive decoding.1
• These results provide a probabilistic framework for analyzing autoregressive LLM decoding, reveal intrinsic probabilistic fingerprints of different language models, and establish a rigorous mathematical foundation for LLM-generated text detection and uncertainty quantification.1

Sources (1)

• [1]Autoregressive Decoding as a Martingale: Characterizing the Stochastic Dynamics of LLM Generation
  arXiv (AI, ML, NLP, CV, robotics, multi-agent) · Oct 12, 01:31 AM

  Despite this probabilistic nature, the stochastic dynamics of autoregressive decoding have rarely been investigated from a rigorous probabilistic perspective.

  Large language models (LLMs) have achieved remarkable success across a wide range of language tasks.

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