What do Language Model Probabilities Represent? From Distribution Estimation to Response Prediction

The notion of language modeling has gradually shifted in recent years from a distribution over finite-length strings to general-purpose prediction models for textual inputs and outputs, following appropriate alignment phases. This paper analyzes the distinction between distribution estimation and response prediction in the context of LLMs, and their often conflicting goals. We examine the training phases of LLMs, which include pretraining, in-context learning, and preference tuning, and also the common use cases for their output probabilities, which include completion probabilities and explicit probabilities as output. We argue that the different settings lead to three distinct intended output distributions. We demonstrate that NLP works often assume that these distributions should be similar, which leads to misinterpretations of their experimental findings. Our work sets firmer formal foundations for the interpretation of LLMs, which will inform ongoing work on the interpretation and use of LLMs' induced distributions.