Probabilistic Attribution For Large Language Models

Abstract

The generative nature of Large Language Models (LLMs) is reflected in the conditional probabilities they compute to sample each response token given the previous tokens. These probabilities encode the distributional structure that the model learns in training and exploits in inference. In this work, we use these probabilities to situate LLMs within the mathematical theory of stochastic processes. We use this framework to design a model-agnostic probabilistic token attribution measure, using Bayes rule to invert the next-token log-probabilities so as to capture the models internal representation of the distribution over token sequences. The representation is independent of the models computational structure. This representation yields the conditional probability of the response given the prompt, and of the response given the prompt with a token marginalized away. Our attribution score is the log of the ratio of these probabilities. We further compute the entropies of a single prompts token distributions, conditioned on the remaining context. The interplay between entropy and attribution score sheds light on LLM behavior. We evaluate 8 models across 7 prompts and investigate anomalies, token sensitivity, response stability, model stability, and training convergence, thereby improving interpretability and guiding users to focus on uncertain or unstable parts of the generation.