Language Model Maps for Prompt-Response Distributions via Log-Likelihood Vectors

We propose a method that represents language models by log-likelihood vectors over prompt-response pairs and constructs model maps for comparing their conditional distributions. In this space, squared Euclidean distances between models are approximately proportional to the KL divergence between the corresponding conditional distributions. Experiments on a large collection of publicly available language models show that the maps capture meaningful global structure, including relationships to model attributes and task performance. The representation also captures systematic shifts induced by prompt modifications and their approximate additive compositionality; we use the vectors to predict downstream task scores and leverage their additive structure to approximate the effects of composite prompt operations without directly observing the corresponding log-likelihood vectors. We further introduce PMI vectors to reduce the influence of unconditional distributions; in some cases, PMI-based model maps better reflect training-data-related differences. Overall, the framework supports the analysis and prediction of input-dependent model behavior.