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

arXiv: https://arxiv.org/abs/2603.18593 · HTML: https://mlsanity.com/paper/2603.18593/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 23 references that are in the map.
- First posted on arXiv 19 Mar 2026.

## Builds on (most cited first, 15 of 15)

- [Sentence-BERT: Sentence Embeddings using Siamese BERT-Networks](https://mlsanity.com/paper/1908.10084/) (2019)
- [Efficient Memory Management for Large Language Model Serving with PagedAttention](https://mlsanity.com/paper/2309.06180/) (2023)
- [Large Language Models are Zero-Shot Reasoners](https://mlsanity.com/paper/2205.11916/) (2022)
- [Distributed Representations of Words and Phrases and their Compositionality](https://mlsanity.com/paper/1310.4546/) (2013)
- [Tulu 3: Pushing Frontiers in Open Language Model Post-Training](https://mlsanity.com/paper/2411.15124/) (2024)
- [Enhancing Chat Language Models by Scaling High-quality Instructional Conversations](https://mlsanity.com/paper/2305.14233/) (2023)
- [Carbontracker: Tracking and Predicting the Carbon Footprint of Training Deep Learning Models](https://mlsanity.com/paper/2007.03051/) (2020)
- [Artificial Hivemind: The Open-Ended Homogeneity of Language Models (and Beyond)](https://mlsanity.com/paper/2510.22954/) (2025)
- [Infinity Instruct: Scaling Instruction Selection and Synthesis to Enhance Language Models](https://mlsanity.com/paper/2506.11116/) (2025)
- [Prompt Repetition Improves Non-Reasoning LLMs](https://mlsanity.com/paper/2512.14982/) (2025)
- [We Should Chart an Atlas of All the World's Models](https://mlsanity.com/paper/2503.10633/) (2025)
- [PhyloLM : Inferring the Phylogeny of Large Language Models and Predicting their Performances in Benchmarks](https://mlsanity.com/paper/2404.04671/) (2024)
- [Mapping 1,000+ Language Models via the Log-Likelihood Vector](https://mlsanity.com/paper/2502.16173/) (2025)
- [Establishing a Scale for Kullback-Leibler Divergence in Language Models Across Various Settings](https://mlsanity.com/paper/2505.15353/) (2025)
- [Likelihood Variance as Text Importance for Resampling Texts to Map Language Models](https://mlsanity.com/paper/2505.15428/) (2025)

## Abstract (arXiv)

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.