This repository accompanies the paper "From Directions to Cones: Multidimensional Representations of Propositional Facts in LLMs", which introduces and evaluates a method for identifying multi-dimensional activation subspaces (cones) that mediate truth behavior in large language models.
Large Language Models can encode factuality internally, even when their outputs are unreliable. Prior work has often approximated truth representations as a single linear direction. We expand on this by discovering multi-dimensional cones of activation vectors that collectively influence whether a model responds truthfully to simple propositional prompts.
The key contributions include:
- Demonstrating that truth is mediated not by a single direction but by a subspace of directions.
- Showing that these cones causally affect model responses across multiple architectures and parameter sizes.
- Confirming that cone-based interventions retain unrelated capabilities (e.g., instruction following) with minimal disruption.
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Sample directions in a learned 2D truth cone
If you use this work, please cite:
yu2025from,
title={From Directions to Cones: Multidimensional Representations of Propositional Facts in {LLM}s},
author={Stanley Yu and Vaidehi Bulusu and Oscar S. Yasunaga and Clayton Lau and Cole Blondin and Vasu Sharma and Kevin Zhu and Sean O'Brien},
booktitle={ACL 2025 Student Research Workshop},
year={2025},
url={https://openreview.net/forum?id=GYaJKGfmXm}
}