The Lattice Representation Hypothesis and Concept Algebra in LLMs
Abstract
We uncover the hidden lattice geometry of large language models (LLMs): a symbolic backbone that grounds conceptual hierarchies and logical operations in embedding space. Our framework unifies the Linear Representation Hypothesis with Formal Concept Analysis (FCA), showing that linear attribute directions with separating thresholds induce a concept lattice via half-space intersections. This geometry enables symbolic reasoning through geometric meet (intersection) and join (union) operations, and admits a canonical form when attribute directions are linearly independent. Experiments on WordNet sub-hierarchies provide empirical evidence that LLM embeddings encode concept lattices and their logical structure, revealing a principled bridge between continuous geometry and symbolic abstraction.
BibTeX
@inproceedings{
xiong2026the,
title={The Lattice Representation Hypothesis and Concept Algebra in {LLM}s},
author={Bo Xiong},
booktitle={The Fourteenth International Conference on Learning Representations},
year={2026},
url={https://openreview.net/forum?id=5K1FG92m5s}
}