@inproceedings{el-shangiti-etal-2025-geometry,
    title = "The Geometry of Numerical Reasoning: Language Models Compare Numeric Properties in Linear Subspaces",
    author = "El-Shangiti, Ahmed Oumar  and
      Hiraoka, Tatsuya  and
      AlQuabeh, Hilal  and
      Heinzerling, Benjamin  and
      Inui, Kentaro",
    editor = "Chiruzzo, Luis  and
      Ritter, Alan  and
      Wang, Lu",
    booktitle = "Proceedings of the 2025 Conference of the Nations of the Americas Chapter of the Association for Computational Linguistics: Human Language Technologies (Volume 2: Short Papers)",
    month = apr,
    year = "2025",
    address = "Albuquerque, New Mexico",
    publisher = "Association for Computational Linguistics",
    url = "https://preview.aclanthology.org/fix-sig-urls/2025.naacl-short.47/",
    pages = "550--561",
    ISBN = "979-8-89176-190-2",
    abstract = "This paper investigates whether large language models (LLMs) utilize numerical attributes encoded in a low-dimensional subspace of theembedding space when answering questions involving numeric comparisons, e.g., Was Cristiano born before Messi? We first identified,using partial least squares regression, these subspaces, which effectively encode the numerical attributes associated with the entities in comparison prompts. Further, we demonstrate causality, by intervening in these subspaces to manipulate hidden states, thereby altering the LLM{'}s comparison outcomes. Experiments conducted on three different LLMs showed that our results hold across different numerical attributes, indicating that LLMs utilize the linearly encoded information for numerical reasoning."
}