The Geometry of Numerical Reasoning: Language Models Compare Numeric Properties in Linear Subspaces

• URL: http://arxiv.org/abs/2410.13194v1
• Date: Thu, 17 Oct 2024 03:44:11 GMT
• Title: The Geometry of Numerical Reasoning: Language Models Compare Numeric Properties in Linear Subspaces
• Authors: Ahmed Oumar El-Shangiti, Tatsuya Hiraoka, Hilal AlQuabeh, Benjamin Heinzerling, Kentaro Inui,
• Abstract summary: This paper investigates whether large language models (LLMs) utilize numerical attributes encoded in a low-dimensional subspace of the embedding space when answering logical comparison questions. We first identified these subspaces using partial least squares regression, which effectively encodes the numerical attributes associated with the entities in comparison prompts.
• Score: 22.31258265337828
• License:
• Abstract: This paper investigates whether large language models (LLMs) utilize numerical attributes encoded in a low-dimensional subspace of the embedding space when answering logical comparison questions (e.g., Was Cristiano born before Messi?). We first identified these subspaces using partial least squares regression, which effectively encodes 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. Experimental results show that our findings hold for different numerical attributes, indicating that LLMs utilize the linearly encoded information for numerical reasoning.

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