The Geometry of Numerical Reasoning: Language Models Compare Numeric Properties in Linear Subspaces
This addresses the problem of understanding numerical reasoning mechanisms in LLMs for researchers in AI and NLP, but it is incremental as it builds on existing work on subspace analysis.
The paper tackled how large language models (LLMs) handle numeric comparisons by identifying low-dimensional subspaces that encode numerical attributes, and demonstrated causality through interventions that alter comparison outcomes, with experiments on three LLMs showing consistent results.
This paper investigates whether large language models (LLMs) utilize numerical attributes encoded in a low-dimensional subspace of the embedding 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.