Ahmed Oumar El-Shangiti

Ahmed Oumar El-Shangiti, Tatsuya Hiraoka, Hilal AlQuabeh et al.

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.

H. V. AlquBoj, Hilal AlQuabeh, Velibor Bojkovic et al.

Humans are believed to perceive numbers on a logarithmic mental number line, where smaller values are represented with greater resolution than larger ones. This cognitive bias, supported by neuroscience and behavioral studies, suggests that numerical magnitudes are processed in a sublinear fashion rather than on a uniform linear scale. Inspired by this hypothesis, we investigate whether large language models (LLMs) exhibit a similar logarithmic-like structure in their internal numerical representations. By analyzing how numerical values are encoded across different layers of LLMs, we apply dimensionality reduction techniques such as PCA and PLS followed by geometric regression to uncover latent structures in the learned embeddings. Our findings reveal that the model's numerical representations exhibit sublinear spacing, with distances between values aligning with a logarithmic scale. This suggests that LLMs, much like humans, may encode numbers in a compressed, non-uniform manner.