PLS-found numeric-comparison subspaces causally control LLM answers

El-Shangiti et al. show LLMs answering numeric-comparison questions encode each entity's numeric attribute in a low-dimensional linear subspace, found via a 5-component PLS regression on the last-token state [el-shangiti-etal-2024-geometry-of-numerical-reasoning] The fit reaches R^2 > 0.8 for birth year, death year and latitude across Llama-3-8B-Instruct, Mistral-7B-Instruct and Qwen2.5-7B-Instruct [el-shangiti-etal-2024-geometry-of-numerical-reasoning] Intervening along the first PLS component flips the model's Yes/No comparison answer far more than an equal-magnitude random control, concentrated in roughly the first half of layers [el-shangiti-etal-2024-geometry-of-numerical-reasoning]