All or None: Identifiable Linear Properties of Next-Token Predictors in Language Modeling
Emanuele Marconato, Sebastien Lachapelle, Sebastian Weichwald, Luigi Gresele
Abstract
We analyze identifiability as a possible explanation for the ubiquity of linear properties across language models, such as the vector difference between the representations of “easy” and “easiest” being parallel to that between “lucky” and “luckiest”. For this, we ask whether finding a linear property in one model implies that any model that induces the same distribution has that property, too. To answer that, we first prove an identifiability result to characterize distribution-equivalent next-token predictors, lifting a diversity requirement of previous results. Second, based on a refinement of relational linearity [Paccanaro and Hinton, 2001; Hernandez et al., 2024], we show how many notions of linearity are amenable to our analysis. Finally, we show that under suitable conditions, these linear properties either hold in all or none distribution equivalent next-token predictors.
BibTeX
@inproceedings{
marconato2025all,
title={All or None: Identifiable Linear Properties of Next-Token Predictors in Language Modeling},
author={Emanuele Marconato and Sebastien Lachapelle and Sebastian Weichwald and Luigi Gresele},
booktitle={The 28th International Conference on Artificial Intelligence and Statistics},
year={2025},
url={https://openreview.net/forum?id=XCmIlemQP5}
}