Results in interpretability suggest that large vision and language models learn implicit linear encodings when models are biased by in-context prompting. However, the existence of similar linear representations in more general adaptation regimes has not yet been demonstrated. In this work, we develop the concept of a task matrix, a linear transformation from a base to finetuned embedding state. We demonstrate that for vision and text models and ten different datasets, a base model augmented with a task matrix achieves results surpassing linear probes, sometimes approaching finetuned levels. Our results validate the existence of cross-layer linear encodings between pretrained and finetuned architectures. Moreover, we show that a data-based approximation for such encodings is both efficient and generalizable to multiple domains. We make our implementation publicly available.
@article{arxiv.2512.14880,
title = {Task Matrices: Linear Maps for Cross-Model Finetuning Transfer},
author = {Darrin O' Brien and Dhikshith Gajulapalli and Eric Xia},
journal= {arXiv preprint arXiv:2512.14880},
year = {2025}
}