Sparse fine-tuning techniques adapt LLMs to downstream tasks by only tuning a sparse subset of model parameters. However, the effectiveness of sparse adaptation depends on optimally selecting the model parameters to be fine-tuned. In this work, we introduce a novel sparse fine-tuning technique named GaLLoP: Gradient-based Sparse Learning on Low-Magnitude Parameters, which fine-tunes only those model parameters which have the largest gradient magnitudes on downstream tasks and the smallest pre-trained magnitudes, intuitively prioritizing parameters that are highly task-relevant, but minimally disruptive to pre-trained knowledge. Our experimentation with LLaMA3 8B and Gemma 2B as base models shows that GaLLoP consistently improves or matches the in-distribution as well as out-of-distribution performance obtained via the usage of other leading parameter-efficient fine-tuning techniques, including LoRA, DoRA, and SAFT. Our analysis demonstrates that GaLLoP mitigates catastrophic forgetting and memorization of task data, as important pre-trained parameters remain unchanged, and stabilizes performance relative to other fine-tuning techniques, robustly generalizing across most random seeds.
@article{arxiv.2510.19778,
title = {GaLLoP: Gradient-based Sparse Learning on Low-Magnitude Parameters},
author = {Anand Choudhary and Yasser Sulaıman and Lukas Mauch and Ghouthi Boukli Hacene and Fabien Cardinaux and Antoine Bosselut},
journal= {arXiv preprint arXiv:2510.19778},
year = {2025}
}