Parameter-efficient fine-tuning (PEFT) has become a popular way to adapt large pre-trained models to new tasks. Most PEFT methods update only a small subset of parameters while freezing the rest, avoiding redundant computation. As they maximize the absolute size of the updates without regard to the parameters’ original scale, the resulting changes in model behavior can be minimal. In contrast, we maximize updates relative to each parameter’s scale, yielding more meaningful downstream adaptation. We propose Gradient-to-Weight Ratio and Entropy-guided Masking (GEM), a parameter scale-aware, distribution-sensitive sparse fine-tuning framework. GEM prioritizes parameters whose updates are significant in proportion to their initial pre-trained values. It also adaptively determines how many parameters to tune at each layer based on the entropy of parameter values, thereby making the most effective use of the computational budget in PEFT. Our empirical study demonstrates the efficacy of GEM on both general-domain tasks (GLUE and SuperGLUE) and domain-specific tasks (GSM8k and MBPP), achieving up to a 1.6% improvement in fine-tuning accuracy over full fine-tuning while updating only 0.1% of model parameters.