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.

Expensive communication cost is a common performance bottleneck in Federated Learning (FL), which makes it less appealing in real-world applications. Many communication-efficient FL methods focus on discarding a part of model updates mostly based on gradient magnitude. In this study, we find that recycling previous updates, rather than simply dropping them, more effectively reduces the communication cost while maintaining FL performance. We propose *FedLUAR*, a Layer-wise Update Aggregation with Recycling scheme for communication-efficient FL. We first define a useful metric that quantifies the extent to which the aggregated gradients influences the model parameter values in each layer. *FedLUAR* selects a few layers based on the metric and recycles their previous updates on the server side. Our extensive empirical study demonstrates that the update recycling scheme significantly reduces the communication cost while maintaining model accuracy. For example, our method achieves nearly the same AG News accuracy as FedAvg, while reducing the communication cost to just 17%.