Merging parameter-efficient task experts has recently gained growing attention as a way to build modular architectures that can be rapidly adapted on the fly for specific downstream tasks, without requiring additional fine-tuning. Typically, LoRA serves as the foundational building block of such parameter-efficient modular architectures, leveraging low-rank weight structures to reduce the number of trainable parameters. In this paper, we study the properties of sparse adapters, which train only a subset of weights in the base neural network, as potential building blocks of modular architectures. First, we propose a simple method for training highly effective sparse adapters, which is conceptually simpler than existing methods in the literature and surprisingly outperforms both LoRA and full fine-tuning in our setting. Next, we investigate the merging properties of these sparse adapters by merging adapters for up to 20 natural language processing tasks, thus scaling beyond what is usually studied in the literature. Our findings demonstrate that sparse adapters yield superior in-distribution performance post-merging compared to LoRA or full model merging. Achieving strong held-out performance remains a challenge for all methods considered.

Federated Learning is a promising paradigm for privacy-preserving collaborative model training. In practice, it is essential not only to continuously train the model to acquire new knowledge but also to guarantee old knowledge the right to be forgotten (i.e., federated unlearning), especially for privacy-sensitive information or harmful knowledge. However, current federated unlearning methods face several challenges, including indiscriminate unlearning of cross-client knowledge, irreversibility of unlearning, and significant unlearning costs. T o this end, we propose a method named FUSED, which first identifies critical layers by analyzing each layer's sensitivity to knowledge and constructs sparse unlearning adapters for sensitive ones. Then, the adapters are trained without altering the original parameters, overwriting the unlearning knowledge with the remaining knowledge. This knowledge overwriting process enables FUSED to mitigate the effects of indiscriminate unlearning. Moreover, the introduction of independent adapters makes unlearning reversible and significantly reduces the unlearning costs. Finally, extensive experiments on three datasets across various unlearning scenarios demonstrate that FUSED's effectiveness is comparable to Retraining, surpassing all other baselines while greatly reducing unlearning costs.