Low-Rank Adaptation (LoRA) is a parameter-efficient technique for rapidly fine-tuning foundation models. In standard LoRA training dynamics, models tend to quickly converge to a local optimum near the initialization. However, this local optimum may not be ideal for out-of-distribution data or tasks such as merging and pruning. In this work, we propose a novel progressive training strategy for LoRA with random layer dropping. This strategy also optimizes the Shapley value of LoRA parameters in each layer, treating each layer as a player in a cooperative game. We refer to this method as Cooperative LoRA (CopRA). Our experimental results demonstrate that parameters trained with CopRA exhibit linear mode connectivity, which enables efficient model merging. This also paves the way for federated learning and multi-task learning via LoRA merging. Additionally, by optimizing the Shapley value, CopRA shows superior performance in pruning tasks.

Accurately measuring protein-RNA binding affinity is crucial in many biological processes and drug design. Previous computational methods for protein-RNA binding affinity prediction rely on either sequence or structure features, unable to capture the binding mechanisms comprehensively. The recent emerging pre-trained language models trained on massive unsupervised sequences of protein and RNA have shown strong representation ability for various in-domain downstream tasks, including binding site prediction. However, applying different-domain language models collaboratively for complex-level tasks remains unexplored. In this paper, we propose CoPRA to bridge pre-trained language models from different biological domains via Complex structure for Protein-RNA binding Affinity prediction. We demonstrate for the first time that cross-biological modal language models can collaborate to improve binding affinity prediction. We propose a Co-Former to combine the cross-modal sequence and structure information and a bi-scope pre-training strategy for improving Co-Former's interaction understanding. Meanwhile, we build the largest protein-RNA binding affinity dataset PRA310 for performance evaluation. We also test our model on a public dataset for mutation effect prediction. CoPRA reaches state-of-the-art performance on all the datasets. We provide extensive analyses and verify that CoPRA can (1) accurately predict the protein-RNA binding affinity; (2) understand the binding affinity change caused by mutations; and (3) benefit from scaling data and model size.