Closed-form merging of parameter-efficient modules for Federated Continual Learning

Model merging has emerged as a crucial technique in Deep Learning, enabling the integration of multiple models into a unified system while preserving performance and scalability. In this respect, the compositional properties of low-rank adaptation techniques (e.g., LoRA) have proven beneficial, as simple averaging LoRA modules yields a single model that mostly integrates the capabilities of all individual modules. Building on LoRA, we take a step further by imposing that the merged model matches the responses of all learned modules. To address this challenge, we introduce LoRM, an alternating optimization strategy that trains one LoRA matrix at a time. This allows solving for each unknown variable individually, thus finding a unique solution. We apply our proposed methodology to Federated Class-Incremental Learning (FCIL), ensuring alignment of model responses both between clients and across tasks. Our method demonstrates stateof-the-art performance across a range of FCIL scenarios. Humans naturally excel at learning a diverse array of skills independently, effortlessly acquiring knowledge across multiple domains throughout their lives. In contrast, the traditional paradigm for artificial neural networks relies on training a unified model on a single, large dataset.