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The non-volatile Resistive RAM (ReRAM) crossbar has shown great potential in accelerating inference in various machine learning models However, it suffers from high reprogramming energy, hindering its usage for on-device adaption to new tasks. Recently, parameter-efficient fine-tuning methods, such as Low-Rank Adaption (LoRA), have been proposed to train few parameters while matching full fine-tuning performance. However, in ReRAM crossbar, the reprogramming cost of LoRA is non-trivial and will increase significantly when adapting to multi-tasks on the device. To address this issue, we are the first to propose LoRAFusion, a parameter-efficient multi-task on-device learning framework for ReRAM crossbar via fusion of pre-trained LoRA modules. LoRAFusion is a group of LoRA modules that are one-time learned based on diverse domain-specific tasks and deployed to the crossbar, acting as the pool of background knowledge. Then given a new unseen task, those LoRA modules are frozen (i.e., no energy-hungry ReRAM cells reprograming), only the proposed learnable layer-wise LoRA fusion coefficient and magnitude vector parameters are trained on-device to weighted-combine pre-trained LoRA modules, which significantly reduces the training parameter size. Our comprehensive experiments show LoRAFusion only uses 3% of the number of trainable parameters in LoRA (148K vs. 4700K), with 0.19% accuracy drop. Codes are available at https://github.com/ASU-ESIC-FAN-Lab/LoRAFusion