As deep learning models expand, the pre-training-fine-tuning paradigm has become the standard approach for handling various downstream tasks. However, shared parameters can lead to diminished performance when dealing with complex datasets involving multiple tasks. While introducing Mixture-of-Experts (MoE) methods has alleviated this issue to some extent, it also significantly increases the number of parameters required for fine-tuning and training time, introducing greater parameter redundancy. To address these challenges, we propose a method for allocating expert numbers based on parameter sensitivity-LoRA-SMoE (A Sensitivity-Driven Expert Allocation Method in LoRA-MoE for Efficient Fine-Tuning). This method rapidly assesses the sensitivity of different tasks to parameters by sampling a small amount of data and using gradient information. It then adaptively allocates expert numbers within a given budget. The process maintains comparable memory consumption to LoRA (Low-Rank Adaptation) while ensuring an efficient and resource-friendly fine-tuning procedure. Experimental results demonstrate that compared to SOTA fine-tuning methods, our LoRA-SMoE approach can enhance model performance while reducing the number of trainable parameters. This significantly improves model performance in resource-constrained environments. Additionally, due to its efficient parameter sensitivity evaluation mechanism, LoRA-SMoE requires minimal computational overhead to optimize expert allocation, making it particularly suitable for scenarios with limited computational resources. All the code in this study will be made publicly available following the acceptance of the paper for publication. Source code is at https://github.com/EMLS-ICTCAS/LoRA-SMoE

As a classical NP-hard problem and the topic of the PACE 2022 competition, the directed feedback vertex set problem (DFVSP) aims to find a minimum subset of vertices such that, when vertices in the subset and all their adjacent edges are removed from the directed graph, the remainder graph is acyclic. In this paper, we propose a threshold-based responsive simulated annealing algorithm called TRSA for solving DFVSP. First, we simplify the problem instances with two new reduction rules proposed in this paper and eight reduction rules from the literature. Then, based on a new solution representation, TRSA solves DFVSP with a fast local search procedure featured by a swap-based neighborhood structure and three neighborhood acceleration strategies. Finally, all these strategies are incorporated into a threshold-based responsive simulated annealing framework. Computational experiments on 140 benchmark instances show that TRSA is highly competitive compared to the state-of-the-art methods. Specifically, TRSA can improve the best known results for 53 instances, while matching the best known results for 79 ones. Furthermore, some important features of TRSA are analyzed to identify its success factors.