Recently, the fault diagnosis domain has witnessed a surge in the popularity of the deep residual shrinkage network (DRSN) due to its robust denoising capabilities. In our previous research, an enhanced version of DRSN named global multi-attention DRSN (GMA-DRSN) is introduced to augment the feature extraction proficiency of DRSN specifically for noised vibration signals. However, the utilization of multiple attention structures in GMA-DRSN leads to an escalation in the computational complexity of the network, which may pose practical deployment challenges. To address this limitation, this paper proposes a lightweight variant of GMA-DRSN, referred to as LGMA-DRSN, building upon our prior work. Firstly, the numerical variation regularity of the adaptive inferred slope parameters in the global parametric rectifier linear unit (GPReLU) is analyzed, where we surprisingly find that a convex parameter combination always occurs in pairs. Based on this convex regularity, the sub-network structure of the adaptive inferred slope with attention mechanism is optimized, which greatly reduces the computational complexity compared to our previous work. Finally, the experimental outcomes demonstrate that LGMA-DRSN not only enhances diagnostic efficiency, but also ensures a high level of diagnostic accuracy in the presence of noise interference, when compared with our prior work.