A potential 6G technology known as intelligent reflecting surface (IRS) has recently gained much attention from academia and industry. However, acquiring the optimized quantized phase shift (QPS) presents challenges for the IRS due to the phenomenon of signaling storms. In this paper, we attempt to solve the above problem by proposing two deep learning models, the global attention phase shift compression network (GAPSCN) and the simplified GAPSCN (S-GAPSCN). In GAPSCN, we propose a novel attention mechanism that emphasizes a greater number of meaningful features than previous attention-related works. Additionally, S-GAPSCN is built with an asymmetric architecture to meet the practical constraints on computation resources of the IRS controller. Moreover, in S-GAPSCN, to compensate for the performance degradation caused by simplifying the model, we design a low-computation complexity joint attention-assisted multi-scale network (JAAMSN) module in the decoder of S-GAPSCN. Simulation results demonstrate that the proposed global attention mechanism achieves prominent performance compared with the existing attention mechanisms and the proposed GAPSCN can achieve reliable reconstruction performance compared with existing state-of-the-art models. Furthermore, the proposed S-GAPSCN can approach the performance of the GAPSCN at a much lower computational cost.