## 3 Experiments
### Ablation Study
#### 3.4.3 The Impact of the Second-Order Feature and Receptive Field Modules  
In this section, we conduct ablation studies at both image level and patient level to verify the effectiveness of each module in HoRFNet under four different magnifications. In Figure 7, we use the backbone network as the baseline and compare the performance changes after introducing the second-order feature module (SeONet), the receptive field module (RFNet), and their combination (HoRFNet) to verify each module's contribution to performance improvement. In Figure 7a, HoRFNet achieves image level recognition accuracies of 97.66%, 98.56%, 99.50%, and 97.43% at 40\(\times\), 100\(\times\), 200\(\times\), and 400\(\times\) magnifications, respectively, demonstrating clear advantages over the other three models. In particular, compared with the Backbone model at the image level, the HoRFNet model has an accuracy increase of 6.35%, 7.36%, 5.63%, and 4.94% at the four magnifications, respectively. On the BreakHis dataset, we conduct an in-depth analysis of the performance of the Backbone, SeONet, and RFNet models, and also compares the performance improvement of high-order and receptive field block units on the Backbone model. In the image level evaluation results presented in Figure 7a, both the second-order feature module (SeONet) and the receptive field module (RFNet) effectively improve classification accuracy across all magnifications, demonstrating clear improvements over the backbone baseline. For example, at 200\(\times\) magnification, the backbone achieves an accuracy of 93.87%, while SeONet and RFNet improve it to 98.01% and 98.34%, respectively, demonstrating the positive contribution of both modules to image level recognition performance. The second-order features more effectively model the high-order relationships among local textures, while the receptive field module enhances the model's ability to perceive multiscale contextual information. However, at 100\(\times\) and 400\(\times\) magnifications, RFNet performs slightly lower than SeONet. For example, at 400\(\times\), RFNet achieves 94.50% compared to 95.05% for SeONet, which may be attributed to the distribution of fine-grained details in the images. At these magnifications, structural boundaries and local contrast become more prominent,  
Figure 7: Ablation study results of HoRFNet at four magnification levels (40\(\times\), 100\(\times\), 200\(\times\), and 400\(\times\)) on the BreakHis dataset. **(a)** Image level classification accuracy. **(b)** Patient level classification accuracy. HoRFNet consistently outperforms the Backbone, SeONet, and RFNet across all settings, demonstrating the effectiveness of integrating second-order pooling and multi-branch receptive field modules. giving second-order features an advantage in modeling local relationships. Nevertheless, RFNet still outperforms the backbone across all magnifications, indicating its effectiveness in enhancing overall feature representation. However, by combining the second-order statistical features and receptive field block, the HoRFNet model can obtain additional gain of 1.84%, 4.00%, 1.16%, and 2.93% higher than the RFNet model, and 2.17%, 2.72%, 1.49%, and 2.38% higher than the SeONet model. In the patient level evaluation presented in Figure 7b, all models exhibit stability across different magnifications, similar to the image level evaluation. For example, at 200\(\times\) magnification, the backbone achieves an accuracy of 93.11%, while SeONet and RFNet increase it to 97.89% and 98.44%, respectively. HoRFNet further improves the accuracy to 99.23%. This trend is consistent across most magnifications. Notably, similar to the image level results, at 100\(\times\) and 400\(\times\) magnifications, RFNet slightly underperforms SeONet but still significantly outperforms the backbone.