## 5 Conclusions  
Based on the influence analysis of the amplitude of classification features and weight of the last linear layer on the back propagation gradient, this paper proposes a BN based new classification approach. Different from the conventional idea of optimization of the cosine distance of Softmax loss, we try to alleviate the gradient vanishing problem by using the scalable batch normalization layer to achieve our goal and it makes the extracted features of the network more effective. The experimental results also prove that the proposed method can improve significantly the accuracy of the network classification in different data sets and different network structures, and is also better than many other improved classification losses. In future research, we could explore a new loss function whose gradient is better than cross-entropy loss. Data curation, T.Z. and W.C.; Funding acquisition, T.Z. and W.C.; Methodology, Q.Z. ; Software, Z.H. ; Supervision, Q.Z. ; Writing--original draft, Z.H. All authors have read and agreed to the published version of the manuscript. This research was funded by the open project fund of the Key Laboratory of intelligent infrared perception, Chinese Academy of Sciences (grant number:CAS-IIRP-2030-03), and the APC was funded by CAS-IIRP-2030-03. The authors declare no conflict of interest. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**CIFAR-100 Results** & **VGG** & **ResNet-18** & **ResNet-50** \\ \hline Cross-entropy Loss & 71.86\% (\(\pm\)0.14\%) & 75.10\% (\(\pm\)0.34\%) & 75.95\% (\(\pm\)0.32\%) \\ AM-SoftMax Loss (s = 7.5, m = 0.35) & 72.85\% (\(\pm\)0.18\%) & 74.97\% (\(\pm\)0.08\%) & 75.68\% (\(\pm\)0.14\%) \\ AM-SoftMax Loss (s = 10, m = 0.5) & 71.97\% (\(\pm\)0.54\%) & 74.40\% (\(\pm\)0.38\%) & 75.61\% (\(\pm\)0.24\%) \\ PEDCC-Loss (s = 7.5, m = 0.35) & 72.53\% (\(\pm\)0.32\%) & 74.86\% (\(\pm\)0.51\%) & 76.19\% (\(\pm\)0.14\%) \\ PEDCC-Loss (s = 10, m = 0.5) & 71.98\% (\(\pm\)0.31\%) & 73.84\% (\(\pm\)0.48\%) & 75.41\% (\(\pm\)0.17\%) \\ Our Loss (m = 0.8) & 73.57\% (\(\pm\)0.25\%) & **76.12\% (\(\pm\)0.31\%)** & 76.56\% (\(\pm\)0.13\%) \\ Our Loss (m = 0.9) & **74.13\% (\(\pm\)0.24\%)** & 76.10\% (\(\pm\)0.12\%) & **76.62\% (\(\pm\)0.17\%)** \\ Our Loss (m = 1) & 73.24\% (\(\pm\)0.06\%) & 76.08\% (\(\pm\)0.30\%) & 76.32\% (\(\pm\)0.51\%) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The experimental results of CIFAR-100 dataset. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**TinyImagenet Results** & **VGG** & **ResNet-18** & **ResNet-50** \\ \hline Cross-entropy Loss & 54.05\% (\(\pm\)0.19\%) & 59.38\% (\(\pm\)0.18\%) & 62.35\% (\(\pm\)0.27\%) \\ AM-SoftMax Loss (s = 7.5, m = 0.35) & 54.57\% (\(\pm\)0.28\%) & 59.48\% (\(\pm\)0.25\%) & 61.83\% (\(\pm\)0.27\%) \\ AM-SoftMax Loss (s = 10, m = 0.5) & 54.62\% (\(\pm\)0.31\%) & 59.26\% (\(\pm\)0.32\%) & 62.40\% (\(\pm\)0.06\%) \\ PEDCC-Loss (s = 7.5, m = 0.35) & 54.91\% (\(\pm\)0.17\%) & 59.13\% (\(\pm\)0.38\%) & 62.38\% (\(\pm\)0.52\%) \\ PEDCC-Loss (s = 10, m = 0.5) & 54.22\% (\(\pm\)0.21\%) & 59.04\% (\(\pm\)0.08\%) & 6242\% (\(\pm\)0.24\%) \\ Our Loss (m = 0.8) & 55.02\% (\(\pm\)0.09\%) & 60.34\% (\(\pm\)0.32\%) & **63.72\% (\(\pm\)0.08\%)** \\ Our Loss (m = 0.9) & 55.13\% (\(\pm\)0.25\%) & 60.12\% (\(\pm\)0.07\%) & 63.09\% (\(\pm\)0.15\%) \\ Our Loss (m = 1) & **55.86\% (\(\pm\)0.26\%)** & **60.61\% (\(\pm\)0.23\%)** & 63.27\% (\(\pm\)0.30\%) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The experimental results of TinyImagenet dataset.