## 4 Experimental Results
### Experimental Results on ImageNet  
We also examine the proposed approach using ImageNet to compress the VGG-16, ResNet-18, and ResNet-50 models. Table 3 shows a comparative analysis of our method's performance against existing tensor decomposition techniques, and other compression strategies like pruning and Low-Rank Matrix decomposition. As these studies focus on providing a decrease in FLOPs, rather than the compression ratio, we also include the FLOPs reduction achieved using tensor decomposition.  
We used our method to compress the VGG-16 neural network, which is the largest deep neural network examined in this paper. The results in Table 3 show that our method yielded higher accuracy at a nearly similar drop in FLOPs as HT-2 [7]. The rest of the methods lead to worse compression results. It is noteworthy that our approach achieved the best Top-5 accuracy in the whole set of methods analyzed.  
When comparing ResNet-18, our technique achieves better accuracy than MUSCO [49] and TRP [50] by 0.14% and 2.18%, respectively, while maintaining an almost similar reduction ratio of FLOPs (4.6\(\times\)). Our models achieve much higher accuracy while reducing FLOPs more effectively compared to existing compression methods that result in noticeable accuracy loss. Specifically, our model achieves a reduction of 2.47\(\times\) in FLOPs and suffers a mere 0.16% decrease in accuracy compared to the original model.  
ResNet-50 is a more extensive and more complex model in comparison to ResNet-18. Table 3 demonstrates that our method shows superior performance across nearly all metrics compared to the other pruning approaches. Concerning the decomposition-based methods, which include Tucker decomposition and low-rank matrix decomposition, it is evident that all the mentioned decomposition-based approaches yielded inferior results in comparison to our approach. Furthermore, with a compression of 2.97\(\times\) FLOPs, our compressed model achieves a Top-5 accuracy loss 0.51% less than the uncompressed model.  
\begin{table}
\begin{tabular}{c c c c c} \hline \multirow{2}{*}{**Model**} & \multirow{2}{*}{**Method**} & **Compression** & \multirow{2}{*}{**Top-1 Acc (\%)**} & \multirow{2}{*}{**Compression**} \\  & & **Method** & & **Ratio** \\ \hline \multirow{8}{*}{Resnet-20} & Standard Tucker [10] & Tucker & \(-\)7.87 & 2.5\(\times\) \\  & Standard Tensor Train [47] & Tensor Train & \(-\)3.76 & 5.6\(\times\) \\  & Standard Tensor Ring [48] & Tensor Ring & \(-\)1.85 & 4.7\(\times\) \\  & PSTR-S [46] & Tensor Ring & \(+\)0.73 & 2.3\(\times\) \\  & PSTR-M [46] & Tensor Ring & \(-\)1.78 & 4.7\(\times\) \\  & Ours & CP & \(+\)1.05 & 2.6\(\times\) \\  & Ours & CP & \(-\)1.32 & 4.7\(\times\) \\ \hline \multirow{8}{*}{Resnet-32} & Standard Tucker [10] & Tucker & \(-\)9.07 & 2.5\(\times\) \\  & Standard Tensor Train [47] & Tensor Train & \(-\)5.20 & 4.6\(\times\) \\ \cline{1-1}  & Standard Tensor Ring [48] & Tensor Ring & \(-\)1.40 & 4.8\(\times\) \\ \cline{1-1}  & PSTR-S [46] & Tensor Ring & \(-\)0.05 & 2.4\(\times\) \\ \cline{1-1}  & PSTR-M [46] & Tensor Ring & \(-\)1.33 & 5.2\(\times\) \\ \cline{1-1}  & Ours & CP & \(-\)0.25 & 2.5\(\times\) \\ \cline{1-1}  & Ours & CP & \(-\)0.81 & 5.2\(\times\) \\ \hline \end{tabular}
\end{table}
Table 2: Comparison with various tensor decomposition methods for ResNet-20 and ResNet-32 on CIFAR-100 dataset.