## 8 Conclusions  
In this paper, we have introduced a novel compression method that combines tensor decomposition with binary neural networks (BNNs) to achieve significant model compression while maintaining competitive performance. By leveraging tensor decomposition techniques such as CP, Tucker, and Tensor Train and integrating them with BNNs, we are able to drastically reduce the parameter size of deep learning models, achieving compression ratios as high as 169\(\times\). This reduction in model size does not come at the expense of accuracy, as demonstrated across various datasets and models, including MNIST, CIFAR-10, CIFAR-100, and ImageNet. Our method also explores the crucial role of rank selection in tensor decomposition. By using a sensitivity-based approach, we ensure that critical layers maintain their representational power, while less important layers are compressed more aggressively. Our analysis of rank selection methods, including random rank selection and VBMF, further highlights the effectiveness of sensitivity-based rank selection in preserving model accuracy while achieving substantial compression. Moreover, our ablation studies show that the choice of initialization, activation functions, and training routines plays a pivotal role in enhancing the performance of the compressed models. Specifically, orthogonal initialization combined with PReLU acti \begin{table}
\begin{tabular}{l c c c c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**UCF-QNRF**} & \multicolumn{2}{c}{**WE**} & \multicolumn{2}{c}{**ShanghaiTech B**} & \multicolumn{2}{c}{**UCF-CC-50**} & \multicolumn{2}{c}{**Floating Point**} \\  & **MAE** & **RMSE** & **MAE** & **RMSE** & **MAE** & **RMSE** & **MAE** & **RMSE** & **Params** & **Compress.** \\ \hline MCNN & 365.2 & 577.2 & 18.8 & 0.0 & 40.3 & 60.0 & 566.4 & 715.3 & 545 KB & – \\ CSRNet & 111.4 & 199.4 & 14.3 & 0.0 & 9.8 & 14.6 & 155.2 & 254.4 & 65 MB & – \\ \hline  & **MAE** & **RMSE** & **MAE** & **RMSE** & **MAE** & **RMSE** & **MAE** & **RMSE** & **Params** & **Compress.** \\ \hline MCNN & 416 & 621.5 & 18.6 & 0.0 & 50.4 & 70.2 & 377.6 & 509.1 & 152 KB & 3.58\(\times\) \\ CSRNet & 121.2 & 198.3 & 15.6 & 0.0 & 16.25 & 25.03 & 233.54 & 266.17 & 2.74 MB & 23\(\times\) \\ \hline \hline \end{tabular}
\end{table} 
Table 15: Comparison between the floating-point models of MCNN and CSRNet and the decomposed binary models. vation and sensitivity-based rank selection yields the best performance across various architectures. These findings provide a comprehensive framework for the deployment of highly compressed yet accurate models on edge devices where computational and memory resources are limited. The application of our method to crowd-counting models (MCNN and CSRNet) demonstrates the practical utility of this approach in real-world scenarios, achieving compression ratios of 3.58\(\times\) and 23\(\times\), respectively. This not only validates our approach across diverse domains but also emphasizes its applicability in edge computing environments, where efficiency is paramount. However, as discussed in Section 7, the balance between compression and performance remains a challenge. Certain architectures experience a slight drop in accuracy after aggressive compression, and the computational overhead introduced by tensor decomposition methods requires further optimization. Finally, future work will focus on addressing these limitations by investigating mixed-precision quantization methods and optimizing tensor decomposition algorithms to reduce computational costs. We also plan to explore hardware accelerations for tensor operations, enabling faster inference and more efficient use of compressed models on edge devices, particularly in real-time applications like autonomous systems and health care. By continuing to refine these techniques, we aim to further enhance the viability of deep learning models on edge platforms while maintaining a balance between compression, accuracy, and computational efficiency. Conceptualization, M.A. and N.B. ; methodology, M.A. ; software, M.A.