## 1 Introduction  
Convolutional neural networks (CNNs) have shown advanced capabilities within a variety of domains. Nowadays, CNNs are becoming more common for use in a wide range of computer vision applications, including object recognition, image classification, and image segmentation. Nevertheless, since CNNs often have complex structures and need a lot of parameters and computational capacity, it might be challenging to apply them to computer vision tasks on edge devices with constrained resources, including embedded systems and mobile devices [1, 2]. For instance, autonomous vehicles need to quickly evaluate camera frames in order to identify and avoid obstacles. The latency is increased significantly when data are sent to the cloud for inference because of queueing and network delays. For this reason, data processing needs to be performed on the device in order to be efficient during the inference. Therefore, neural networks could be compressed to reduce their size, allowing compressed versions of CNNs to operate on edge devices with limited resources. Several popular techniques to decrease redundancy in neural network parameters include pruning [3, 4], sparsification [5, 6], quantization [7, 8], and low-rank tensor decomposition [9, 10]. Among these techniques, the tensor decomposition-based compression method is currently attracting growing interest. By decomposing the enormous weight tensors of CNNs into several compact tensor cores, tensor decomposition could result in a significant compression ratio with little accuracy reduction. The low-rank tensor decomposition method attempts to approximate the representation of the original high-order tensors using low-rank tensors. The most prevalent approaches are Tucker decomposition [10] and Canonical Polyadic (CP) decomposition [11]. Due to its core tensors, Tucker decomposition often seems to compress less than CP decomposition. Therefore, we undertook further study into the use of low-rank CP decomposition for compressing entire CNN layers. However, CP decomposition has not been efficient for compressing CNNs due to the CP instability issue [12; 13], which often impairs fine-tuning after decomposition. To overcome this problem, we propose two stable and efficient methods based on sensitivity. First, we apply sensitivity constraints for efficient optimization in CP decomposition. The sensitivity criterion reveals that traditional CP decomposition lacks robustness when subjected to minor perturbations in factor matrices, which denotes sensitivity dropping. In the optimization process, the sensitivity of the decomposition is able to be estimated and minimized to prevent degeneracy and instability in CP decomposition. Secondly, another approach to address the issue of CP decomposition instability involves the use of iterative fine-tuning, which is guided by sensitivity order. The lack of stability in CP decomposition leads to poor training results during fine-tuning, as the loss of function fails to reduce or may even be magnified when all layers are decomposed and then fine-tuned only once in the last step. Therefore, we use an iterative fine-tuning approach, performing CP decomposition and fine-tuning layer-by-layer. Furthermore, the determination of the sequence of decomposition and fine-tuning is based on the sensitivity of each layer. In general, layers with a higher sensitivity have a more significant impact on the network output and are more challenging to fine-tune. Therefore, we prioritize fine-tuning these layers for better accuracy. The experimental findings demonstrate that the aforementioned instability may be effectively addressed via sensitivity-constrained optimization and iterative fine-tuning techniques. In the context of tensor decomposition, the issue of rank selection is another challenge worth mentioning. The significance of tensor ranks lies in their ability to balance the compression ratio and model capabilities.