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Deploying deep convolutional neural network (CNN) models on ubiquitous Internet of Things (IoT) devices has attracted much attention from industry and academia since it greatly facilitates our lives by providing various rapid-response services. Due to the limited resources of IoT devices, cloud-assisted training of CNN models has become the mainstream. However, most existing related works suffer from a large amount of model parameter transmission and weak model robustness. To this end, this paper proposes a cloud-assisted CNN training framework with low model parameter transmission and strong model robustness. In the proposed framework, we first introduce MonoCNN, which contains only a few learnable filters, and other filters are nonlearnable. These nonlearnable filter parameters are generated according to certain rules, i.e., the filter generation function (FGF), and can be saved and reproduced by a few random seeds. Thus, the cloud server only needs to send these learnable filters and a few seeds to the IoT device. Compared to transmitting all model parameters, sending several learnable filter parameters and seeds can significantly reduce parameter transmission. Then, we investigate multiple FGFs and enable the IoT device to use the FGF to generate multiple filters and combine them into MonoCNN. Thus, MonoCNN is affected not only by the training data but also by the FGF. The rules of the FGF play a role in regularizing the MonoCNN, thereby improving its robustness. Experimental results show that compared to state-of-the-art methods, our proposed framework can reduce a large amount of model parameter transfer between the cloud server and the IoT device while improving the performance by approximately 2.2% when dealing with corrupted data. The code is available at https://github.com/evoxlos/mono-cnn-pytorch.