In laser remote cutting, a cut through is usually realized by repeating a scanning process for several ablation cycles. The material removal rate depends primarily on the laser power, feed rate and number of cycles. Too few cycles will not achieve a full penetration, whereas too many cycles may cause the workpiece to reweld on the sheet. In either case, the workpiece cannot be detached from the sheet. In this contribution, we present an in-situ monitoring system using convolutional neural networks (CNN), from recordings of the process zone during remote cutting to detect full penetration in thin electrical sheets. The monitoring system, based on a high-speed camera is attached to a conventional laser scanner, whereby the optical detection path is aligned coaxially to the incident laser. Images with a size of 256x256 pixels are recorded with a sample rate of 20∙10³ frames per seconds and an exposure time of 20 µs. Without external illumination, the thermal radiation of the process zone is captured in the VIS spectrum. A data set of images is labeled for cycles before a cut through, during a full penetration and for too many cycles, to train the networks. As a result, a full penetration is recognized by the trained CNN models and the detection accuracy of AlexNet, VGGNet, and ResNet are compared.