Whilst advances in lasers now allow the processing of practically any material, further optimisation in precision and efficiency is highly desirable, in particular via the development of real-time detection and feedback systems. Here, we demonstrate the application of neural networks for system monitoring via visual observation of the work-piece during laser processing. Specifically, we show quantification of unintended laser beam modifications, namely translation and rotation, along with real-time closed-loop feedback capable of halting laser processing immediately after machining through a ∼450 nm thick copper layer. We show that this approach can detect translations in beam position that are smaller than the pixels of the camera used for observation. We also show a method of data augmentation that can be used to significantly reduce the quantity of experimental data needed for training a neural network. Unintentional beam translations and rotations are detected concurrently, hence demonstrating the feasibility for simultaneous identification of many laser machining parameters. Neural networks are an ideal solution, as they require zero understanding of the physical properties of laser machining, and instead are trained directly from experimental data.