Synchrotron light sources, arguably among the most powerful tools of modern scientific discovery, are presently undergoing a major transformation to provide orders of magnitude higher brightness and transverse coherence enabling the most demanding experiments. In these experiments, overall source stability will soon be limited by achievable levels of electron beam size stability, presently on the order of several microns, which is still 1-2 orders of magnitude larger than already demonstrated stability of source position and current. Until now source size stabilization has been achieved through corrections based on a combination of static predetermined physics models and lengthy calibration measurements, periodically repeated to counteract drift in the accelerator and instrumentation. We now demonstrate for the first time how the application of machine learning allows for a physics- and model-independent stabilization of source size relying only on previously existing instrumentation. Such feed-forward correction based on a neural network that can be continuously online retrained achieves source size stability as low as 0.2  μm (0.4%) rms, which results in overall source stability approaching the subpercent noise floor of the most sensitive experiments.