The high dynamics of laser beam welding (LBW) in several manufacturing processes ranging from automobile production to precision mechanics requires the introduction of new fast real time controls. In the last few years, algorithms for the control of constant-orientation LBW processes have been introduced. Nevertheless, some real life processes are also performed changing the welding orientation during the process. In this paper experimental results obtained by the use of a new CNN based strategy for the control of curved welding seams are discussed. It is based on the real time adjustment of the laser power by the detection of the full penetration hole in process images. The control algorithm has been implemented on the Eye-RIS system v1.2 leading to a visual closed loop control solution with controlling rates up to 6 kHz.