Intensity degenerate orbital angular momentum (OAM) modes are impossible to recognize by direct visual inspection even using available machine learning techniques. We are reporting speckle-learned convolutional neural network (CNN) for the recognition of intensity degenerate Laguerre–Gaussian (LG_{p , l}) modes, intensity degenerate LG superposition modes, and intensity degenerate perfect optical vortices. The CNN is trained on the simulated one-dimensional far-field intensity speckle patterns of the corresponding intensity degenerate OAM modes. The trained CNN recognizes intensity degenerate OAM modes with an accuracy >99 % . Speckle-learned CNNs are also capable of recognizing intensity degenerate OAM modes even under the presence of high Gaussian white noise and atmospheric turbulence with an accuracy >97 % .