Machine learning has emerged as a powerful tool for physicists for building empirical models from the data. We exploit two convolutional networks, namely Alexnet and wavelet scattering network for the classification of orbital angular momentum (OAM) beams. We present a comparative study of these two methods for the classification of 16 OAM modes having radial and azimuthal phase profiles and eight OAM superposition modes with and without atmospheric turbulence effects. Instead of direct OAM intensity images, we have used the corresponding speckle intensities as an input to the model. Our study demonstrates a noise and alignment-free OAM mode classifier having maximum accuracy of >94  %   and >99  %   for with and without turbulence, respectively. The main advantage of this method is that the mode classification can be done by capturing a small region of the speckle intensity having a sufficient number of speckle grains. We also discuss this smallest region that needs to be captured and the optimal resolution of the detector required for mode classification.