A.1 Group Theoretic Understanding of Optical Fibre Transmission Modes When a light beam propagates in free space or in a transparent homogeneous medium, its transverse intensity profile generally changes. Despite this, there exist certain distributions that do not change intensity profile as they traverse. These fixed profiles are the transmission modes of the space. The development of group equivariant networks exploits a similar principle, where these networks are constructed under the more general principle of finding basis functions called irreducible representations of some group. Thus a function on the group can be composed as a linear combination of the corresponding irreducible representations.

This model takes advantage of the of the azimuthal correlations known to exist in fibre speckle patterns and naturally accounts for the difference in spatial arrangement between input and speckle patterns. In addition, we use a second post-processing network to remove circular artifacts, fill gaps, and sharpen the images, which is required due to the nature of optical fibre transmission. This two stage approach allows for the inspection of the predicted images produced by the more robust physically motivated equivariant model, which could be useful in a safety-critical application, or by the output of both models, which produces high quality images. Further, this model can scale to previously unachievable resolutions of imaging with multi-mode optical fibres and is demonstrated on 256 256 pixel images.