Re grid representation - The convolution operator is translation equivariant. (waving hands, it means that the translation operated on the Input Signal is still detectable in the output features set)<p>However, it was shown many times that coupling the convolution operator with a pooling layer achieves translation invariance by means of dimensionality reduction.<p>Moreover, rotational equivariance (and subsequently invariance) is an active area of research. There's an interesting talk (<a href="https://www.youtube.com/watch?v=-UKL3kOlOds&list=PLlMMtlgw6qNjROoMNTBQjAcdx53kV50cS&index=18" rel="nofollow">https://www.youtube.com/watch?v=-UKL3kOlOds&list=PLlMMtlgw6q...</a>) by Boomsma/Frellsen about the use of spherical convolutions in deep learning applications of molecular structures.