Sketch of the convolution algorithm developed in this work. The elements p₁ and p₂ of the vector m correspond to two pixels on map (in this case 0 and 4). p1 and p2 are associated to nine elements each, in vector M. The first of this nine elements corresponds to the pixel itself, while the subsequent ones corresponds to its eight neighbors. The neighbors are visited, and unrolled in the M vector, following a clockwise order staring from the NW direction. The filter (in grey) is also unrolled in a nine element long vector, using the same convention. Convolution is then implemented as a standard 1D convolutional layer with a stride of 9, and the output is the m′ convolved vector (map), which has the same number of elements (pixels) as the input m. In the figure, numbers over the pixels do not represent the values of the pixels but their unique index: in practical applications, these indices will be those associated to an ordering scheme and a map resolution N_side. Colors are the same as in Fig. 1, to underline the similarity.