  Deep neural networks are composed of layers of parametrised linear operations
intertwined with non linear activations. In basic models, such as the
multi-layer perceptron, a linear layer operates on a simple input vector
embedding of the instance being processed, and produces an output vector
embedding by straight multiplication by a matrix parameter. In more complex
models, the input and output are structured and their embeddings are higher
order tensors. The parameter of each linear operation must then be controlled
so as not to explode with the complexity of the structures involved. This is
essentially the role of convolution models, which exist in many flavours
dependent on the type of structure they deal with (grids, networks, time series
etc.). We present here a unified framework which aims at capturing the essence
of these diverse models, allowing a systematic analysis of their properties and
their mutual enrichment. We also show that attention models naturally fit in
the same framework: attention is convolution in which the structure itself is
adaptive, and learnt, instead of being given a priori.
