the skinned vertex-based models SMPL [@SMPL:2015] and MANO [@MANO:SIGGRAPHASIA:2017], respectively. SMPL and MANO are non-linear and require (a) joint localisation and (b) solving special optimisation problems in order to project a new shape to the space of the models. In this paper, we take a different approach introducing a new family of differentiable Morphable Models, which can be applied on a variety of objects, with strong (body) and less strong (face) articulations. Our methods have better representational power and also do not require any additional supervision.\
**Geometric Deep Learning** is a set of recent methods trying to generalise neural networks to non-Euclidean domains such as graphs and manifolds [@bronstein2017geometric]. Such methods have achieved promising results in geometry processing and computer graphics [@masci2015geodesic; @boscaini2016learning], computational chemistry [@duvenaud2015convolutional; @gilmer2017neural], and network science [@kipfGCN; @monti2017geometric]. Multiple approaches have been proposed to construct convolution-like operations, including spectral methods [@bruna2013spectral; @defferrard2016convolutional; @kipfGCN; @yi2017syncspeccnn], local charting based [@masci2015geodesic; @boscaini2016learning; @monti2017geometric; @fey2018splinecnn; @spirals] and soft attention [@velivckovic2017graph; @verma2018feastnet]. Finally, graph or mesh coarsening techniques [@defferrard2016convolutional; @ying2018hierarchical] have been proposed, equivalent to image pooling.

Spiral Convolutional Networks
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Spiral Convolution {#spiral_theory}
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For the following discussion, we assume to be given a manifold, discretised as a triangular mesh 