$\mathcal{M} = (\mathcal{V,E,F})$ where $\mathcal{V}=\{1, \dots, n\}$, $\mathcal{E}$, and $\mathcal{F}$ denote the sets of vertices, edges, and faces respectively. Furthermore, let ${f:V\rightarrow\mathbb{R}}$, a function representing the vertex features.

One of the key challenges in developing convolution-like operators on graphs or manifolds is the lack of a global system of coordinates that can be associated with each point. The first intrinsic mesh convolutional architectures such as GCNN [@masci2015geodesic], ACNN [@boscaini2016learning] or MoNet [@monti2017geometric] overcame this problem by constructing a [*local*]{} system of coordinates $\mathbf{u}(x,y)$ around each vertex $x$ of the mesh, in which a set of local weighting functions $w_1,\hdots, w_L$ is applied to aggregate information from the vertices $y$ of the neighborhood $\mathcal{N}(x)$. This allows to define ‘patch operators’ generalising the sliding window filtering in images: $$\label{soft_attn}
    (f\star g)_x = \sum_{\ell=1}^L g_\ell \sum_{y\in\mathcal{N}(x)} w_\ell(\mathbf{u}(x,y)) f(y)$$ where $\sum_{y\in\mathcal{N}(x)} w_\ell(\mathbf{u}(x,y)) f(y)$ are ‘soft pixels’ ($L$ in total), $f$ are akin to pixel intensity in images, and $g_\ell$ the filter weights. The problem of the absence of a global coordinate system is equivalent to the absence of canonical ordering of the vertices, and the patch-operator based approaches can be also interpreted as attention mechanisms, as in [@velivckovic2017graph] and [@verma2018feastnet]. In particular, the absence 