of ordering does not allow the construction of a “1-1” mapping between neighbouring features $f(y)$ and and filter weights $g_\ell$, thus a “all-to-all” mapping is performed via learnable *soft-attention* weights $w_\ell(\mathbf{u}(x,y))$. In the Euclidean setting, such operators boil down to the classical convolution, since an ordering can be obtained via the global coordinate system.

Besides the lack of a global coordinate system, another motivation for patch-operator based approaches when working on meshes, is the need for *insensitivity to meshing* of the continuous surface, ideally, each patch operator should be independent of the underlying graph topology.

[0.35]{} ![Spiral ordering on a mesh and an image patch[]{data-label="spiral_fig"}](Spiral_on_Mesh.png "fig:"){width="\linewidth"} \[spiral\_mesh\]

[0.33]{} ![Spiral ordering on a mesh and an image patch[]{data-label="spiral_fig"}](Spiral_on_Grid.png "fig:"){width="\linewidth"} \[spiral\_image\]

However, all the methods falling into this family, come at the cost of high computational complexity and parameter count and can be hard to optimise. Moreover, patch-operator based methods specifically designed for meshes, require hand-crafting and pre-computing the local systems of coordinates. To this end, in this paper we make a crucial observation in order to overcome the disadvantages of the aforementioned approaches: the issues of the absence of a global ordering and insensitivity to graph topology are irrelevant when dealing 