[HN Gopher] Spherical CNNs (2018)
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       Spherical CNNs (2018)
        
       Author : rkp8000
       Score  : 13 points
       Date   : 2025-06-16 19:28 UTC (2 days ago)
        
 (HTM) web link (arxiv.org)
 (TXT) w3m dump (arxiv.org)
        
       | smath wrote:
       | also relevant to 3d modeling of molecules using in drug
       | discovering modeling -- and a subset of these authors have
       | published along those lines more recently -- for e.g.
       | https://arxiv.org/abs/2104.13478
        
       | rkp8000 wrote:
       | A notable and interesting point of this article is that
       | convolutions and correlations (convolutions without flipping the
       | filter) are quite a bit more subtle on the sphere than on
       | Cartesian spaces. For a convolution between a function and a
       | filter on R^N you just "slide" the filter around, integrating at
       | each shift, which produces another function on R^N. On a sphere,
       | however, there is not a clear cut way to slide a filter around a
       | sphere. For instance, there are multiple ways to slide a filter
       | centered at the north pole to the south pole, which will result
       | in different filter orientations.
       | 
       | More generally, the space of rotations, which is the argument of
       | the convolution (analogous to the shift amount being the argument
       | of a standard convolution), is 3D (3 Euler angles), whereas the
       | space of points on the sphere is 2D (polar and azimuthal angles).
       | Thus, whereas convolution over R^N returns a function over R^N,
       | convolution over the sphere actually returns a function over the
       | 3D rotation group SO(3). This has interesting consequences for
       | e.g. the convolution theorem on the sphere, which is not as clear
       | cut as simply rewriting the standard convolution theorem in
       | spherical terms.
        
       | voxleone wrote:
       | Great subject, thanks. I recently built SpinStep[0], a tool for
       | visualizing and stepping through SCNN computations.
       | 
       | It lets you upload a model, then see--layer by layer--how inputs
       | are transformed, which kernels activate, and how feature maps
       | evolve. It's a hands-on exploration of what's actually happening
       | under the hood in Spherical CNNs.
       | 
       | For anyone who's been frustrated by the opaque "black-box" nature
       | of CNNs, SpinStep might be a fun way to poke around and build
       | intuition.
       | 
       | [0] https://github.com/VoxleOne/SpinStep/blob/main/docs/index.md
        
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