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That operator looks eerily similar to the one in Clifford Algebra. And C.A. generalizes nicely* out of 3D, too. * I found that current Clifford Algebra Python
by Scene_Cast2 3y ago
That operator looks eerily similar to the one in Clifford Algebra. And C.A. generalizes nicely* out of 3D, too.
* I found that current Clifford Algebra Python libraries don't handle high dimensional (even 32D, fairly primitive by ML standards) spaces.
- Jenz 3y agoTime to give Julia a shot! It has this amazing package [1] for geometric algebras in up to a very high number of dimensions. [1]: https://github.com/chakravala/Grassmann.jl https://github.com/chakravala/Grassmann.jl
- eigenspace 3y ago> don't handle high dimensional (even 32D, fairly primitive by ML standards) spaces. You're confusing two different notions of dimensionality here. The Geometric Algebra of 32D is actually a 2^16 (i.e. 65536) dimensional vector space. So it's like talking about vectors in 65536 dimensions, or the space of 256x256 matrices.
- aleph_minus_one 3y ago> The Geometric Algebra of 32D is actually a 2^16 (i.e. 65536) dimensional vector space. Rather a 2^32-dimensional vector space. :-)
- Scene_Cast2 3y agoI had a problem where I wanted to rotate a high dimensional vector. This was ages ago, so I don't remember the exact terminology. What I ended up doing is writing out the geometric algebra equations by hand (with only the first order bivectors IIRC) and coding that up. Having an option in the library to not have all the higher order bivectors if I don't need higher order operations would be nice.
- eigenspace 3y agoYeah what you want then is a 'sparse' bivector.