
Group theoretical methods in machine learning (2008) [pdf] - adamnemecek
https://people.cs.uchicago.edu/~risi/papers/KondorThesis.pdf
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sdenton4
I'm familiar with Risi's work on using Fourier transform on groups for object
tracking. Basic idea is that the usual Fourier transform is a construction on
Z_n, which generalizes to antsy finite groups. Important examples are binary
vectors (Z_2 __n) and permutations. The twin hypotheses are that learning on
Fourier space is easier, and that learning on these other specialized groups
for which we understand the transform is a useful pursuit.

For the permutation group, you get matrices instead of numbers for the Fourier
coefficients. The matrices themselves have nice interpretations (eg,
interactions of unordered pairs or ordered triples of elements in the
permutation), but the actual entries of the matrices are all but impossible to
motivate, imho. (Much like how it's easier to understand the magnitude of a
regular Fourier coefficient than the phase.)

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ssivark
A related article that some might find interesting:

Why does Deep Learning work? - A perspective from Group Theory --
[https://arxiv.org/abs/1412.6621](https://arxiv.org/abs/1412.6621)

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crb002
groupMembership :: Perm -> Bool

semigroupMembership :: Endo -> Bool

The latter is much more interesting.

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eachro
Would love to hear people's thoughts on this. I don't have the mathematical
background to understand this work.

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photoJ
Very good and interesting work!

