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A Theory of Neural Computation with Clifford Algebras (2005) [pdf] (uni-kiel.de)
56 points by adamnemecek on Sept 14, 2017 | hide | past | favorite | 6 comments

I'm not really aware about this application of Clifford algebra. I'll summarize it as the algebra that operated on sets of scalars, vectors, matrices, and up, so we can use both addition and multiplication between Clifford objects. Just my recollection.

+ I would assume then that keeping track of Clifford objects per neuron is not biological plausible.

+ I would then also assume that geometric manipulations are handled differently than through Clifford algebra.

Just saying because biology is mentioned in a few places in the thesis as motivation.

Additional information for Clifford Algebra can be found here:


Oh that article again. It starts out great but I just get so worried about his well-being when I read the epilogue.

Rationalist thinking has taught us to scoff at anything greater than examining physical reality by scientific method - greatest tragedy of the Enlightenment

You are right. I should be more open to other perspectives outside the paradigm I was taught. That's the only way to go against the historical pattern discussed in the Structure of Scientific Revolutions. Thank you.

As I recall, the most interesting feature of these networks is that they do better when learning geometric features in the presence of noise. Without the added geometric structure baked into the network, the real neural nets overfit and 'learn the noise' to a much greater extent.

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