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Summary by Hugo Larochelle 4 years ago
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Typo encore -> encoder

Typo decode g -> decoder g

Thanks! Corrected above :-)

Good summary from your side. I am also working on disentanglement of factor of variations on different direction. Can you shed some light on why we should not expect any form of disentanglement if we can replace f, and g with r.f and r_inv.g where r is a bijective function; as discussed in paper.

Good question. Actually the comment in the paper is that if you replace $f$ by $r \circ f$ or $r(f(x))$ and $g$ by $g \circ r^{-1}$ or $g(r^{-1}(h))$ (I think there's a typo in the paper for the latter), then $g(r^{-1}(r(f(x)))) = g(f(x))$ and thus you get the same reconstruction error. So that suggests that the reconstruction error objective itself doesn't impose axis-aligned disentanglement, since any bijective function could entangle the representation while keeping the reconstruction the same. Hope this helps!

Thanks! It helped :)

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