I think questions about representations and symmetry are really interesting.<p>Have you looked at deep symmetry networks? (I think the right way to frame the idea is in terms of group convolutions, which I outlined here: <a href="http:&#x2F;&#x2F;colah.github.io&#x2F;posts&#x2F;2014-12-Groups-Convolution&#x2F;" rel="nofollow">http:&#x2F;&#x2F;colah.github.io&#x2F;posts&#x2F;2014-12-Groups-Convolution&#x2F;</a>)