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I've been out of academia for a long time, but isn't the notion that 'natural' high dimensional data lies on low dimensional manifolds the basic premise of all
by siavosh 8y ago
I've been out of academia for a long time, but isn't the notion that 'natural' high dimensional data lies on low dimensional manifolds the basic premise of all machine learning techniques?
- xtacy 8y agoYes, the authors mention it in the introduction as a "well accepted manifold assumption."
- cs702 8y agoYes, of course, this has long been a widely held assumption. That's why we call it the "manifold hypothesis." As far as I know, no one has been able to show -- with mathematical rigor -- that this is why deep learning works so well on so many challenging perceptual ("cognitive") tasks. That seems significant to me.
- byt143 8y agoIs this dual in any way to the information bottleneck hypothesis?
- improbable22 8y agoBut have they actually shown any such thing? There are some ambitious words, then some very elementary definitions, and some "theorems"... and then it ends?