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I’ve always enjoyed this framing of the subject, the idea of mapping anything as hyperplanes existing in a solution space is one of the ideas that really blew m
by sota_pop 1y ago
I’ve always enjoyed this framing of the subject, the idea of mapping anything as hyperplanes existing in a solution space is one of the ideas that really blew my hair back during my academic studies. I would nitpick at your “dots in a circle example - with the stoner reference joke” I could be mistaken, but common practice isn’t to “move to a higher dimension”, but use a kernel (i.e. parameterize the points into the polar |r,theta> basis). All things considered, nice article.
- theahura 1y agoI'm pulling directly from Chris Olah's blog post with that example. But I will say that in practice, its always surprising how increasing the dimensionality of a neural network magically solves all sorts of problems. You could use a kernel if you don't have more computation available, but given more computation adding a dimension is strictly more flexible (and is capable of separating a much wider range of datasets)
- benl 1y agoYour explanation of finding a surface to separate good reasoning traces from bad reasoning traces in a high dimensional space worked as a great framing of the problem. It seems though that the surface will be fractal - the distance between a good trace and a bad trace could be arbitrarily small. If so then the work required to find and compute better and better surfaces will grow arbitrarily large. I wonder if there is a rigorous way to determine if the surface is fractal or not.