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A lot of these are really cool/thought-provoking. I'd love to hear anyone's thoughts on... Mathematical Challenge 6: Computational Duality Duality in mathema
by bo1024 14y ago
A lot of these are really cool/thought-provoking.
I'd love to hear anyone's thoughts on...
Mathematical Challenge 6: Computational Duality
Duality in mathematics has been a profound tool for theoretical understanding. Can it be extended to develop principled computational techniques where duality and geometry are the basis for novel algorithms?
Mathematical Challenge 7: Occam’s Razor in Many Dimensions
As data collection increases can we “do more with less” by finding lower bounds for sensing complexity in systems? This is related to questions about entropy maximization algorithms.
- Dn_Ab 14y agoThere are many definitions of duality in mathematics so I am not entirely clear on 6. For example the notion of duals from category theory has already been very helpful in understanding or developing many algorithms. In fact a generous viewing will allow for even enterprise software in the form of LINQ and Observables to have made use of duals in their development. I am neither clear on 7. I wish I knew what he meant about MaxEnt in particular, there's a lot of neat explorations from the connections between entropy and learning. But specific to what I interpret as a better Occam's Razor, my vote will have to go to Marcus Hutter as the person who is currently doing the most interesting work in that area. Specifically his work on approximating universal priors. Schmidhuber also has interesting stuff on complexity, search for his talks - they're great.