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This seems almost tautologically false to me. This seems to imply that if you implement SHA-256 in Julia, you can differentiate it and solve it backwards via SG
by darawk 8y ago
This seems almost tautologically false to me. This seems to imply that if you implement SHA-256 in Julia, you can differentiate it and solve it backwards via SGD. Is there something i'm missing here? There must be some limitations.
- nextos 8y agoWell, the limitations are the usual limitations in mathematical analysis. Despite being differentiable, if your function has a very complicated structure you will get stuck in local minima with high probability. People are referring to limitations regarding expressiveness.
- deleted 8y ago[deleted]
- cs702 8y agoYes, of course there are limitations. But those limitations are not imposed by the language or the tools; they're imposed by the limits of mathematics. In hindsight, perhaps my language was too fast and loose. Thanks for pointing that out.
- dnautics 8y agoSha-256 has integer and galois field operations, which are not generally differentiable in the numeric sense, although the NSA has a strong differentiable cryptanalysis program where they presumably do magic tricks like approximating these integer functions as real valued, so what you are saying might be possible.