I know that it would be computationally unfeasible. Yes, given infinite time and infinite energy, a neural net could crack SHA256. BUT (and I think this is the point @tylerl is making) because hash functions have no discernible patterns, a neural net would not be able to do any better than the naive brute-force of building a lookup table by computing the hash of every possible string. Such a lookup table would have more entries ( 2256) than there are atoms on the planet earth ( 2166) - so at least with our current level of technology it's "impossible" to hold such a table in memory or store it on any disk. Similarly, for your neural net to perform noticeably better than a dice-roll, the number of neurons you would need would probably also exceed the number of atoms on the planet.

In bitcoin mining, blocks, private keys, and public keys there can be found some connection to SHA256 mentioned somewhere. This makes SHA256 interesting to investigate. In this article we are going to focus on SHA256. We will dive into the code of SHA256, while also investigating the semantics of the cryptographic hash function. We will also break SHA256 down to its basic components and do some machine learning for fun.