I'm drinking Kool Aid? OK. I'm mostly arguing about the use of Static Analysis and other typical means of verifying programs, and the ineffectiveness of those verification methods on neural networks. People use that as an argument against the safety of NNs.
Set of all computer programs has two subsets.
S = { s | Static Analysis can be performed on s }
N = { n | n makes use of a neural network } with N ⊄ S
Let n ∈ N and s ∈ S. There are a certain set of programming tasks
T = { t | t can be solved with n but not s }
Thus any claim that using n to solve t is "unsafe" because you cannot perform Static Analysis on it is absolute BS, because programs s ∈ S can't even solve the damn problem!
Just using set notation doesn't make an argument precise. You are begging some questions in your definition here.
For example, how do we know that a task solves a particular problem if we can't perform static analysis on it? It may give the appearance of working and then degrade radically under certain conditions. That really matters if you're using it for safety-critical applications and the problem space is large enough that it can't be exhaustively tested.
Set of all computer programs has two subsets.
Let n ∈ N and s ∈ S. There are a certain set of programming tasks Thus any claim that using n to solve t is "unsafe" because you cannot perform Static Analysis on it is absolute BS, because programs s ∈ S can't even solve the damn problem!