The argument is fairly straightforward: Let n be the number of seed bits of the CSPRNG. Assume there exists an ANN that approximates the CSPRNG so that the number of possibly wrong output bits is at most polylogarithmic in n (otherwise you haven't really gained much insight from the ANN). Assume further that the ANN is sufficiently small so that a forward pass through the ANN takes at most polynomial time in n. Then you can create a polynomial-time algorithm that (i) runs the ANN on the observed CSPRNG samples/by querying the oracle, and then (ii) brute-forces the possible error bits in polynomial time, thereby recovering the full seed. But this is a contradiction with the assumption that the CSPRNG is secure, i.e. that it admits no polynomial-time adversary, q.e.d.