That's the great thing about Anubis: it's not client-side. Not entirely anyways. Similar to public key encryption schemes, it exploits the computational complexity of certain functions to solve the challenge. It can't just say "solved, let me through" because the client has to calculate a number, based on the parameters of the challenge, that fits certain mathematical criteria, and then present it to the server. That's the "proof of work" component.

A challenge could be something like "find the two prime factors of the semiprime 1522605027922533360535618378132637429718068114961380688657908494580122963258952897654000350692006139". This number is known as RSA-100, it was first factorized in 1991, which took several days of CPU time, but checking the result is trivial since it's just integer multiplication. A similar semiprime of 260 decimal digits still hasn't been factorized to this day. You can't get around mathematics, no matter how advanced your AI model is.