Abstract: How can we trust the correctness of a learned model on a particular input of interest? Model accuracy is typically measured *on average* over a distribution of inputs, giving no guarantee for any fixed input. This paper proposes a theoretically-founded solution to this problem: to train *Self-Proving models* that prove the correctness of their output to a verification algorithm $V$ via an Interactive Proof. We devise a generic method for learning Self-Proving models, and we prove convergence bounds under certain assumptions. As an empirical exploration, our learning method is used to train a Self-Proving transformer that computes the Greatest Common Divisor (GCD) *and* proves the correctness of its answer.