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 theoreticallyfounded 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. SelfProving models satisfy that, with high probability over an input sampled from a given distribution, the model generates a correct output and successfully proves its correctness to V. The soundness property of V guarantees that, for every input, no model can convince V of the correctness of an incorrect output. Thus, a Self-Proving model proves correctness of most of its outputs, while all incorrect outputs (of any model) are detected by V. We devise and analyze two generic methods for learning Self-Proving models: Transcript Learning (TL) which relies on access to transcripts of accepting interactions, and Reinforcement Learning from Verifier Feedback (RLVF) which trains a model by emulating interactions with the verifier.

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. Self-Proving models satisfy that, with high probability over a random input, the model generates a correct output *and* successfully proves its correctness to $V\!$. The *soundness* property of $V$ guarantees that, for *every* input, no model can convince $V$ of the correctness of an incorrect output. Thus, a Self-Proving model proves correctness of most of its outputs, while *all* incorrect outputs (of any model) are detected by $V$. We devise a generic method for learning Self-Proving models, and we prove convergence bounds under certain assumptions. The theoretical framework and results are complemented by experiments on an arithmetic capability: computing the greatest common divisor (GCD) of two integers. Our learning method is used to train a Self-Proving transformer that computes the GCD *and* proves the correctness of its answer.