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 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 a generic methods for learning Self-Proving models, and prove its convergence 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.

Fixed author listing.

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 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 a generic methods for learning Self-Proving models, and prove its convergence 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.

Corrected the statement of Theorem 4.1 and a typo in its proof, and added several clarifications:
- Added Table 1 and "Scope" paragraph to page 2.
- Added Remark 3.5.
- Improved Figure 2.
- Added Appendix B.
- Merged Appendices D and E.

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.