How can we trust the correctness of a learned model on a particular input of
interest? Model accuracy is typically measured \emph{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 \emph{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.

通过训练自证明模型，该论文提出了一种基于理论的方法来解决如何在特定输入上验证学习模型的正确性的问题。通过交互证明以高概率证明模型的正确输出并成功向验证算法证明其正确性，并通过实验验证了其在计算最大公约数方面的效果。

证明自身正确性的模型

Models That Prove Their Own Correctness

We consider settings in which the right notion of fairness is not captured by
simple mathematical definitions (such as equality of error rates across
groups), but might be more complex and nuanced and thus require elicitation
from individual or collective stakeholders. We introduce a framework in which
pairs of individuals can be identified as requiring (approximately) equal
treatment under a learned model, or requiring ordered treatment such as
"applicant Alice should be at least as likely to receive a loan as applicant
Bob". We provide a provably convergent and oracle efficient algorithm for
learning the most accurate model subject to the elicited fairness constraints,
and prove generalization bounds for both accuracy and fairness. This algorithm
can also combine the elicited constraints with traditional statistical fairness
notions, thus "correcting" or modifying the latter by the former. We report
preliminary findings of a behavioral study of our framework using human-subject
fairness constraints elicited on the COMPAS criminal recidivism dataset.

介绍了一种框架，在该框架中，可以将成对的个体标识为需要（大约）相等的待遇。我们引入了一种算法，可以在满足预设的公平性约束条件下学习最准确的模型，并证明了其准确性和公平性的泛化界限。该算法还可以将传统的统计公平概念与 elicited constraints 相结合，从而通过前者 “纠正” 或修改后者。我们使用在 COMPAS 犯罪再犯率数据集上 elicited 的 human-subject 公平性约束条件的行为学研究报告了初步结果。