Alexis Akira Toda

Alexis Akira Toda

Can artificial intelligence (AI) refute economic theory? I document experiments in which I asked several AI models (Gemini, Refine, Claude, and ChatGPT) to check the correctness of four published papers in economic theory, each containing an error that I helped identify or correct. ChatGPT Pro performed best, occasionally constructing counterexamples and corrected proofs, while other models fared worse. However, no model located a true error without substantial human guidance, and data contamination complicates interpretation. I argue that a competent human paired with a frontier model can outperform current peer review, but AI cannot yet refute economic theory on its own.

Ken'ichiro Tanaka, Alexis Akira Toda

The maximum entropy principle is a powerful tool for solving underdetermined inverse problems. This paper considers the problem of discretizing a continuous distribution, which arises in various applied fields. We obtain the approximating distribution by minimizing the Kullback-Leibler information (relative entropy) of the unknown discrete distribution relative to an initial discretization based on a quadrature formula subject to some moment constraints. We study the theoretical error bound and the convergence of this approximation method as the number of discrete points increases. We prove that (i) the theoretical error bound of the approximate expectation of any bounded continuous function has at most the same order as the quadrature formula we start with, and (ii) the approximate discrete distribution weakly converges to the given continuous distribution. Moreover, we present some numerical examples that show the advantage of the method and apply to numerically solving an optimal portfolio problem.