The analogy theorem in Hoare logic
This provides verifiable guarantees for knowledge transfer in machine learning, addressing a fundamental limitation for researchers and practitioners, though it is incremental in applying existing logical frameworks to a known bottleneck.
The paper tackles the problem of lacking rigorous mathematical justification for transferring machine learning models between data domains by formalizing analogy using first-order and Hoare logic, proving a theorem with necessary and sufficient conditions, and achieving F1 scores of 0.84 and 0.88 on MNIST and USPS data for convolutional neural networks and random forests.
The introduction of machine learning methods has led to significant advances in automation, optimization, and discoveries in various fields of science and technology. However, their widespread application faces a fundamental limitation: the transfer of models between data domains generally lacks a rigorous mathematical justification. The key problem is the lack of formal criteria to guarantee that a model trained on one type of data will retain its properties on another.This paper proposes a solution to this problem by formalizing the concept of analogy between data sets and models using first-order logic and Hoare logic.We formulate and rigorously prove a theorem that sets out the necessary and sufficient conditions for analogy in the task of knowledge transfer between machine learning models. Practical verification of the analogy theorem on model data obtained using the Monte Carlo method, as well as on MNIST and USPS data, allows us to achieving F1 scores of 0.84 and 0.88 for convolutional neural networks and random forests, respectively.The proposed approach not only allows us to justify the correctness of transfer between domains but also provides tools for comparing the applicability of models to different types of data.The main contribution of the work is a rigorous formalization of analogy at the level of program logic, providing verifiable guarantees of the correctness of knowledge transfer, which opens new opportunities for both theoretical research and the practical use of machine learning models in previously inaccessible areas.