A Mathematical-logic Perspective for Analyzing Machine Learning Models

Abstract

Machine learning (ML) has achieved remarkable success. There are various types of machine learning methods. However, the previous categorization of these models was simply based on the paradigm of learning. What kind of data and environment can be used for learning becomes the only concern, but whether the trained model is competent for a specific task is less discussed. Guiding ideology of what machine learning models are competent for a given application scenario is urgently needed. To solve this problem, we believe that this requires a logical analysis of the external properties of the learned models. In this paper, we propose a perspective for analyzing machine learning models by applying mathematical logic, which helps determine whether a model is up to a given task. In addition, we construct an analysis case and illustrate that the structural objects can be mapped to the class labels in machine learning. We believe this perspective will open a new field of analyzing machine learning with mathematical logic.