Mathematical equivalence of the MNIST dataset and philosophical predicate space

Abstract

Similarity judgments are widely believed to underlie various human cognitive processes, including pattern recognition, and the concept of similarity serves as a basic explanatory notion to describe these processes in machine learning. In this study, a mathematical framework for associating the concept of similarity that has been the subject of analysis in the context of the philosophy of science with the concept of similarity in machine learning is examined. In particular, the mathematical equivalence of the Modified National Institute of Standards and Technology (MNIST) dataset as an inner product space and the philosophical predicate space is shown. The mathematical equivalence of a feature space in machine learning and the philosophical predicate space would allow for the application of the philosophical analysis of the concept of similarity to the concept of similarity in machine learning, which would lead to the detection of a potential flaw in machine learning methods. Conversely, it would allow the mathematical formulation of the concept of similarity in machine learning to be applied to solving philosophical problems on the concept of similarity. The equivalence can be expected to yield such bidirectional implications and a mutually beneficial relation between the fields of machine learning and philosophy of science.