What Machine Learning Tells Us About the Mathematical Structure of Concepts

TL;DR

This paper explores the mathematical foundations of concepts across philosophy, cognitive science, and machine learning, proposing a unified framework that integrates various approaches to deepen our understanding of cognition and AI.

Contribution

It categorizes and synthesizes four mathematical approaches to concepts, bridging philosophical theories and machine learning models for interdisciplinary insights.

Findings

Identifies four distinct mathematical frameworks for concepts.

Bridges philosophical and machine learning perspectives.

Provides a comprehensive framework for future research.

Abstract

This paper examines the connections among various approaches to understanding concepts in philosophy, cognitive science, and machine learning, with a particular focus on their mathematical nature. By categorizing these approaches into Abstractionism, the Similarity Approach, the Functional Approach, and the Invariance Approach, the study highlights how each framework provides a distinct mathematical perspective for modeling concepts. The synthesis of these approaches bridges philosophical theories and contemporary machine learning models, providing a comprehensive framework for future research. This work emphasizes the importance of interdisciplinary dialogue, aiming to enrich our understanding of the complex relationship between human cognition and artificial intelligence.