On Linear Separability of the MNIST Handwritten Digits Dataset

2026-03-13

AI Summary

This study systematically investigates the linear separability of the MNIST handwritten digit dataset, resolving a long-standing debate in the literature. By exhaustively examining all class combinations under both binary and one-versus-rest classification settings, the authors conduct empirical evaluations on the training set, test set, and their union, integrating theoretical insights from linear separability with modern optimization tools. The work presents the first complete characterization of MNIST’s separability boundaries under linear classification, uncovering its structural properties across different data partitions and classification strategies. These findings fill a critical gap in the foundational understanding of this benchmark dataset and provide a rigorous basis for informed model selection and theoretical analysis in machine learning research.

Technology Category

• Machine Learning: Learning with Manifolds
• Natural Language Processing: Interpretability, Analysis, and Evaluation of NLP Models
• Computer Vision: Adversarial Attacks & Robustness

Application Category

• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets
• Web Mining and Content Analysis: Machine learning and data science for the Web
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs

Abstract

The MNIST dataset containing thousands of handwritten digit images is still a fundamental benchmark for evaluating various pattern-recognition and image-classification models. Linear separability is a key concept in many statistical and machine-learning techniques. Despite the long history of the MNIST dataset and its relative simplicity in size and resolution, the question of whether the dataset is linearly separable has never been fully answered -- scientific and informal sources share conflicting claims. This paper aims to provide a comprehensive empirical investigation to address this question, distinguishing pairwise and one-vs-rest separation of the training, the test and the combined sets, respectively. It reviews the theoretical approaches to assessing linear separability, alongside state-of-the-art methods and tools, then systematically examines all relevant assemblies, and reports the findings.

Problem

• linear separability
• MNIST
• handwritten digits
• pattern recognition
• image classification

Innovation

• linear separability
• MNIST dataset
• pairwise classification
• one-vs-rest
• empirical investigation