# On Linear Separability of the MNIST Handwritten Digits Dataset

arXiv: https://arxiv.org/abs/2603.12850 · HTML: https://mlsanity.com/paper/2603.12850/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 25 references that are in the map.
- First posted on arXiv 13 Mar 2026.

## Builds on (most cited first, 8 of 8)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [CVXPY: A Python-Embedded Modeling Language for Convex Optimization](https://mlsanity.com/paper/1603.00943/) (2016)
- [A Rewriting System for Convex Optimization Problems](https://mlsanity.com/paper/1709.04494/) (2017)
- [Clarabel: An interior-point solver for conic programs with quadratic objectives](https://mlsanity.com/paper/2405.12762/) (2024)
- [An Ensemble of Simple Convolutional Neural Network Models for MNIST Digit Recognition](https://mlsanity.com/paper/2008.10400/) (2020)
- [A Perceptron-based Fine Approximation Technique for Linear Separation](https://mlsanity.com/paper/2309.06049/) (2023)
- [A faster dual algorithm for the Euclidean minimum covering ball problem](https://mlsanity.com/paper/1706.10256/) (2017)
- [Binary Classification as a Phase Separation Process](https://mlsanity.com/paper/2009.02467/) (2020)

## Built on by (most cited first, 2 of 2)

- [An Iterative Geometric Approach to Optimizing Separating Hyperplanes](https://mlsanity.com/paper/2607.17282/) (2026)
- [A Geometrical Approach to Constructing Neural Networks for Perfect Training-set Classification](https://mlsanity.com/paper/2610.17312/) (2026)

## Abstract (arXiv)

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.