Tensor network to learn the wavefunction of data

TL;DR

This paper introduces a tensor network model that learns and characterizes the entire set of handwritten digit images, enabling both classification and sampling, and provides insights into the data's structure through quantum-inspired measures.

Contribution

The work presents a novel tensor network architecture that captures the full set of data, allowing for simultaneous classification and sampling, and applies quantum-inspired analysis to understand data complexity.

Findings

The total number of handwritten digit 3 images in MNIST is approximately 2^72.

The tensor network effectively models the indicator function of the full data set.

Quantum entanglement measures reveal the data's structural properties.

Abstract

How many different ways are there to handwrite digit 3? To quantify this question imagine extending a dataset of handwritten digits MNIST by sampling additional images until they start repeating. We call the collection of all resulting images of digit 3 the "full set." To study the properties of the full set we introduce a tensor network architecture which simultaneously accomplishes both classification (discrimination) and sampling tasks. Qualitatively, our trained network represents the indicator function of the full set. It therefore can be used to characterize the data itself. We illustrate that by studying the full sets associated with the digits of MNIST. Using quantum mechanical interpretation of our network we characterize the full set by calculating its entanglement entropy. We also study its geometric properties such as mean Hamming distance, effective dimension, and size. The latter answers the question above -- the total number of black and white threes written MNIST style is $2^{72}$.