Qualitative Projection Using Deep Neural Networks

TL;DR

This paper introduces qualitative projection, a novel method for abstracting data in deep neural networks by relating inputs to specific filter-based qualities, demonstrated through classifying MNIST digits by their resemblance to CIFAR dataset categories.

Contribution

It refines the concept of abstraction in DNNs to include filter-qualified qualities, introducing qualitative projection as a new approach for data abstraction and classification.

Findings

Qualitative projection effectively abstracts MNIST digits based on CIFAR categories.

The method enables classification of digits by their resemblance to specific object qualities.

Demonstrates the generality of qualitative projection across different datasets.

Abstract

Deep neural networks (DNN) abstract by demodulating the output of linear filters. In this article, we refine this definition of abstraction to show that the inputs of a DNN are abstracted with respect to the filters. Or, to restate, the abstraction is qualified by the filters. This leads us to introduce the notion of qualitative projection. We use qualitative projection to abstract MNIST hand-written digits with respect to the various dogs, horses, planes and cars of the CIFAR dataset. We then classify the MNIST digits according to the magnitude of their dogness, horseness, planeness and carness qualities, illustrating the generality of qualitative projection.