# Interpretations of Deep Learning by Forests and Haar Wavelets

## TL;DR

This paper offers new interpretations of ReLU deep learning by linking it to decision forests and Haar wavelet functions, providing insights into its classification and approximation capabilities.

## Contribution

It introduces two novel perspectives: viewing certain ReLU networks as forests and approximating Haar wavelet functions, enhancing understanding of deep learning's theoretical properties.

## Key findings

- ReLU deep learning can be equivalent to decision forests in classification.
- ReLU networks can approximate Haar wavelet functions with arbitrary precision.
- Generalization of results from ReLU to sigmoid-unit deep learning.

## Abstract

This paper presents a basic property of region dividing of ReLU (rectified linear unit) deep learning when new layers are successively added, by which two new perspectives of interpreting deep learning are given. The first is related to decision trees and forests; we construct a deep learning structure equivalent to a forest in classification abilities, which means that certain kinds of ReLU deep learning can be considered as forests. The second perspective is that Haar wavelet represented functions can be approximated by ReLU deep learning with arbitrary precision; and then a general conclusion of function approximation abilities of ReLU deep learning is given. Finally, generalize some of the conclusions of ReLU deep learning to the case of sigmoid-unit deep learning.