1. Introduction

A Symbolic Regression (SR) method called SRNet to mine hidden semantics of each network layer in Neural Network (Multi-Layer Perceptron). SRNet is an evolutionary computing algorithm, leveraging Multi-Chromosomes Cartesian Genetic Programming (MCCGP) to find mathmatical formulas $f_i(x)*w_i+b_i$ for each network layer, white-boxing the black box.

This paper has been accepted by GECCO-22, see our paper for more.

2. Code

Projects

Note that for the simplicity of experimental analysis, we divide the SRNet into 2 projects, namely srnet-clas and srnet-reg, for classification task and regression task respectively. It is easy to combine both projects into one single project since the code of SRNet (package at srnet-clas/CGPNet or srnet-reg/CGPNet) is easy to implement for both classification task and regression task.

Requirements

Make sure you have installed the following pacakges before start running our code:

• pytorch 1.8.1
• sympy 1.8
• numpy 1.21.0
• joblib 1.0.1

Our experiments were running in Ubuntu 18.04 with Intel(R) Xeon(R) Gold 5218R CPU @ 2.10GHz and RTX3090. The python version is 3.9

3. Experiments

For both regression and classification task, see srnet-clas/README.md and srnet-reg/README.md for more details about how to reproduce our experimental results.

Here we show our experimental figures in our paper:

Convergence

The convergence curves for all dataset:

Semantics (Mathematical Expressions)

Combining these expressions, we can obtain the overall expressions for all NNs:

Comparison

We compare SRNet to LIME and MAPLE on both regression and classification tasks.

Regression

Classifiation

Decision boundary:

Accuracy:

4. Cite

Please cite our paper if you use the code.