Exploring Hidden Semantics in Neural Networks with Symbolic Regression

TL;DR

This paper introduces SRNet, a symbolic regression method that uncovers explicit mathematical representations of neural networks, enhancing interpretability by revealing hidden semantics across layers.

Contribution

SRNet employs Cartesian genetic programming and an evolutionary strategy to extract explicit mathematical expressions from neural networks, a novel approach for interpretability.

Findings

SRNet accurately reveals complex layer relationships.

It outperforms LIME and MAPLE in interpolation accuracy.

It effectively approximates the real model on practical datasets.

Abstract

Many recent studies focus on developing mechanisms to explain the black-box behaviors of neural networks (NNs). However, little work has been done to extract the potential hidden semantics (mathematical representation) of a neural network. A succinct and explicit mathematical representation of a NN model could improve the understanding and interpretation of its behaviors. To address this need, we propose a novel symbolic regression method for neural works (called SRNet) to discover the mathematical expressions of a NN. SRNet creates a Cartesian genetic programming (NNCGP) to represent the hidden semantics of a single layer in a NN. It then leverages a multi-chromosome NNCGP to represent hidden semantics of all layers of the NN. The method uses a (1+$\lambda$) evolutionary strategy (called MNNCGP-ES) to extract the final mathematical expressions of all layers in the NN. Experiments on 12 symbolic regression benchmarks and 5 classification benchmarks show that SRNet not only can reveal the complex relationships between each layer of a NN but also can extract the mathematical representation of the whole NN. Compared with LIME and MAPLE, SRNet has higher interpolation accuracy and trends to approximate the real model on the practical dataset.