Symbolic regression

In this project, building on the ideas from Martius et al.¹ my friend @SilenceInTheBox and I implemented a neural network that is capable of learning symbolic expression. In layer.py we implement symbolic and linear layers that compute the forward pass using the SciPy library. This allows us to obtain analytical expressions from the trained network and conveniently simply them. In symbolic_regression.ipynb, we train a simple network of two symbolic and three linear layers to obtain the polynomial $x^4- 2 x^2 + 1$. The output of the trained neural network simplifies to $0.986237x^4−0.00102282x^3−1.95504x^2+0.00101377x+0.992526$.

Footnotes

1. Extrapolation and learning equations ↩