PruneSymNet: A Symbolic Neural Network and Pruning Algorithm for
  Symbolic Regression
Min Wu Weijun Li Lina Yu Wenqiang Li Jingyi Liu Yanjie Li Meilan Hao
Symbolic regression aims to derive interpretable symbolic expressions from
data in order to better understand and interpret data. %which plays an
important role in knowledge discovery and interpretable machine learning.
  In this study, a symbolic network called PruneSymNet is proposed for symbolic
regression. This is a novel neural network whose activation function consists
of common elementary functions and operators. The whole network is
differentiable and can be trained by gradient descent method. Each subnetwork
in the network corresponds to an expression, and our goal is to extract such
subnetworks to get the desired symbolic expression.
  Therefore, a greedy pruning algorithm is proposed to prune the network into a
subnetwork while ensuring the accuracy of data fitting. The proposed greedy
pruning algorithm preserves the edge with the least loss in each pruning, but
greedy algorithm often can not get the optimal solution. In order to alleviate
this problem, we combine beam search during pruning to obtain multiple
candidate expressions each time, and finally select the expression with the
smallest loss as the final result. It was tested on the public data set and
compared with the current popular algorithms. The results showed that the
proposed algorithm had better accuracy.