Contrary to the use of genetic programming, the neural network approach to
symbolic regression can scale well with high input dimension and leverage
gradient methods for faster equation searching. Common ways of constraining
expression complexity have relied on multistage pruning methods with
fine-tuning, but these often lead to significant performance loss. In this
work, we propose SymbolNet, a neural network approach to symbolic regression in
a novel framework that enables dynamic pruning of model weights, input
features, and mathematical operators in a single training, where both training
loss and expression complexity are optimized simultaneously. We introduce a
sparsity regularization term per pruning type, which can adaptively adjust its
own strength and lead to convergence to a target sparsity level. In contrast to
most existing symbolic regression methods that cannot efficiently handle
datasets with more than $O$(10) inputs, we demonstrate the effectiveness of our
model on the LHC jet tagging task (16 inputs), MNIST (784 inputs), and SVHN
(3072 inputs).

基于神经网络的符号回归方法中引入了动态修剪，用于同时优化训练损失和表达复杂度，通过稀疏正则化适应性地调整修剪类型的目标稀疏度，并在多个数据集上证明了其有效性。