Popov Sergei, Lazarev Mikhail, Belavin Vladislav, Derkach Denis, Ustyuzhanin Andrey
Department of Computer Science, Higher School of Economics, Moscow, Russia.
National University of Science and Technology MISIS, Moscow, Russia.
PeerJ Comput Sci. 2023 Mar 7;9:e1241. doi: 10.7717/peerj-cs.1241. eCollection 2023.
There are many problems in physics, biology, and other natural sciences in which symbolic regression can provide valuable insights and discover new laws of nature. Widespread deep neural networks do not provide interpretable solutions. Meanwhile, symbolic expressions give us a clear relation between observations and the target variable. However, at the moment, there is no dominant solution for the symbolic regression task, and we aim to reduce this gap with our algorithm. In this work, we propose a novel deep learning framework for symbolic expression generation variational autoencoder (VAE). We suggest using a VAE to generate mathematical expressions, and our training strategy forces generated formulas to fit a given dataset. Our framework allows encoding apriori knowledge of the formulas into fast-check predicates that speed up the optimization process. We compare our method to modern symbolic regression benchmarks and show that our method outperforms the competitors under noisy conditions. The recovery rate of SEGVAE is 65% on the Ngyuen dataset with a noise level of 10%, which is better than the previously reported SOTA by 20%. We demonstrate that this value depends on the dataset and can be even higher.
在物理学、生物学和其他自然科学中有许多问题，符号回归可以在其中提供有价值的见解并发现新的自然规律。广泛使用的深度神经网络并不能提供可解释的解决方案。与此同时，符号表达式为我们提供了观测值与目标变量之间的清晰关系。然而，目前符号回归任务没有占主导地位的解决方案，我们旨在用我们的算法缩小这一差距。在这项工作中，我们提出了一种用于符号表达式生成的新型深度学习框架——变分自编码器（VAE）。我们建议使用VAE来生成数学表达式，并且我们的训练策略迫使生成的公式拟合给定的数据集。我们的框架允许将公式的先验知识编码到快速检查谓词中，从而加快优化过程。我们将我们的方法与现代符号回归基准进行比较，结果表明我们的方法在有噪声的条件下优于竞争对手。在噪声水平为10%的Ngyuen数据集上，SEGVAE的恢复率为65%，比之前报道的最优方法高出20%。我们证明这个值取决于数据集，甚至可能更高。
