Traditional machine learning is generally treated as a black-box optimization
problem and does not typically produce interpretable functions that connect
inputs and outputs. However, the ability to discover such interpretable
functions is desirable. In this work, we propose GINN-LP, an interpretable
neural network to discover the form and coefficients of the underlying equation
of a dataset, when the equation is assumed to take the form of a multivariate
Laurent Polynomial. This is facilitated by a new type of interpretable neural
network block, named the "power-term approximator block", consisting of
logarithmic and exponential activation functions. GINN-LP is end-to-end
differentiable, making it possible to use backpropagation for training. We
propose a neural network growth strategy that will enable finding the suitable
number of terms in the Laurent polynomial that represents the data, along with
sparsity regularization to promote the discovery of concise equations. To the
best of our knowledge, this is the first model that can discover arbitrary
multivariate Laurent polynomial terms without any prior information on the
order. Our approach is first evaluated on a subset of data used in SRBench, a
benchmark for symbolic regression. We first show that GINN-LP outperforms the
state-of-the-art symbolic regression methods on datasets generated using 48
real-world equations in the form of multivariate Laurent polynomials. Next, we
propose an ensemble method that combines our method with a high-performing
symbolic regression method, enabling us to discover non-Laurent polynomial
equations. We achieve state-of-the-art results in equation discovery, showing
an absolute improvement of 7.1% over the best contender, by applying this
ensemble method to 113 datasets within SRBench with known ground-truth
equations.

提出了 GINN-LP，这是一个可解释的神经网络，用于发现数据集的潜在方程的形式和系数，该方程被假设为多变量劳伦多多项式的形式。通过一种新类型的可解释神经网络块，名为 “幂项逼近块”，由对数和指数激活函数组成，为此提供了便利。在符号回归的基准数据集 SRBench 的子集上对我们的方法进行了评估，证明了我们方法在多变量劳伦多多项式形式的 48 个真实方程生成的数据集上优于现有的符号回归方法。然后，提出了一种将我们的方法与高性能符号回归方法相结合的集成方法，使我们能够发现非劳伦多多项式方程，通过将这种集成方法应用于 SRBench 中的 113 个已知基准方程数据集，取得了在方程发现方面的最新成果，相比最佳竞争者，有 7.1% 的绝对改进。