I introduce a unified framework for interpreting neural network classifiers
tailored toward automated scientific discovery. In contrast to neural
network-based regression, for classification, it is in general impossible to
find a one-to-one mapping from the neural network to a symbolic equation even
if the neural network itself bases its classification on a quantity that can be
written as a closed-form equation. In this paper, I embed a trained neural
network into an equivalence class of classifying functions that base their
decisions on the same quantity. I interpret neural networks by finding an
intersection between this equivalence class and human-readable equations
defined by the search space of symbolic regression. The approach is not limited
to classifiers or full neural networks and can be applied to arbitrary neurons
in hidden layers or latent spaces or to simplify the process of interpreting
neural network regressors.

基于统一框架，我提出了一种解释神经网络分类器的方法，该方法旨在自动化科学发现，通过将训练好的神经网络嵌入到一组基于相同数量的分类函数的等价类中，并通过搜索符号回归的搜索空间定义的人类可读方程与该等价类之间的交集来解释神经网络。

使用符号回归梯度解释神经网络分类器的封闭形式

Closed-Form Interpretation of Neural Network Classifiers with Symbolic  Regression Gradients

Getting good performance out of numerical equation solvers requires that the
user has provided stable and efficient functions representing their model.
However, users should not be trusted to write good code. In this manuscript we
describe ModelingToolkit (MTK), a symbolic equation-based modeling system which
allows for composable transformations to generate stable, efficient, and
parallelized model implementations. MTK blurs the lines of traditional symbolic
computing by acting directly on a user's numerical code. We show the ability to
apply graph algorithms for automatically parallelizing and performing index
reduction on code written for differential-algebraic equation (DAE) solvers,
"fixing" the performance and stability of the model without requiring any
changes to on the user's part. We demonstrate how composable model
transformations can be combined with automated data-driven surrogate generation
techniques, allowing machine learning methods to generate accelerated
approximate models within an acausal modeling framework. These reduced models
are shown to outperform the Dymola Modelica compiler on an HVAC model by 590x
at 3\% error. Together, this demonstrates MTK as a system for bringing the
latest research in graph transformations directly to modeling applications.

这篇论文介绍了 ModelingToolkit (MTK) 这一符号方程为基础的建模工具，该工具可以通过组合变换来生成稳定、高效和并行的模型实现。MTK 通过对用户的数值代码进行处理来提高性能和稳定性，并演示了如何将机器学习方法应用于减少模型复杂性并加速近似建模。