Abstract
Deep Neural Networks (DNNs) deliver impressive performance but their black-box nature limits deployment in high-stakes domains requiring transparency. We introduce Compositional Function Networks (CFNs), a novel framework that builds inherently interpretable models by composing elementary mathematical functions with clear semantics. Unlike existing interpretable approaches that are limited to simple additive structures, CFNs support diverse compositional patterns -- sequential, parallel, and conditional -- enabling complex feature interactions while maintaining transparency. A key innovation is that CFNs are fully differentiable, allowing efficient training through standard gradient descent. We demonstrate CFNs' versatility across multiple domains, from symbolic regression to image classification with deep hierarchical networks. Our empirical evaluation shows CFNs achieve competitive performance against black-box models (96.24% accuracy on CIFAR-10) while outperforming state-of-the-art interpretable models like Explainable Boosting Machines. By combining the hierarchical expressiveness and efficient training of deep learning with the intrinsic interpretability of well-defined mathematical functions, CFNs offer a powerful framework for applications where both performance and accountability are paramount.
Abstract (translated)
深度神经网络（DNNs）展现出卓越的性能，但其黑箱特性限制了它们在需要透明度的关键领域中的应用。我们引入了一种新的框架——组合函数网络（CFNs），该框架通过组合具有明确语义的基本数学函数来构建固有的可解释模型。与现有的仅限于简单加法结构的可解释方法不同，CFNs支持多样化的组合模式——顺序、并行和条件组合，这使得它们能够在保持透明性的同时处理复杂的特征交互。 一个关键创新点是，CFNs完全可微分，允许通过标准梯度下降进行高效的训练。我们展示了CFNs在多个领域的灵活性，从符号回归到使用深度层次网络的图像分类。我们的实证评估表明，CFNs在与黑箱模型（如CIFAR-10数据集上的96.24%准确性）竞争性能的同时，还超过了最新的可解释性模型，例如可解释增强机。 通过将深度学习中的分层表达能力和高效的训练方法与明确定义的数学函数所固有的可解释性相结合，CFNs为那些需要兼顾高性能和问责制的应用提供了一个强大的框架。
URL
https://arxiv.org/abs/2507.21004
