用可解释的数学函数组合构建高性能模型，兼顾准确率与透明度。
Compositional Function Networks: A High-Performance Alternative to Deep Neural Networks with Built-in Interpretability
- 通过可解释的数学函数组合实现复杂特征交互
- 在CIFAR-10上达96.24%准确率，超越现有可解释模型
- 适合需要高可信度的医疗、金融等关键领域
深度神经网络虽性能出色，但其黑箱特性限制了在高风险场景中的应用。本文提出组合函数网络（CFNs），通过具有明确语义的初等数学函数组合构建内在可解释模型。不同于仅支持简单加法结构的已有方法，CFNs支持序列、并行和条件等多种组合模式，能表达复杂特征关系的同时保持透明性。关键创新在于全可微设计，支持标准梯度下降高效训练。实证表明，CFNs在符号回归、图像分类等多领域表现优异，在CIFAR-10上达到96.24%准确率，优于当前主流可解释模型（如Explainable Boosting Machines）。该框架融合深度学习的层次表达能力与可解释数学函数的透明性，为性能与问责并重的应用提供有力工具。
原文摘要 · Abstract (English)
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.
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