Compositional Function Networks: A High-Performance Alternative to Deep Neural Networks with Built-in Interpretability

TL;DR

Compositional Function Networks (CFNs) offer a highly interpretable, versatile, and trainable alternative to traditional deep neural networks, achieving competitive accuracy while maintaining transparency across various domains.

Contribution

CFNs introduce a novel, fully differentiable framework that supports complex compositional patterns for interpretable models, surpassing existing methods in flexibility and performance.

Findings

CFNs achieve 96.24% accuracy on CIFAR-10.

CFNs outperform state-of-the-art interpretable models.

CFNs support diverse compositional patterns like sequential, parallel, and conditional.

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.