# CoFrNets: Interpretable Neural Architecture Inspired by Continued Fractions

arXiv: https://arxiv.org/abs/2506.05586 · HTML: https://mlsanity.com/paper/2506.05586/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 48 references that are in the map.
- First posted on arXiv 5 Jun 2025.

## Builds on (most cited first, 21 of 21)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Densely Connected Convolutional Networks](https://mlsanity.com/paper/1608.06993/) (2016)
- [MobileNetV2: Inverted Residuals and Linear Bottlenecks](https://mlsanity.com/paper/1801.04381/) (2018)
- [XLNet: Generalized Autoregressive Pretraining for Language Understanding](https://mlsanity.com/paper/1906.08237/) (2019)
- [Sharpness-Aware Minimization for Efficiently Improving Generalization](https://mlsanity.com/paper/2010.01412/) (2020)
- [Dynamic Routing Between Capsules](https://mlsanity.com/paper/1710.09829/) (2017)
- [Towards Robust Interpretability with Self-Explaining Neural Networks](https://mlsanity.com/paper/1806.07538/) (2018)
- [The Expressive Power of Neural Networks: A View from the Width](https://mlsanity.com/paper/1709.02540/) (2017)
- [Neural Additive Models: Interpretable Machine Learning with Neural Nets](https://mlsanity.com/paper/2004.13912/) (2020)
- [Explanations based on the Missing: Towards Contrastive Explanations with Pertinent Negatives](https://mlsanity.com/paper/1802.07623/) (2018)
- [InterpretML: A Unified Framework for Machine Learning Interpretability](https://mlsanity.com/paper/1909.09223/) (2019)
- [Evaluating the Robustness of Neural Networks: An Extreme Value Theory Approach](https://mlsanity.com/paper/1801.10578/) (2018)
- [Rethinking Cooperative Rationalization: Introspective Extraction and Complement Control](https://mlsanity.com/paper/1910.13294/) (2019)
- [LassoNet: A Neural Network with Feature Sparsity](https://mlsanity.com/paper/1907.12207/) (2019)
- [Boolean Decision Rules via Column Generation](https://mlsanity.com/paper/1805.09901/) (2018)
- [Pad'e Activation Units: End-to-end Learning of Flexible Activation Functions in Deep Networks](https://mlsanity.com/paper/1907.06732/) (2019)
- [Deep Polynomial Neural Networks](https://mlsanity.com/paper/2006.13026/) (2020)
- [TED: Teaching AI to Explain its Decisions](https://mlsanity.com/paper/1811.04896/) (2018)
- [Model Agnostic Multilevel Explanations](https://mlsanity.com/paper/2003.06005/) (2020)

## Built on by (most cited first, 3 of 3)

- [High-order Interactions Modeling for Interpretable Multi-Agent Q-Learning](https://mlsanity.com/paper/2510.20218/) (2025)
- [CoFrGeNet: Continued Fraction Architectures for Language Generation](https://mlsanity.com/paper/2601.21766/) (2026)
- [CFNN: Continued Fraction Neural Network](https://mlsanity.com/paper/2603.20634/) (2026)

## Abstract (arXiv)

In recent years there has been a considerable amount of research on local post hoc explanations for neural networks. However, work on building interpretable neural architectures has been relatively sparse. In this paper, we present a novel neural architecture, CoFrNet, inspired by the form of continued fractions which are known to have many attractive properties in number theory, such as fast convergence of approximations to real numbers. We show that CoFrNets can be efficiently trained as well as interpreted leveraging their particular functional form. Moreover, we prove that such architectures are universal approximators based on a proof strategy that is different than the typical strategy used to prove universal approximation results for neural networks based on infinite width (or depth), which is likely to be of independent interest. We experiment on nonlinear synthetic functions and are able to accurately model as well as estimate feature attributions and even higher order terms in some cases, which is a testament to the representational power as well as interpretability of such architectures. To further showcase the power of CoFrNets, we experiment on seven real datasets spanning tabular, text and image modalities, and show that they are either comparable or significantly better than other interpretable models and multilayer perceptrons, sometimes approaching the accuracies of state-of-the-art models.