# CauchyNet: Compact and Data-Efficient Learning using Holomorphic Activation Functions

arXiv: https://arxiv.org/abs/2510.10195 · HTML: https://mlsanity.com/paper/2510.10195/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 32 references that are in the map.
- First posted on arXiv 11 Oct 2025.

## Builds on (most cited first, 17 of 17)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecasting](https://mlsanity.com/paper/2012.07436/) (2020)
- [Learning both Weights and Connections for Efficient Neural Networks](https://mlsanity.com/paper/1506.02626/) (2015)
- [An Empirical Evaluation of Generic Convolutional and Recurrent Networks for Sequence Modeling](https://mlsanity.com/paper/1803.01271/) (2018)
- [Energy and Policy Considerations for Deep Learning in NLP](https://mlsanity.com/paper/1906.02243/) (2019)
- [SqueezeNet: AlexNet-level accuracy with 50x fewer parameters and <0.5MB model size](https://mlsanity.com/paper/1602.07360/) (2016)
- [N-BEATS: Neural basis expansion analysis for interpretable time series forecasting](https://mlsanity.com/paper/1905.10437/) (2019)
- [Discrete Diffusion Modeling by Estimating the Ratios of the Data Distribution](https://mlsanity.com/paper/2310.16834/) (2023)
- [Wasserstein GAN](https://mlsanity.com/paper/1701.07875/) (2017)
- [Carbon Emissions and Large Neural Network Training](https://mlsanity.com/paper/2104.10350/) (2021)
- [Recurrent Neural Networks for Multivariate Time Series with Missing Values](https://mlsanity.com/paper/1606.01865/) (2016)
- [Comprehensive Survey of Complex-Valued Neural Networks: Insights into Backpropagation and Activation Functions](https://mlsanity.com/paper/2407.19258/) (2024)
- [Predicting the Encoding Error of SIRENs](https://mlsanity.com/paper/2410.21645/) (2024)

## Abstract (arXiv)

A novel neural network inspired by Cauchy's integral formula, is proposed for function approximation tasks that include time series forecasting, missing data imputation, etc. Hence, the novel neural network is named CauchyNet. By embedding real-valued data into the complex plane, CauchyNet efficiently captures complex temporal dependencies, surpassing traditional real-valued models in both predictive performance and computational efficiency. Grounded in Cauchy's integral formula and supported by the universal approximation theorem, CauchyNet offers strong theoretical guarantees for function approximation. The architecture incorporates complex-valued activation functions, enabling robust learning from incomplete data while maintaining a compact parameter footprint and reducing computational overhead. Through extensive experiments in diverse domains, including transportation, energy consumption, and epidemiological data, CauchyNet consistently outperforms state-of-the-art models in predictive accuracy, often achieving a 50% lower mean absolute error with fewer parameters. These findings highlight CauchyNet's potential as an effective and efficient tool for data-driven predictive modeling, particularly in resource-constrained and data-scarce environments.