# Pad'e Neurons for Efficient Neural Models

arXiv: https://arxiv.org/abs/2601.04005 · HTML: https://mlsanity.com/paper/2601.04005/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 37 of its 64 references that are in the map.
- First posted on arXiv 7 Jan 2026.

## Builds on (most cited first, 30 of 37)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [Gaussian Error Linear Units (GELUs)](https://mlsanity.com/paper/1606.08415/) (2016)
- [Wide Residual Networks](https://mlsanity.com/paper/1605.07146/) (2016)
- [Photo-Realistic Single Image Super-Resolution Using a Generative Adversarial Network](https://mlsanity.com/paper/1609.04802/) (2016)
- [Enhanced Deep Residual Networks for Single Image Super-Resolution](https://mlsanity.com/paper/1707.02921/) (2017)
- [Inception-v4, Inception-ResNet and the Impact of Residual Connections on Learning](https://mlsanity.com/paper/1602.07261/) (2016)
- [Deformable Convolutional Networks](https://mlsanity.com/paper/1703.06211/) (2017)
- [Real-Time Single Image and Video Super-Resolution Using an Efficient Sub-Pixel Convolutional Neural Network](https://mlsanity.com/paper/1609.05158/) (2016)
- [Joint Autoregressive and Hierarchical Priors for Learned Image Compression](https://mlsanity.com/paper/1809.02736/) (2018)
- [KAN: Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2404.19756/) (2024)
- [Learned Image Compression with Discretized Gaussian Mixture Likelihoods and Attention Modules](https://mlsanity.com/paper/2001.01568/) (2020)
- [BasicVSR++: Improving Video Super-Resolution with Enhanced Propagation and Alignment](https://mlsanity.com/paper/2104.13371/) (2021)
- [Sketch-based Manga Retrieval using Manga109 Dataset](https://mlsanity.com/paper/1510.04389/) (2015)
- [ELIC: Efficient Learned Image Compression with Unevenly Grouped Space-Channel Contextual Adaptive Coding](https://mlsanity.com/paper/2203.10886/) (2022)
- [CompressAI: a PyTorch library and evaluation platform for end-to-end compression research](https://mlsanity.com/paper/2011.03029/) (2020)
- [A General and Adaptive Robust Loss Function](https://mlsanity.com/paper/1701.03077/) (2017)
- [Adan: Adaptive Nesterov Momentum Algorithm for Faster Optimizing Deep Models](https://mlsanity.com/paper/2208.06677/) (2022)
- [Pad'e Activation Units: End-to-end Learning of Flexible Activation Functions in Deep Networks](https://mlsanity.com/paper/1907.06732/) (2019)
- [MLIC++: Linear Complexity Multi-Reference Entropy Modeling for Learned Image Compression](https://mlsanity.com/paper/2307.15421/) (2023)
- [Quadratic Residual Networks: A New Class of Neural Networks for Solving Forward and Inverse Problems in Physics Involving PDEs](https://mlsanity.com/paper/2101.08366/) (2021)
- [Self-Organized Operational Neural Networks with Generative Neurons](https://mlsanity.com/paper/2004.11778/) (2020)
- [Operational Neural Networks](https://mlsanity.com/paper/1902.11106/) (2019)
- [QuadraLib: A Performant Quadratic Neural Network Library for Architecture Optimization and Design Exploration](https://mlsanity.com/paper/2204.01701/) (2022)

## Abstract (arXiv)

Neural networks commonly employ the McCulloch-Pitts neuron model, which is a linear model followed by a point-wise non-linear activation. Various researchers have already advanced inherently non-linear neuron models, such as quadratic neurons, generalized operational neurons, generative neurons, and super neurons, which offer stronger non-linearity compared to point-wise activation functions. In this paper, we introduce a novel and better non-linear neuron model called Pad'e neurons (Paons), inspired by Pad'e approximants. Paons offer several advantages, such as diversity of non-linearity, since each Paon learns a different non-linear function of its inputs, and layer efficiency, since Paons provide stronger non-linearity in much fewer layers compared to piecewise linear approximation. Furthermore, Paons include all previously proposed neuron models as special cases, thus any neuron model in any network can be replaced by Paons. We note that there has been a proposal to employ the Pad'e approximation as a generalized point-wise activation function, which is fundamentally different from our model. To validate the efficacy of Paons, in our experiments, we replace classic neurons in some well-known neural image super-resolution, compression, and classification models based on the ResNet architecture with Paons. Our comprehensive experimental results and analyses demonstrate that neural models built by Paons provide better or equal performance than their classic counterparts with a smaller number of layers. The PyTorch implementation code for Paon is open-sourced at https://github.com/onur-keles/Paon.