# APALU: A Trainable, Adaptive Activation Function for Deep Learning Networks

arXiv: https://arxiv.org/abs/2402.08244 · HTML: https://mlsanity.com/paper/2402.08244/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 33 references that are in the map.
- First posted on arXiv 13 Feb 2024.

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

- [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)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Squeeze-and-Excitation Networks](https://mlsanity.com/paper/1709.01507/) (2017)
- [Going Deeper with Convolutions](https://mlsanity.com/paper/1409.4842/) (2014)
- [MobileNets: Efficient Convolutional Neural Networks for Mobile Vision Applications](https://mlsanity.com/paper/1704.04861/) (2017)
- [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)
- [KPConv: Flexible and Deformable Convolution for Point Clouds](https://mlsanity.com/paper/1904.08889/) (2019)
- [Fast and Accurate Deep Network Learning by Exponential Linear Units (ELUs)](https://mlsanity.com/paper/1511.07289/) (2015)
- [Towards Total Recall in Industrial Anomaly Detection](https://mlsanity.com/paper/2106.08265/) (2021)
- [Self-Normalizing Neural Networks](https://mlsanity.com/paper/1706.02515/) (2017)
- [PaDiM: a Patch Distribution Modeling Framework for Anomaly Detection and Localization](https://mlsanity.com/paper/2011.08785/) (2020)
- [Multiresolution Knowledge Distillation for Anomaly Detection](https://mlsanity.com/paper/2011.11108/) (2020)
- [Same Same But DifferNet: Semi-Supervised Defect Detection with Normalizing Flows](https://mlsanity.com/paper/2008.12577/) (2020)
- [Learning Activation Functions: A new paradigm for understanding Neural Networks](https://mlsanity.com/paper/1906.09529/) (2019)
- [Parametric Exponential Linear Unit for Deep Convolutional Neural Networks](https://mlsanity.com/paper/1605.09332/) (2016)

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

- [Zorro: A Flexible and Differentiable Parametric Family of Activation Functions That Extends ReLU and GELU](https://mlsanity.com/paper/2409.19239/) (2024)
- [Developing Training Procedures for Piecewise-linear Spline Activation Functions in Neural Networks](https://mlsanity.com/paper/2509.18161/) (2025)
- [FlexAct: Why Learn when you can Pick?](https://mlsanity.com/paper/2601.06441/) (2026)

## Abstract (arXiv)

Activation function is a pivotal component of deep learning, facilitating the extraction of intricate data patterns. While classical activation functions like ReLU and its variants are extensively utilized, their static nature and simplicity, despite being advantageous, often limit their effectiveness in specialized tasks. The trainable activation functions also struggle sometimes to adapt to the unique characteristics of the data. Addressing these limitations, we introduce a novel trainable activation function, adaptive piecewise approximated activation linear unit (APALU), to enhance the learning performance of deep learning across a broad range of tasks. It presents a unique set of features that enable it to maintain stability and efficiency in the learning process while adapting to complex data representations. Experiments reveal significant improvements over widely used activation functions for different tasks. In image classification, APALU increases MobileNet and GoogleNet accuracy by 0.37% and 0.04%, respectively, on the CIFAR10 dataset. In anomaly detection, it improves the average area under the curve of One-CLASS Deep SVDD by 0.8% on the MNIST dataset, 1.81% and 1.11% improvements with DifferNet, and knowledge distillation, respectively, on the MVTech dataset. Notably, APALU achieves 100% accuracy on a sign language recognition task with a limited dataset. For regression tasks, APALU enhances the performance of deep neural networks and recurrent neural networks on different datasets. These improvements highlight the robustness and adaptability of APALU across diverse deep-learning applications.