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We propose a novel activation function that implements piece-wise orthogonal non-linear mappings based on permutations. It is straightforward to implement, and very computationally efficient, also it has little memory requirements. We…

Neural and Evolutionary Computing · Computer Science 2017-02-02 Artem Chernodub , Dimitri Nowicki

Activation sparsity refers to the existence of considerable weakly-contributed elements among activation outputs. As a prevalent property of the models using the ReLU activation function, activation sparsity has been proven a promising…

Machine Learning · Computer Science 2025-01-08 Chenyang Song , Xu Han , Zhengyan Zhang , Shengding Hu , Xiyu Shi , Kuai Li , Chen Chen , Zhiyuan Liu , Guangli Li , Tao Yang , Maosong Sun

We propose the Hyperbolic Tangent Exponential Linear Unit (TeLU), a neural network hidden activation function defined as TeLU(x)=xtanh(exp(x)). TeLU's design is grounded in the core principles of key activation functions, achieving strong…

Machine Learning · Computer Science 2025-01-03 Alfredo Fernandez , Ankur Mali

The dominant paradigm in modern neural networks relies on simple, monotonically-increasing activation functions like ReLU. While effective, this paradigm necessitates large, massively-parameterized models to approximate complex functions.…

Machine Learning · Computer Science 2025-08-27 Shiko Kudo

Even in recent neural network architectures such as Transformers and Extended LSTM (xLSTM), and traditional ones like Convolutional Neural Networks, Activation Functions are an integral part of nearly all neural networks. They enable more…

Machine Learning · Computer Science 2024-10-01 Matias Roodschild , Jorge Gotay-Sardiñas , Victor A. Jimenez , Adrian Will

The design of activation functions remains a pivotal component in optimizing deep neural networks. While prevailing choices like Swish and GELU demonstrate considerable efficacy, they often exhibit domain-specific optima. This work…

Machine Learning · Computer Science 2025-06-02 Gaurav Sarkar , Jay Gala , Subarna Tripathi

Well-known activation functions like ReLU or Leaky ReLU are non-differentiable at the origin. Over the years, many smooth approximations of ReLU have been proposed using various smoothing techniques. We propose new smooth approximations of…

Machine Learning · Computer Science 2021-09-28 Koushik Biswas , Sandeep Kumar , Shilpak Banerjee , Ashish Kumar Pandey

The most widely used activation functions in current deep feed-forward neural networks are rectified linear units (ReLU), and many alternatives have been successfully applied, as well. However, none of the alternatives have managed to…

Machine Learning · Computer Science 2018-06-27 Leon René Sütfeld , Flemming Brieger , Holger Finger , Sonja Füllhase , Gordon Pipa

The Rectified Linear Unit is currently a state-of-the-art activation function in deep convolutional neural networks. To combat ReLU's dying neuron problem, we propose the Parametric Variational Linear Unit (PVLU), which adds a sinusoidal…

Computer Vision and Pattern Recognition · Computer Science 2021-12-20 Aarush Gupta , Shikhar Ahuja

Deep learning models are effective for sequential data modeling, yet commonly used activation functions such as ReLU, LeakyReLU, and PReLU often exhibit gradient instability when applied to noisy, non-stationary financial time series. This…

Machine Learning · Computer Science 2026-01-26 George Awiakye-Marfo , Elijah Agbosu , Victoria Mawuena Barns , Samuel Asante Gyamerah

A pivotal aspect in the design of neural networks lies in selecting activation functions, crucial for introducing nonlinear structures that capture intricate input-output patterns. While the effectiveness of adaptive or trainable activation…

Machine Learning · Computer Science 2024-08-06 Farhad Pourkamali-Anaraki , Tahamina Nasrin , Robert E. Jensen , Amy M. Peterson , Christopher J. Hansen

Large Language Models (LLMs) have achieved remarkable capabilities, but their immense computational demands during training remain a critical bottleneck for widespread adoption. Low-rank training has received attention in recent years due…

Machine Learning · Computer Science 2026-05-06 Jiaxi Li , Lu Yin , Li Shen , Jinjin Xu , Yuhui Liu , Wenwu Wang , Shiwei Liu , Xilu Wang

Large Language Models (LLMs) have demonstrated remarkable performance across a wide range of tasks, but their deployment is often constrained by substantial memory footprints and computational costs. While prior work has achieved…

Machine Learning · Computer Science 2026-02-04 Jiangyong Yu , Xiaomeng Han , Xing Hu , Chen Xu , Zhe Jiang , Dawei Yang

The choice of activation function in deep networks has a significant effect on the training dynamics and task performance. At present, the most effective and widely-used activation function is ReLU. However, because of the non-zero mean,…

Computer Vision and Pattern Recognition · Computer Science 2020-03-03 Yuan Zhou , Dandan Li , Shuwei Huo , Sun-Yuan Kung

An appropriate choice of the activation function (like ReLU, sigmoid or swish) plays an important role in the performance of (deep) multilayer perceptrons (MLP) for classification and regression learning. Prototype-based classification…

Machine Learning · Computer Science 2019-01-21 Thomas Villmann , John Ravichandran , Andrea Villmann , David Nebel , Marika Kaden

Biological neural systems employ diverse neurotransmitters -- glutamate, GABA, dopamine, acetylcholine -- to implement distinct signal-processing modalities within shared neural circuits. In contrast, modern transformers apply a single…

Machine Learning · Computer Science 2026-03-17 Daniel Nobrega Medeiros

The recent trend of large language models (LLMs) is to increase the scale of both model size (\aka the number of parameters) and dataset to achieve better generative ability, which is definitely proved by a lot of work such as the famous…

In this paper, we explore the concept of adding learn-able slope and mean shift parameters to an activation function to improve the total response region. The characteristics of an activation function depend highly on the value of…

Machine Learning · Computer Science 2019-12-24 S. Balaji , T. Kavya , Natasha Sebastian

In this paper, we introduce the Hyperbolic Tangent Exponential Linear Unit (TeLU), a novel neural network activation function, represented as $f(x) = x{\cdot}tanh(e^x)$. TeLU is designed to overcome the limitations of conventional…

Machine Learning · Computer Science 2024-02-06 Alfredo Fernandez , Ankur Mali

Activation functions are crucial in deep learning models since they introduce non-linearity into the networks, allowing them to learn from errors and make adjustments, which is essential for learning complex patterns. The essential purpose…

Machine Learning · Computer Science 2023-10-17 Koushik Biswas , Meghana Karri , Ulaş Bağcı