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The loss function used to train a neural network is strongly connected to its output layer from a statistical point of view. This technical report analyzes common activation functions for a neural network output layer, like linear, sigmoid,…

Machine Learning · Computer Science 2025-11-10 Fernando Berzal

In the field of pattern recognition, achieving high accuracy is essential. While training a model to recognize different complex images, it is vital to fine-tune the model to achieve the highest accuracy possible. One strategy for…

Visual attention has been extensively studied for learning fine-grained features in both facial expression recognition (FER) and Action Unit (AU) detection. A broad range of previous research has explored how to use attention modules to…

Computer Vision and Pattern Recognition · Computer Science 2022-03-24 Xiaotian Li , Zhihua Li , Huiyuan Yang , Geran Zhao , Lijun Yin

Deep Neural Networks have been shown to be beneficial for a variety of tasks, in particular allowing for end-to-end learning and reducing the requirement for manual design decisions. However, still many parameters have to be chosen in…

Neural and Evolutionary Computing · Computer Science 2018-08-03 Mina Basirat , Peter M. Roth

Over the past few years, there has been a significant amount of research focused on studying the ReLU activation function, with the aim of achieving neural network convergence through over-parametrization. However, recent developments in…

Machine Learning · Computer Science 2023-03-30 Yeqi Gao , Sridhar Mahadevan , Zhao Song

We present a domain decomposition-based deep learning method for solving elliptic and parabolic interface problems with discontinuous coefficients in two to ten dimensions. Our Multi-Activation Function (MAF) approach employs two…

Numerical Analysis · Mathematics 2025-12-23 Qijia Zhai

One of the distinguishing characteristics of modern deep learning systems is that they typically employ neural network architectures that utilize enormous numbers of parameters, often in the millions and sometimes even in the billions.…

Machine Learning · Statistics 2021-11-15 Ben Adlam , Jake Levinson , Jeffrey Pennington

As AI becomes a native component of 6G network control, AI models must adapt to continuously changing conditions, including the introduction of new features and measurements driven by multi-vendor deployments, hardware upgrades, and…

Machine Learning · Computer Science 2025-10-10 Yannis Belkhiter , Seshu Tirupathi , Giulio Zizzo , Merim Dzaferagic , John D. Kelleher

We consider the task of automated estimation of facial expression intensity. This involves estimation of multiple output variables (facial action units --- AUs) that are structurally dependent. Their structure arises from statistically…

Computer Vision and Pattern Recognition · Computer Science 2017-04-17 Robert Walecki , Ognjen , Rudovic , Vladimir Pavlovic , Björn Schuller , Maja Pantic

Facial action unit (AU) detection and face alignment are two highly correlated tasks since facial landmarks can provide precise AU locations to facilitate the extraction of meaningful local features for AU detection. Most existing AU…

Computer Vision and Pattern Recognition · Computer Science 2018-11-20 Zhiwen Shao , Zhilei Liu , Jianfei Cai , Lizhuang Ma

This article proposes a Universal Activation Function (UAF) that achieves near optimal performance in quantification, classification, and reinforcement learning (RL) problems. For any given problem, the optimization algorithms are able to…

Machine Learning · Computer Science 2022-11-07 Brosnan Yuen , Minh Tu Hoang , Xiaodai Dong , Tao Lu

Rectified linear unit (ReLU) activations can also be thought of as 'gates', which, either pass or stop their pre-activation input when they are 'on' (when the pre-activation input is positive) or 'off' (when the pre-activation input is…

Machine Learning · Computer Science 2021-06-15 Chandrashekar Lakshminarayanan , Amit Vikram Singh

It is well-known that overparametrized neural networks trained using gradient-based methods quickly achieve small training error with appropriate hyperparameter settings. Recent papers have proved this statement theoretically for highly…

Machine Learning · Computer Science 2020-04-13 Abhishek Panigrahi , Abhishek Shetty , Navin Goyal

Neural Networks (NNs) are the method of choice for building learning algorithms. Their popularity stems from their empirical success on several challenging learning problems. However, most scholars agree that a convincing theoretical…

Numerical Analysis · Mathematics 2021-01-01 Ronald DeVore , Boris Hanin , Guergana Petrova

The choice of activation functions in deep networks has a significant effect on the training dynamics and task performance. Currently, the most successful and widely-used activation function is the Rectified Linear Unit (ReLU). Although…

Neural and Evolutionary Computing · Computer Science 2017-10-30 Prajit Ramachandran , Barret Zoph , Quoc V. Le

We present a simple, effective, and general activation function we term ACON which learns to activate the neurons or not. Interestingly, we find Swish, the recent popular NAS-searched activation, can be interpreted as a smooth approximation…

Computer Vision and Pattern Recognition · Computer Science 2021-04-19 Ningning Ma , Xiangyu Zhang , Ming Liu , Jian Sun

Despite the empirical success of DNN, their internal training dynamics remain difficult to characterize. In ReLU-based models, the activation pattern induced by a given input determines the piecewise-linear region in which the network…

The success of artificial neural networks (ANNs) hinges greatly on the judicious selection of an activation function, introducing non-linearity into network and enabling them to model sophisticated relationships in data. However, the search…

Machine Learning · Computer Science 2024-05-24 Haoyuan Sun , Zihao Wu , Bo Xia , Pu Chang , Zibin Dong , Yifu Yuan , Yongzhe Chang , Xueqian Wang

Implicit Neural Representations (INRs) have emerged as a powerful framework for modeling continuous signals. The spectral bias of ReLU-based networks is a well-established limitation, restricting their ability to capture fine-grained…

Computer Vision and Pattern Recognition · Computer Science 2025-05-27 Alireza Morsali , MohammadJavad Vaez , Mohammadhossein Soltani , Amirhossein Kazerouni , Babak Taati , Morteza Mohammad-Noori

Alignment faking (AF) refers to a model strategically complying with a training objective to avoid behavioural modification while preserving its deployment preferences. Understanding when and why AF arises matters as models grow better at…

Artificial Intelligence · Computer Science 2026-05-28 Nathaniel Mitrani Hadida , Rhea Karty , David Williams-King , Alan Cooney