Neural networks have proven to be a highly effective tool for solving complex problems in many areas of life. Recently, their importance and practical usability have further been reinforced with the advent of deep learning. One of the important conditions for the success of neural networks is the choice of an appropriate activation function introducing non-linearity into the model. Many types of these functions have been proposed in the literature in the past, but there is no single comprehensive source containing their exhaustive overview. The absence of this overview, even in our experience, leads to redundancy and the unintentional rediscovery of already existing activation functions. To bridge this gap, our paper presents an extensive survey involving 400 activation functions, which is several times larger in scale than previous surveys. Our comprehensive compilation also references these surveys; however, its main goal is to provide the most comprehensive overview and systematization of previously published activation functions with links to their original sources. The secondary aim is to update the current understanding of this family of functions.
Indian Institute of Information Technology, Allahabad（印度理工学院信息技术学院（阿拉哈巴德））；Techno India University（泰克诺印度大学）；Indian Statistical Institute（印度统计研究所）
Neural networks have shown tremendous growth in recent years to solve numerous problems. Various types of neural networks have been introduced to deal with different types of problems. However, the main goal of any neural network is to transform the non-linearly separable input data into more linearly separable abstract features using a hierarchy of layers. These layers are combinations of linear and nonlinear functions. The most popular and common non-linearity layers are activation functions (AFs), such as Logistic Sigmoid, Tanh, ReLU, ELU, Swish and Mish. In this paper, a comprehensive over…
Activation functions shape the outputs of artificial neurons and, therefore, are integral parts of neural networks in general and deep learning in particular. Some activation functions, such as logistic and relu, have been used for many decades. But with deep learning becoming a mainstream research topic, new activation functions have mushroomed, leading to confusion in both theory and practice. This paper provides an analytic yet up-to-date overview of popular activation functions and their properties, which makes it a timely resource for anyone who studies or applies neural networks.
In the last decade, an active area of research has been devoted to design novel activation functions that are able to help deep neural networks to converge, obtaining better performance. The training procedure of these architectures usually involves optimization of the weights of their layers only, while non-linearities are generally pre-specified and their (possible) parameters are usually considered as hyper-parameters to be tuned manually. In this paper, we introduce two approaches to automatically learn different combinations of base activation functions (such as the identity function, ReL…
Stony Brook University（石溪大学）；Tencent AI Lab（腾讯人工智能实验室）
Multi-task learning (MTL) is a common paradigm that seeks to improve the generalization performance of task learning by training related tasks simultaneously. However, it is still a challenging problem to search the flexible and accurate architecture that can be shared among multiple tasks. In this paper, we propose a novel deep learning model called Task Adaptive Activation Network (TAAN) that can automatically learn the optimal network architecture for MTL. The main principle of TAAN is to derive flexible activation functions for different tasks from the data with other parameters of the net…
The weight initialization and the activation function of deep neural networks have a crucial impact on the performance of the training procedure. An inappropriate selection can lead to the loss of information of the input during forward propagation and the exponential vanishing/exploding of gradients during back-propagation. Understanding the theoretical properties of untrained random networks is key to identifying which deep networks may be trained successfully as recently demonstrated by Samuel et al (2017) who showed that for deep feedforward neural networks only a specific choice of hyperp…
Adaptive Parametric Activation: Unifying and Generalising Activation Functions Across Tasks
Huawei Noah’s Ark Lab（华为诺亚实验室）；Department of Computing, Imperial College London（帝国理工学院计算机系）；Department of Computer Science, University of Liverpool（利物浦大学计算机科学系）；Department of Engineering, King’s College London（伦敦国王学院工程系）
We investigate the loss surface of neural networks. We prove that even for one-hidden-layer networks with "slightest" nonlinearity, the empirical risks have spurious local minima in most cases. Our results thus indicate that in general "no spurious local minima" is a property limited to deep linear networks, and insights obtained from linear networks may not be robust. Specifically, for ReLU(-like) networks we constructively prove that for almost all practical datasets there exist infinitely many local minima. We also present a counterexample for more general activations (sigmoid, tanh, arctan…
Technische Universität Wien (TU Wien)（维也纳工业大学（TU Wien））
Deep Neural Networks (DNNs) are widely being adopted for safety-critical applications, e.g., healthcare and autonomous driving. Inherently, they are considered to be highly error-tolerant. However, recent studies have shown that hardware faults that impact the parameters of a DNN (e.g., weights) can have drastic impacts on its classification accuracy. In this paper, we perform a comprehensive error resilience analysis of DNNs subjected to hardware faults (e.g., permanent faults) in the weight memory. The outcome of this analysis is leveraged to propose a novel error mitigation technique which …
Centre for Frontier AI Research, A*STAR（新加坡科技研究局前沿人工智能研究中心）；New York University（纽约大学）；Nanyang Technological University（南洋理工大学）；Tianjin University（天津大学）；University of South Carolina（南卡罗来纳大学）
Adversarial training (AT) is one of the most effective ways for improving the robustness of deep convolution neural networks (CNNs). Just like common network training, the effectiveness of AT relies on the design of basic network components. In this paper, we conduct an in-depth study on the role of the basic ReLU activation component in AT for robust CNNs. We find that the spatially-shared and input-independent properties of ReLU activation make CNNs less robust to white-box adversarial attacks with either standard or adversarial training. To address this problem, we extend ReLU to a novel Sp…
University of California San Diego（加州大学圣地亚哥分校）；Academia Sinica（中央研究院）；Taiwan AI Labs（台湾人工智能实验室）
Recent years have seen adversarial losses been applied to many fields. Their applications extend beyond the originally proposed generative modeling to conditional generative and discriminative settings. While prior work has proposed various output activation functions and regularization approaches, some open questions still remain unanswered. In this paper, we aim to study the following two research questions: 1) What types of output activation functions form a well-behaved adversarial loss? 2) How different combinations of output activation functions and regularization approaches perform empi…
Polynomial Composition Activations: Unleashing the Dynamics of Large Language Models
School of Mathematical Sciences, Peking University（北京大学数学科学学院）；Seed-Foundation-Model, ByteDance（字节跳动种子大模型部）；Capital University of Economics and Business（首都经济贸易大学）
Université Laval（拉瓦尔大学）；Inria（法国国家信息与自动化研究所）；University College London（伦敦大学学院）
We present a comprehensive study of multilayer neural networks with binary activation, relying on the PAC-Bayesian theory. Our contributions are twofold: (i) we develop an end-to-end framework to train a binary activated deep neural network, (ii) we provide nonvacuous PAC-Bayesian generalization bounds for binary activated deep neural networks. Our results are obtained by minimizing the expected loss of an architecture-dependent aggregation of binary activated deep neural networks. Our analysis inherently overcomes the fact that binary activation function is non-differentiable. The performance…
Tsinghua University（清华大学）；University of Illinois at Chicago（伊利诺伊大学芝加哥分校）
Learning to hash has been widely applied to approximate nearest neighbor search for large-scale multimedia retrieval, due to its computation efficiency and retrieval quality. Deep learning to hash, which improves retrieval quality by end-to-end representation learning and hash encoding, has received increasing attention recently. Subject to the ill-posed gradient difficulty in the optimization with sign activations, existing deep learning to hash methods need to first learn continuous representations and then generate binary hash codes in a separated binarization step, which suffer from substa…
University of Wisconsin-Madison（威斯康星大学麦迪逊分校）；The Chinese University of Hong Kong（香港中文大学）
To verify safety and robustness of neural networks, researchers have successfully applied abstract interpretation, primarily using the interval abstract domain. In this paper, we study the theoretical power and limits of the interval domain for neural-network verification. First, we introduce the interval universal approximation (IUA) theorem. IUA shows that neural networks not only can approximate any continuous function $f$ (universal approximation) as we have known for decades, but we can find a neural network, using any well-behaved activation function, whose interval bounds are an arbitra…
Otto von Guericke University Magdeburg（马格德堡奥托·冯·格里克大学）
Deep Learning based Automatic Speech Recognition (ASR) models are very successful, but hard to interpret. To gain better understanding of how Artificial Neural Networks (ANNs) accomplish their tasks, introspection methods have been proposed. Adapting such techniques from computer vision to speech recognition is not straight-forward, because speech data is more complex and less interpretable than image data. In this work, we introduce Gradient-adjusted Neuron Activation Profiles (GradNAPs) as means to interpret features and representations in Deep Neural Networks. GradNAPs are characteristic re…
Activation Steering Induces Emergent Misalignment: Steering Vector Construction and Comprehensive Evaluation
Nanyang Technological University（南洋理工大学）；Sun Yat-sen University（中山大学）；University of Science and Technology of China（中国科学技术大学）；National University of Singapore（新加坡国立大学）
The last decade, (2012 - 2022), saw an unprecedented advance in machine learning (ML) techniques, particularly deep learning (DL). As a result of the proven capabilities of DL, a large amount of work has been presented and studied in almost every field. Since 2012, when the convolution neural networks have been reintroduced in the context of \textit{ImagNet} competition, DL continued to achieve superior performance in many challenging tasks and problems. Wireless communications, in general, and medium access control (MAC) techniques, in particular, were among the fields that were heavily affec…
VŠB-Technical University of Ostrava（俄斯特拉发技术大学）；Machine Intelligence Research Labs (MIR Labs)（机器智能研究实验室）
Over the past two decades, the feedforward neural network (FNN) optimization has been a key interest among the researchers and practitioners of multiple disciplines. The FNN optimization is often viewed from the various perspectives: the optimization of weights, network architecture, activation nodes, learning parameters, learning environment, etc. Researchers adopted such different viewpoints mainly to improve the FNN's generalization ability. The gradient-descent algorithm such as backpropagation has been widely applied to optimize the FNNs. Its success is evident from the FNN's application …
Change Detection Methods for Remote Sensing in the Last Decade: A Comprehensive Review
University of Liverpool（利物浦大学）；Beihang University（北京航空航天大学）；Cambridge University（剑桥大学）；Institute of Automation, Chinese Academy of Sciences（中国科学院自动化研究所）
University of Wisconsin-Madison（威斯康星大学麦迪逊分校）；Facebook AI Research（Facebook人工智能研究院）
Out-of-distribution (OOD) detection has received much attention lately due to its practical importance in enhancing the safe deployment of neural networks. One of the primary challenges is that models often produce highly confident predictions on OOD data, which undermines the driving principle in OOD detection that the model should only be confident about in-distribution samples. In this work, we propose ReAct--a simple and effective technique for reducing model overconfidence on OOD data. Our method is motivated by novel analysis on internal activations of neural networks, which displays hig…
Exploration of Activation Fault Reliability in Quantized Systolic Array-Based DNN Accelerators
Tallinn University of Technology（塔林理工大学）；University of Alberta（阿尔伯塔大学）；Shahid Bahonar University of Kerman（克尔曼沙希德·巴霍纳尔大学）；York University（约克大学）；Mälardalen University（梅拉达伦大学）
Shanghai Jiao Tong University（上海交通大学）；Yitu Tech（依图科技）；University College London（伦敦大学学院）
Class labels have been empirically shown useful in improving the sample quality of generative adversarial nets (GANs). In this paper, we mathematically study the properties of the current variants of GANs that make use of class label information. With class aware gradient and cross-entropy decomposition, we reveal how class labels and associated losses influence GAN's training. Based on that, we propose Activation Maximization Generative Adversarial Networks (AM-GAN) as an advanced solution. Comprehensive experiments have been conducted to validate our analysis and evaluate the effectiveness o…
National University of Defense Technology（中国人民解放军国防科技大学）；University of Oulu（奥卢大学）；University of Waterloo（滑铁卢大学）；University of Maryland（马里兰大学）
Texture is a fundamental characteristic of many types of images, and texture representation is one of the essential and challenging problems in computer vision and pattern recognition which has attracted extensive research attention. Since 2000, texture representations based on Bag of Words (BoW) and on Convolutional Neural Networks (CNNs) have been extensively studied with impressive performance. Given this period of remarkable evolution, this paper aims to present a comprehensive survey of advances in texture representation over the last two decades. More than 200 major publications are cite…
Computational Tradeoffs of Optimization-Based Bound Tightening in ReLU Networks
Universidad de Chile（智利大学）；Bucknell University（巴克内尔大学）；Pontificia Universidad Católica de Chile（智利天主教大学）；Universidad de O’Higgins（奥希金斯大学）；Instituto Sistemas Complejos de Ingeniería (ISCI)（复杂系统工程研究所）
Academy of Mathematics and Systems Science, Chinese Academy of Sciences（中国科学院数学与系统科学研究院）；The First Affiliated Hospital of Guangzhou Medical University（广州医科大学附属第一医院）；State Key Laboratory of Respiratory Disease（呼吸疾病国家重点实验室）；University of Wisconsin-Madison（威斯康星大学麦迪逊分校）；University of Chinese Academy of Sciences（中国科学院大学）
Lung cancer is the commonest cause of cancer deaths worldwide, and its mortality can be reduced significantly by performing early diagnosis and screening. Since the 1960s, driven by the pressing needs to accurately and effectively interpret the massive volume of chest images generated daily, computer-assisted diagnosis of pulmonary nodule has opened up new opportunities to relax the limitation from physicians' subjectivity, experiences and fatigue. And the fair access to the reliable and affordable computer-assisted diagnosis will fight the inequalities in incidence and mortality between popul…
University of Verona（维罗纳大学）；University of Florida（佛罗里达大学）
In the last decade, Human Activity Recognition (HAR) has become a vibrant research area, especially due to the spread of electronic devices such as smartphones, smartwatches and video cameras present in our daily lives. In addition, the advance of deep learning and other machine learning algorithms has allowed researchers to use HAR in various domains including sports, health and well-being applications. For example, HAR is considered as one of the most promising assistive technology tools to support elderly's daily life by monitoring their cognitive and physical function through daily activit…
