Review and Comparison of Commonly Used Activation Functions for Deep Neural Networks (2010.09458v1)

Abstract: The primary neural networks decision-making units are activation functions. Moreover, they evaluate the output of networks neural node; thus, they are essential for the performance of the whole network. Hence, it is critical to choose the most appropriate activation function in neural networks calculation. Acharya et al. (2018) suggest that numerous recipes have been formulated over the years, though some of them are considered deprecated these days since they are unable to operate properly under some conditions. These functions have a variety of characteristics, which are deemed essential to successfully learning. Their monotonicity, individual derivatives, and finite of their range are some of these characteristics (Bach 2017). This research paper will evaluate the commonly used additive functions, such as swish, ReLU, Sigmoid, and so forth. This will be followed by their properties, own cons and pros, and particular formula application recommendations.

• The paper demonstrates that ReLU and its variants provide superior training efficiency and accuracy compared to traditional activation functions on the CIFAR-10 dataset.
• It analyzes various functions, detailing their mathematical properties and challenges such as vanishing gradients and the 'dying ReLU' effect.
• The study emphasizes selecting activation functions based on specific network architectures, encouraging further research into novel functions like Swish.

Analysis and Evaluation of Activation Functions in Deep Neural Networks

The paper "Review and Comparison of Commonly Used Activation Functions for Deep Neural Networks" by Tomasz Szandała presents a detailed examination of activation functions, key components that shape the decision-making ability of neural networks. The role of activation functions is pivotal as they significantly influence the performance and learning efficacy of the entire network. This paper explores various commonly used activation functions such as ReLU, Sigmoid, Tanh, and newer alternatives like Swish, providing an encompassing evaluation of their benefits and limitations, as well as insights into their applicability across different neural network architectures.

Deep learning applications span multiple use cases, including voice analysis, object classification, and pattern recognition, harnessing the capabilities of neural networks with numerous hidden layers. The paper outlines how deeper neural network architectures, such as VGGNet and ResNet, have emerged, offering better performance linked to increased layers. A critical challenge associated with these architectures is the selection of appropriate activation functions, which substantially impacts the efficacy of training algorithms like backpropagation.

Several activation functions are meticulously analyzed in this paper, emphasizing their mathematical formulations, differentiability, and computational efficiency. Among the examined functions, Sigmoid and Tanh are identified as traditional S-shaped activations, suitable for producing non-linear outputs while facing issues like vanishing gradients. In contrast, the Rectified Linear Unit (ReLU) function and its variations, including Leaky ReLU, are highlighted for their efficiency and ability to mitigate the vanishing gradient problem, albeit with their own challenges such as the "dying ReLU" phenomenon.

The exploration covers advanced activation functions like Softsign and Maxout, which offer distinct mathematical properties aimed at optimizing specific learning scenarios. Particularly, Swish, a novel activation function, is discussed for its purported advantages over ReLU in deeper networks due to its higher computational demands and improved mitigation of the vanishing gradient problem.

The comparative analysis conducted in the paper involves empirical evaluation using the CIFAR-10 dataset, which comprises color images across ten classes. The neural network employed in these experiments features two convolutional layers, and each activation function's performance is assessed based on classification accuracy and training speed. Notably, ReLU-based networks demonstrate superior performance, corroborating ReLU's continued reliability in practical applications. Moreover, the empirical results underscore ReLU's efficiency in training time, a crucial factor in large-scale deep learning applications.

From a theoretical and practical perspective, the implications of this paper underscore the absence of a one-size-fits-all solution regarding activation function choices. The nuanced performance characteristics of each activation function necessitate careful consideration based on the specific requirements of the neural network model and the application domain. For future developments, the paper suggests exploring further novel activations and adapting function properties to suit the complexity and scale of evolving deep learning tasks.

The insights provided by Szandała’s paper are valuable for researchers and practitioners aiming to optimize neural network performance through informed activation function selection. As deep learning continues to evolve and applications increase in complexity, the prudent choice and application of activation functions remain integral to achieving high-performance outcomes.