Activation Functions in Artificial Neural Networks: A Systematic Overview (2101.09957v1)

Abstract: 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.

• The paper provides a systematic categorization of activation functions, detailing their mathematical properties and impact on training dynamics.
• It evaluates common functions such as sigmoid, ReLU, and adaptive variants, highlighting issues like vanishing gradients and dead neurons.
• The framework bridges theoretical analysis with practical recommendations, encouraging data-driven approaches for optimal neural network design.

Overview of Activation Functions in Artificial Neural Networks

The paper "Activation Functions in Artificial Neural Networks: A Systematic Overview" by Johannes Lederer provides a comprehensive examination of activation functions, which are pivotal in defining the output of neurons in neural networks (NNs). The paper systematically analyzes various activation functions, categorizing them and evaluating their properties both mathematically and in terms of practical implications.

Introduction to Activation Functions

Activation functions are essential components of artificial neurons and inherently govern the behavior and performance of neural networks. Historically, functions like logistic and ReLU have dominated the field, but with the advent of deep learning, a plethora of new activation functions have emerged. This paper seeks to demystify activation functions by offering a rigorous and structured overview that bridges theoretical constructs and practical utility.

Common Activation Functions

The discussion in the paper spans several categories of activation functions:

1. Sigmoid Functions: These functions include the logistic sigmoid, hyperbolic tangent (Tanh), the inverse tangent (Arctan), and the softsign. Sigmoid functions are inherently bounded and differentiable, often inspired by biological neuron firing patterns. They function by compressing inputs to a limited output range but are prone to issues such as vanishing gradients. The paper provides detailed derivatives and output properties of these functions.
2. Piecewise-Linear Functions: Among these, the ReLU (Rectified Linear Unit) stands out due to its simplicity and effectiveness in mitigating the vanishing gradient problem, further expanding into variants like Leaky ReLU (LReLU). These functions are computationally efficient but introduce issues like dead neurons in ReLU networks, which the paper discusses comprehensively.
3. Other Activation Functions: The paper also covers newer functions like Swish and parametric functions, where parameters can be tuned or learned, adding a layer of adaptability. Functions like Swish, which is non-monotonic, offer potential advantages in expressiveness.

Mathematical Properties and Practical Implications

The analysis explores the expressivity of these functions, particularly focusing on computational efficiency and how the choice of function impacts the training dynamics of neural networks. For instance, ReLU networks are shown to outperform purely linear models by incorporating nonlinear decision boundaries, thereby enhancing network capacity. The differentiability of functions like Softplus offers mathematical elegance, although this may come at a higher computational cost.

Speculative Discussion on Future Directions

The exploration of activation functions remains dynamic, driven by both theoretical insights and empirical validation. This paper encourages automating the search for optimal activations and data-driven adaptations, hinting at integration within broader neural network architectures for improved performance.

In summary, the paper by Lederer is an invaluable resource for researchers and practitioners seeking a nuanced understanding of activation functions. It combines mathematical rigor with practical recommendations, positioning itself as a foundational text for ongoing research and development in neural networks. The systematic framework laid out by Lederer may influence future innovation in activation function design, potentially leading to more robust and adaptive neural architectures in artificial intelligence.