Language
Country/Area
No result found
The Mysterious Activation Function: Why Nonlinearity Allows Neural Networks to Solve Complex Problems?
The core of an artificial neural network lies in the activation function of each of its nodes, which calculates the output of the node based on specific input values and their weights. Through nonlinear activation functions, neural networks are able to calculate complex problems, just like the ability to see patterns in countless data, allowing simple nodes to solve very difficult problems. From the BERT model in 2018 to various computer vision models, several activation functions have contributed to the advancement of artificial intelligence in their own unique ways.
When the activation function is nonlinear, a two-layer neural network can be proved to be a universal function approximator, which is called the universal approximation theorem.
Comparison of Activation Functions
Different activation functions differ in mathematical properties. First, nonlinearity is key. The nonlinear nature of the activation function allows even fewer nodes to handle many complex problems. For example, the ReLU activation function is one of the most popular choices at present. Its characteristic is that the activation value increases linearly when the input is greater than zero, and is zero when the input is negative, thus avoiding the "vanishing gradient" problem.
Activation functions with limited range are generally more stable in gradient-based training methods, while activation functions with unlimited range are more efficient.
Common types of activation functions
Activation functions can be divided into three categories: ridge functions, radial functions, and fold functions. Different types of functions have different effects in various applications. For example, when using a linear activation function, the performance of the neural network will be limited to its single-layer structure. For multi-layer neural networks, using non-saturating activation functions such as ReLU usually works better for a wide range of data.
Ridge Activation Function
This type of function includes linear activation, ReLU activation, etc. The characteristic of these functions is that they respond in a linear manner to certain input values, which makes neural networks very effective when processing linearly structured data.
In biologically inspired neural networks, the activation function usually represents the firing rate of action potentials in a cell.
Radial Activation Function
The radial activation function used in the radial basis function network can be a Gaussian function or a multiple high-order function. This type of function is very suitable for processing multi-dimensional data and can provide better data fitting effects in most cases.
Folding Activation Function
Folding activation functions are widely used in pooling layers in convolutional neural networks. The characteristic of these functions is that they can aggregate the inputs, such as taking the average, minimum or maximum value, which helps to reduce the amount of calculation and Improve the computational efficiency of the model.
The Development of Quantum Activation Functions
In quantum neural networks, nonlinear activation functions can be flexibly implemented through the design of quantum circuits. Such a design not only improves computing power, but also retains characteristics such as superposition within the quantum circuit, paving the way for the development of future quantum computing technology.
Practical Application of Activation Functions
Although mathematical properties are not the only factor affecting the performance of activation functions, their design still has a decisive influence on the effectiveness of deep learning models. From a practical application perspective, choosing a suitable activation function can enable the model to learn patterns in the data more efficiently and play its unique role in different scenarios.In the practice of deep learning, understanding the characteristics of all activation functions helps to find the best solution.
The diversity of activation functions and their nonlinear characteristics enable neural networks to effectively handle complex problems. What new activation functions will appear in the future, and how will they further promote the evolution of artificial intelligence technology?
