ReLU, Sigmoid, Tanh activation functions detailed explanation

ReLU、Sigmoid、Tanh 激活函数详解

在神经网络中，激活函数是引入非线性因素的关键。它们将神经元的输入转化为输出，决定了神经元是否被激活。下面我们详细介绍三种常见的激活函数：ReLU、Sigmoid 和 Tanh。

1. ReLU（Rectified Linear Unit，修正线性单元）

  • 函数形式： f(x) = max(0, x)
  • 特点：
    • 优点：
      • 计算简单，收敛速度快。
      • 解决了Sigmoid函数在深层网络中容易出现的梯度消失问题。
      • 大部分神经元的输出为正，使得网络更容易学习。
    • 缺点：
      • 神经元可能出现“死亡”现象，即输出始终为0，导致权重无法更新。
  • 图像：

Image of ReLU activation function

  • 应用场景：
    • 深度神经网络中作为默认的激活函数。
    • CNN中，通常在卷积层后使用ReLU。

2. Sigmoid

  • 函数形式： f(x) = 1 / (1 + exp(-x))
  • 特点：
    • 优点：
      • 输出值在0到1之间，可以表示概率。
    • 缺点：
      • 计算量较大。
      • 饱和问题：当输入很大或很小时，导数接近于0，导致梯度消失，难以训练深层网络。
  • 图像：

Image of Sigmoid activation function

  • 应用场景：
    • 输出层，将神经网络的输出映射到0到1之间，表示概率。
    • 某些特定的场景，如二分类问题。

3. Tanh（双曲正切）

  • 函数形式： f(x) = (exp(x) - exp(-x)) / (exp(x) + exp(-x))
  • 特点：
    • 优点：
      • 输出值在-1到1之间，输出的均值是0，使得下一层网络的输入均值为0，加速收敛。
      • 解决了Sigmoid函数的饱和问题，但程度不如ReLU。
    • 缺点：
      • 计算量比ReLU大。
  • 图像：

Image of Tanh activation function

  • 应用场景：
    • 隐藏层，作为ReLU的替代。
    • RNN中，有时会使用Tanh。

总结

激活函数 公式 优点 缺点 应用场景
ReLU max(0, x) 计算简单，收敛快，缓解梯度消失 神经元可能“死亡” 深度神经网络
Sigmoid 1 / (1 + exp(-x)) 输出为概率，适用于二分类 计算量大，饱和问题 输出层，二分类
Tanh (exp(x) - exp(-x)) / (exp(x) + exp(-x)) 输出均值为0，缓解饱和问题 计算量比ReLU大 隐藏层，RNN

选择合适的激活函数

  • 一般情况下，ReLU是首选，因为它计算简单，收敛速度快，效果好。
  • 对于输出层，如果需要输出概率值，可以使用Sigmoid。
  • 对于隐藏层，如果遇到梯度消失问题，可以尝试Tanh或LeakyReLU。

影响激活函数选择因素

  • 网络深度：对于深层网络，ReLU更适合。
  • 数据分布：不同的数据分布可能需要不同的激活函数。
  • 优化算法：优化算法的选择也会影响激活函数的效果。

其他激活函数

除了ReLU、Sigmoid和Tanh，还有LeakyReLU、ELU、Swish等激活函数，它们在不同的场景下有各自的优势。

选择激活函数时，需要结合具体的任务和网络结构，进行实验和对比，才能找到最适合的激活函数。

Detailed Explanation of ReLU, Sigmoid, and Tanh Activation Functions

In neural networks, activation functions are key to introducing non-linear factors. They transform the input of neurons into output, determining whether the neuron is activated. Below we introduce three common activation functions in detail: ReLU, Sigmoid, and Tanh.

1. ReLU (Rectified Linear Unit)

  • Function Formula: f(x) = max(0, x)
  • Features:
    • Pros:
      • Simple calculation, fast convergence speed.
      • Solves the gradient vanishing problem that easily occurs with Sigmoid functions in deep networks.
      • The output of most neurons is positive, making the network easier to learn.
    • Cons:
      • Neurons may experience the “dying” phenomenon, where the output is consistently 0, leading to weights not being updated.
  • Image:

Image of ReLU activation function

  • Application Scenarios:
    • Used as the default activation function in deep neural networks.
    • In CNNs, ReLU is usually used after convolutional layers.

2. Sigmoid

  • Function Formula: f(x) = 1 / (1 + exp(-x))
  • Features:
    • Pros:
      • Output values are between 0 and 1, which can represent probability.
    • Cons:
      • Larger computational load.
      • Saturation problem: When the input is very large or very small, the derivative approaches 0, leading to gradient vanishing, making it difficult to train deep networks.
  • Image:

Image of Sigmoid activation function

  • Application Scenarios:
    • Output layer, mapping the neural network output to between 0 and 1 representing probability.
    • Certain specific scenarios, like binary classification problems.

3. Tanh (Hyperbolic Tangent)

  • Function Formula: f(x) = (exp(x) - exp(-x)) / (exp(x) + exp(-x))
  • Features:
    • Pros:
      • Output values are between -1 and 1, and the mean of the output is 0, making the input mean of the next layer 0, accelerating convergence.
      • Solves the saturation problem of the Sigmoid function, but not as effectively as ReLU.
    • Cons:
      • Computational load is larger than ReLU.
  • Image:

Image of Tanh activation function

  • Application Scenarios:
    • Hidden layers, as an alternative to ReLU.
    • Sometimes used in RNNs.

Summary

Activation Function Formula Pros Cons Application Scenarios
ReLU max(0, x) Simple calculation, fast convergence, mitigates gradient vanishing Neurons may “die” Deep Neural Networks
Sigmoid 1 / (1 + exp(-x)) Output is probability, suitable for binary classification Large calculation, saturation problem Output layer, Binary Classification
Tanh (exp(x) - exp(-x)) / (exp(x) + exp(-x)) Output mean is 0, mitigates saturation problem Larger calculation than ReLU Hidden layers, RNN

Choosing the Suitable Activation Function

  • Generally, ReLU is the first choice because it is simple to calculate, converges fast, and works well.
  • For the output layer, if you need to output probability values, you can use Sigmoid.
  • For hidden layers, if you encounter gradient vanishing problems, you can try Tanh or LeakyReLU.

Factors Influencing Activation Function Selection

  • Network Depth: For deep networks, ReLU is more suitable.
  • Data Distribution: Different data distributions may require different activation functions.
  • Optimization Algorithm: The choice of optimization algorithm can also affect the effectiveness of the activation function.

Other Activation Functions

Besides ReLU, Sigmoid, and Tanh, there are also activation functions like LeakyReLU, ELU, Swish, etc., which have their own advantages in different scenarios.

When choosing an activation function, you need to combine specific tasks and network structures to conduct experiments and comparisons in order to find the most suitable activation function.