Understanding LeCun's Tanh Activation Function
In the field of artificial neural networks, an activation function is an important component of a neuron, used to introduce non-linearity in solving complex problems. The choice of activation function plays a crucial role in determining the performance of a neural network in terms of accuracy and convergence rate. One such popular activation function is the LeCun's Tanh, named after the French computer scientist Yann LeCun who introduced it.
The Definition of LeCun's Tanh
The mathematical expression of LeCun's Tanh is given as $f\left(x\right) = 1.7159\tanh\left(\frac{2}{3}x\right)$. The function takes an input value x, scales it by a factor of 2/3, applies the hyperbolic tangent function, and scales the output by a factor of 1.7159. The two constants in the function were chosen to keep the variance of the output close to 1. The hyperbolic tangent function, denoted by tanh, maps the input to the range of -1 to 1, thereby introducing non-linearity to the neuron's output.
The Advantages of LeCun's Tanh
LeCun's Tanh has several advantages over other activation functions such as the sigmoid function and the ReLU function. The sigmoid function, although widely used, has a problem called "vanishing gradient" where the gradient of the function approaches zero as the input tends towards positive or negative infinity. This makes it unsuitable for deep neural networks that require optimization through gradient descent. LeCun's Tanh overcomes this problem by producing outputs between a range of -1 and 1, preventing the vanishing gradient effect.
Similarly, the ReLU function, which is known for its simplicity and computational efficiency, has a disadvantage called "dying ReLU problem", where the neuron output becomes zero for negative inputs and remains stuck, resulting in the neuron becoming inactive. LeCun's Tanh avoids this issue by providing non-linear outputs for all inputs, effectively avoiding the "dying" of the neuron.
The Applications of LeCun's Tanh
LeCun's Tanh finds a wide range of applications in the field of deep learning, particularly in convolutional neural networks (CNNs) and recurrent neural networks (RNNs). In CNNs, the activation function is applied to the convolutional and pooling layers, whereas in RNNs, it is used to introduce non-linearity to the sequential input data. LeCun's Tanh has been used successfully in several image classification and speech recognition tasks, and its performance has been shown to be superior to that of other activation functions.
In summary, LeCun's Tanh activation function is an effective way to introduce non-linearity and prevent the vanishing gradient and dying ReLU problems in neural networks. Its simplicity, computational efficiency, and superior performance make it a popular choice for deep learning applications.
