Both tanh and softmax are activation functions used in neural networks, but they are used for different purposes and in different parts of the network.
Tanh is the hyperbolic tangent function, which takes a real-valued number as input and returns a value between -1 and 1. It is defined as follows:
tanh(x) = (e^x - e^-x) / (e^x + e^-x)
The tanh activation function is commonly used in the hidden layers of a neural network. It is a non-linear function that maps the input values to a range between -1 and 1, and it is symmetric around the origin. This makes it useful for normalizing the input values and preventing them from becoming too large or too small, which can lead to unstable behavior in the network. Tanh is also useful for modeling complex relationships between inputs and outputs.
Softmax is a function that takes a vector of real numbers as input and returns a probability distribution over those numbers. It is defined as follows:
softmax(x_i) = e^(x_i) / (sum_j e^(x_j))
where x_i is the i-th element of the input vector, and the sum is taken over all elements of the vector.
Each element of the output vector produced by softmax is in the range of [0, 1]. Furthermore, the sum of all elements in the output vector is equal to 1, which means that the output vector represents a probability distribution over the inputs.
The softmax activation function, on the other hand, is commonly used in the output layer of a neural network. It takes a vector of real-valued inputs and normalizes them into a probability distribution over the output classes. The softmax function ensures that the output probabilities sum to 1, which makes it useful for classification tasks where the goal is to predict the probability of an input belonging to each of several classes.
In summary, tanh and softmax are both important activation functions in neural networks, but they are used for different purposes. tanh is useful for modeling complex relationships between inputs and outputs in the hidden layers, while softmax is useful for producing a probability distribution over the output classes in the final layer. The choice of activation function depends on the specific requirements of the neural network and the problem it is trying to solve.
Tanh is the hyperbolic tangent function, which takes a real-valued number as input and returns a value between -1 and 1. It is defined as follows:
tanh(x) = (e^x - e^-x) / (e^x + e^-x)
The tanh activation function is commonly used in the hidden layers of a neural network. It is a non-linear function that maps the input values to a range between -1 and 1, and it is symmetric around the origin. This makes it useful for normalizing the input values and preventing them from becoming too large or too small, which can lead to unstable behavior in the network. Tanh is also useful for modeling complex relationships between inputs and outputs.
Softmax is a function that takes a vector of real numbers as input and returns a probability distribution over those numbers. It is defined as follows:
softmax(x_i) = e^(x_i) / (sum_j e^(x_j))
where x_i is the i-th element of the input vector, and the sum is taken over all elements of the vector.
Each element of the output vector produced by softmax is in the range of [0, 1]. Furthermore, the sum of all elements in the output vector is equal to 1, which means that the output vector represents a probability distribution over the inputs.
The softmax activation function, on the other hand, is commonly used in the output layer of a neural network. It takes a vector of real-valued inputs and normalizes them into a probability distribution over the output classes. The softmax function ensures that the output probabilities sum to 1, which makes it useful for classification tasks where the goal is to predict the probability of an input belonging to each of several classes.
In summary, tanh and softmax are both important activation functions in neural networks, but they are used for different purposes. tanh is useful for modeling complex relationships between inputs and outputs in the hidden layers, while softmax is useful for producing a probability distribution over the output classes in the final layer. The choice of activation function depends on the specific requirements of the neural network and the problem it is trying to solve.
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