!1ae#~s0t0n-“`python
def sigmoid(x):
“””Sigmoid function.
“””
return 1 / (1 + math.exp(-x))
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def relu(x):
“””ReLU function.
“””
return max(0, x)
def tanh(x):
“””Tanh function.
“””
return (math.exp(x) – math.exp(-x)) / (math.exp(x) + math.exp(-x))
def softmax(x):
“””Softmax function.
“””
exps = [math.exp(xi) for xi in x]
return [expi / sum(exps) for expi in exps]
1. `sigmoid(x)`: The sigmoid function is a smooth, S-shaped function that squashes input values between 0 and 1. It is often used in binary classification problems, where the output represents the probability of an input belonging to a particular class.
2. `relu(x)`: The ReLU function simply sets all negative input values to 0 and leaves positive values unchanged. Its main advantage is its simplicity and computational efficiency, making it a popular choice for deep neural networks.
3. `tanh(x)`: The tanh function is similar to the sigmoid function, but it produces output values between -1 and 1 instead of 0 and 1. It is often used in recurrent neural networks (RNNs) and long short-term memory (LSTM) networks.
4. `softmax(x)`: The softmax function is used in multi-class classification problems. It converts input values into a probability distribution, where each element represents the probability of the input belonging to a specific class. The sum of all output probabilities is always 1.
These activation functions play a crucial role in neural networks by introducing non-linearity and allowing the network to learn complex patterns in data. The choice of activation function depends on the specific problem being solved and the desired network architecture.
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