sigmoid function

Question 1

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Answer 1

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Question 2

sigmoid function

Answer 2

The sigmoid function, also known as the logistic function, is a type of activation function used in machine learning algorithms, especially in neural networks. Its mathematical formula is:
S(x) = 1 / (1 + e^-x) Here, ‘e’ is the base of the natural logarithm and ‘x’ is the input to the function.

Question 3

2. Value Range

Answer 3

The sigmoid function outputs a value between 0 and 1. This property makes it particularly useful for models where the output needs to be a probability, such as in binary classification problems.

Question 4

3. S-Shaped Curve

Answer 4

The sigmoid function forms an ‘S’-shaped curve when plotted on a graph. It starts near 0 for negative infinity, increases to 0.5 at x=0, and approaches 1 as x goes to positive infinity.

Question 5

4. Non-linear

Answer 5

The sigmoid function is non-linear. This makes it possible to adjust the output of the neurons based on the input and weights, which allows neural networks to learn from the error gradients during the backpropagation process.

Question 6

5. Gradient/Vanishing Gradient

Answer 6

The gradient of the sigmoid function is highest when the input is 0, and it is very close to 0 when the input is far from 0 (either in the positive or negative direction). This results in a problem called the vanishing gradient problem, where the gradients are so small that the weights and biases of the network hardly change during the learning process.

Question 7

6. Binary Classification

Answer 7

The sigmoid function is widely used in binary classification problems. It can take any real-valued number and map it into a value between 0 and 1, making it suitable for transforming the output of a linear model into a probability.

Question 8

7. Drawbacks

Answer 8

As mentioned, the sigmoid function can lead to a vanishing gradient problem, slowing down the training. It is also not zero-centered, which can make the optimization process more challenging.