Which properties are true for the sigmoid activation function? convex monotonically nondecreasing invertible has a zero gradient at multiple points none are true
The sigmoid activation function is commonly used in artificial neural networks and is defined as:
sigmoid(x) = 1 / (1 + exp(-x))
where x is the input value to the function. Here are some properties of the sigmoid activation function:
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Convexity: The sigmoid function is not convex since its second derivative can be negative for some input values. A function is convex if its second derivative is non-negative for all input values.
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Monotonicity: The sigmoid function is monotonically non-decreasing, which means that if the input value to the function increases, then the output value also increases. However, it is not strictly monotonically increasing, as there are certain regions where the gradient of the function is close to zero.
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Invertibility: The sigmoid function is invertible since it passes the horizontal line test. In other words, each input value maps to a unique output value, and each output value maps to a unique input value.
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Zero gradient: The sigmoid function has a zero gradient at the points where its output is 0.5. This happens when the input value is 0, and when it approaches positive and negative infinity. However, it does not have zero gradients at multiple points.
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