What is the derivative of the ReLU function?
Understand the Problem
The question is asking for the derivative of the ReLU (Rectified Linear Unit) function, which is commonly used in machine learning and neural networks. The ReLU function is defined as f(x) = max(0, x), and its derivative will be piecewise and depend on the value of x.
Answer
f'(x) = 0 for x < 0; f'(x) = 1 for x > 0; undefined at x = 0
The derivative of the ReLU function is: f'(x) = 0 for x < 0; f'(x) = 1 for x > 0; and it is undefined for x = 0.
Answer for screen readers
The derivative of the ReLU function is: f'(x) = 0 for x < 0; f'(x) = 1 for x > 0; and it is undefined for x = 0.
More Information
The ReLU function, used frequently in neural networks, offers computational efficiency and mitigates the vanishing gradient problem, despite having an undefined derivative at x=0.
Tips
A common mistake is assuming the derivative of ReLU at x=0 is either 0 or 1. It's important to note that it is actually undefined.
Sources
- ReLU derivative in backpropagation - neural network - Stack Overflow - stackoverflow.com
- What is the derivative of the ReLU activation function? - stats.stackexchange.com
- Dissecting Relu: A deceptively simple activation function - ML-DAWN - mldawn.com
