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GATE DA 2025 Q48: Properties of the ReLU activation function

Question

Which of the following statements is/are correct about the rectified linear unit (ReLU) activation function defined as ReLU⁡(x)=max⁡(x,0)\operatorname{ReLU}(x) = \max(x, 0), where x∈Rx \in \mathbb{R}?

Try it: multiple select: one or more correct options

Select one or more options
Select all correct options. No negative marking, no partial marks.
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Answer: A, C (official GATE 2025 final answer key)

Concept used: Continuity and differentiability of piecewise-linear functions.

First step: Compare the left and right derivatives at 0: they are 0 and 1. For option D, try a counter-example such as a=2a = 2 or a=−1a = -1.

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Source: official GATE 2025 DA question paper and final answer key, organised by IIT Roorkee. Question paper · Answer key

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