Rectified Linear Activation Function

EASY10 pts

In deep learning, activation functions are crucial non-linear transformations that enable neural networks to learn complex patterns. Without them, stacking multiple linear layers would simply collapse into a single linear transformation, severely limiting the network's expressive power.

The Rectified Linear activation function has become one of the most widely adopted activation functions in modern neural network architectures. Its elegant simplicity and computational efficiency have made it the default choice for hidden layers in many state-of-the-art models.

Mathematical Definition:

The rectified linear function is defined as:

$$f(z) = \max(0, z)$$

This can also be expressed piecewise as:

$$f(z) = \begin{cases} z & \text{if } z > 0 \ 0 & \text{if } z \leq 0 \end{cases}$$

Key Properties:

Non-linearity: Despite its simple formulation, the function introduces essential non-linearity at the threshold point (z = 0)
Sparsity: By outputting zero for all negative inputs, it naturally creates sparse activations in neural networks
Computational Efficiency: Involves only a simple comparison and selection operation—no expensive exponentials or divisions
Gradient Behavior: The gradient is either 0 or 1, which helps mitigate the vanishing gradient problem common with sigmoid-like activations

Your Task:

Write a function that implements the rectified linear activation function. Given a single floating-point input value, your function should:

Return the input value unchanged if it is strictly positive (z > 0)
Return zero (0) if the input is zero or negative (z ≤ 0)

Example

Input

z = 0

Output

0

Explanation

When the input is exactly zero, the rectified linear function returns 0. The function only passes through positive values, and zero is treated as a non-positive input that gets mapped to zero output.

Example

Input

z = 1

Output

1

Explanation

When the input is positive (z = 1 > 0), the rectified linear function acts as an identity function and returns the input unchanged. The value 1 passes through without modification.

Example

Input

z = -1

Output

0

Explanation

For negative inputs, the rectified linear function outputs zero. Since -1 < 0, the function suppresses this activation, returning 0 instead of the negative value. This 'rectification' behavior is what gives the function its name.

Accepted1/1·100% Acceptance

Constraints

-10⁸ ≤ z ≤ 10⁸
Input z is a floating-point number (can be an integer represented as float)
Output should maintain the same precision as input for positive values

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Rectified Linear Activation Function

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