Easy

ReLU Backward Pass

Easy

~10 min

code completion

ReLU Backward Pass

The ReLU activation function is:

ReLU (x) = max (0, x)

Its derivative is a step function:

\frac{\partial ReLU}{\partial x _{i}} = {10 x_{i} > 0 x_{i} \leq 0

During backpropagation we apply the chain rule: multiply the upstream gradient d_out by this local derivative element-wise:

\frac{\partial L}{\partial x _{i}} = d_o u t_{i} \cdot 1 [x_{i} > 0]

Gradients only flow through neurons that were active (positive) during the forward pass. Neurons where $x_{i} \leq 0$ receive zero gradient — the so-called dead neuron problem with ReLU.

Your task:

Implement relu_backward(x, d_out) that returns the gradient of the loss with respect to the pre-activation input x.

Example Tests

Mixed signs: gradient flows only where x > 0

Input: {"x":[1,-1,2],"d_out":[0.5,0.5,0.5]}

Expected: [0.5,0,0.5]

All negative: gradient is zero everywhere (dead neurons)

Input: {"x":[-1,-2,-3],"d_out":[1,1,1]}

Expected: [0,0,0]

All positive: upstream gradient passes through unchanged

Input: {"x":[1,2,3],"d_out":[2,3,4]}

Expected: [2,3,4]

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