Hard

MSE Loss Gradient

Hard

~15 min

code completion

Gradient of MSE Loss

To train a model with gradient descent, we need to compute how the loss changes with respect to the predictions — the gradient $\frac{\partial L}{\partial y ^}$ .

For MSE loss $L = \frac{1}{m} \sum_{i} (\overset{y}{^}_{i} - y_{i})^{2}$ :

\frac{\partial L}{\partial y ^ _{i}} = \frac{2 ( y ^ _{i} - y _{i} )}{m}

This gradient vector is then backpropagated through the network to update the weights.

Note: prediction minus true (not true minus prediction). Getting this sign wrong flips gradient descent into gradient ascent!

Your task:

Implement mse_gradient(y_true, y_pred) that returns the gradient vector.

Example Tests

y_pred above y_true: positive gradient

Input: {"y_pred":[2,2,2],"y_true":[1,2,3]}

Expected: [0.66667,0,-0.66667]

Perfect predictions: zero gradient

Input: {"y_pred":[1,2,3],"y_true":[1,2,3]}

Expected: [0,0,0]

Single prediction

Input: {"y_pred":[1],"y_true":[3]}

Expected: [-4]

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