Which Numbers Have a Slope?

A model predicts $\hat{y} = wx + b$ . Its loss on a single training example $(x, y)$ is the squared error

$L(w, b) = \left(wx + b - y\right)^2$

Before training begins, the team fixes the learning rate at $\alpha = 0.1$ and the number of epochs at $E = 50$ . The training example is $x = 2$ , $y = 5$ , and the current parameters are $w = 1$ , $b = 1$ .

Evaluate $\dfrac{\partial L}{\partial w}$ and $\dfrac{\partial L}{\partial b}$ at this setting — and decide whether $\dfrac{\partial L}{\partial \alpha}$ is something you could compute as well.

Which Numbers Have a Slope?

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