Inferece equation

[avishai111]

In your lecture on the inference equation looks like this:

And on the other hand, the reference of the score looks like:
s = hat(w_0)@hat(x_i)
How does it work out?
It is clear to me that the equation above returns between 0 and 1.
But what you implemented in the code returns between -1 and 1.
But the first equation multiplies by alpha in the inference, and the second does not.
I would love your opinion on this
Thanks