After one exact parameter update, the same toy example can be run forward again with only w11 changed. This lesson recomputes the immediate arithmetic effect without making a training or convergence claim.
highlighted = computed this step
Use the updated weight
Now keep the same input and change only w11 to 3/2. The first hidden weighted sum uses x1=1, x2=2, unchanged w12=1, and b1=-1.
z1new=3/2⋅1+1⋅2−1
Recompute the hidden activation
The first hidden pre-activation is 3/2*1 + 1*2 - 1 = 5/2. Since that is positive, ReLU stays open and h1 becomes 5/2. The second hidden activation remains 0.
z1new=5/2,h1new=5/2
Recompute output and loss
With h1=5/2 and h2=0, the output is yhat=5/2. The target is y=3, so the same-example loss is (5/2 - 3) squared = 1/4.
Lnew=(5/2−3)2=1/4
Compare on the same example
The old loss on this same row was 1. After changing only w11, the recomputed loss is 1/4. This is the immediate arithmetic effect on the same example only: not training, not convergence, not learning, and no generalization claim is made.