Backprop with Multiple (x1,x2,y) Data Points — Line Chart & Layout

x1
x2
Bias(H)
(=1)
h1
h2
Bias(O)
(=1)
ŷ

Dataset (multiple points)

Enter multiple rows of (x1, x2, y). Then click "Train 1 Epoch".

x1 x2 y

Epoch MSE History (Line Chart)

Math Equations (Reference)

For each data point d in an epoch:
1) Forward pass: z(1) = W(1)x + b(1)
a(1) = sigmoid(z(1))
z(2) = W(2)a(1) + b(2)
a(2) = sigmoid(z(2))
MSEd = 1/2 (y - a(2))²

2) Backward pass (sample-by-sample update):
δ(2) = (a(2) - y) . sigmoid'(z(2))
δ(1) = (W(2))ᵀ δ(2) . sigmoid'(z(1))
W(l) ← W(l) - η δ(l) (a(l-1))ᵀ
b(l) ← b(l) - η δ(l)

3) At end of epoch, compute mean MSE = (1 / N) Σ MSEd.