A logistic regression computation graph

Input x = 2Weight w = 0.50

u = w · x1.000∂L/∂u = -0.500

Bias b = -1.00

z = u + b0.000∂L/∂z = -0.500

a = sigmoid(z)0.500∂L/∂a = -2.000

Target y = 1

L = binary cross entropy(a, y)0.693∂L/∂L = 1.000

Sigmoid

a = σ (z) = \frac{1}{1 + e^{- z}}

a = 1 / (1 + exp(0.000)) = 0.500

Binary cross entropy

L = - y \ln (a) - (1 - y) \ln (1 - a)

L = -1 ln(0.500) - 0 ln(0.500) = 0.693

Parameter gradients

∂L/∂w = -1.000 ∂L/∂b = -0.500

A small increase in w or b would reduce the loss here.