Weight update Δwj for GD, mini-batch GD and SGD
15 → 25 → 1 network, sigmoid + binary cross-entropy, no biases. Derive the gradient, then see how many examples each method averages over.
Answer: options 1, 2 and 3. Gradient per example is (ŷ − y)·hj. GD: sum over all N, ÷ N. Mini-batch: sum over B, ÷ B. SGD: one example, no division. Option 4 counts σ′ twice; option 5 has the wrong B/N scaling; option 6 is the mini-batch rule labelled as SGD.