Let \(W_{๐๐}\) represents weight between node \(๐\) at layer \(๐\) andโฆ
2019
Letย \(W_{๐๐}\)ย represents weight between nodeย \(๐\)ย at layerย \(๐\)ย and nodeย \(๐\)ย at layerย \((๐โ1)\)ย of a given multilayer perceptron. The weight updation using gradient descent method is given by
- A.
\(\textbf{W}_{ij}(t+1) = \textbf{W}_{ij}(t)+ \alpha \dfrac{\partial \textbf{E}}{\partial \textbf{W}_{ij}}, 0 \leq \alpha \leq 1\) - B.
\(\textbf{W}_{ij}(t+1) = \textbf{W}_{ij}(t)- \alpha \dfrac{\partial \textbf{E}}{\partial \textbf{W}_{ij}}, 0 \leq \alpha \leq 1\) - C.
\(\textbf{W}_{ij}(t+1) = \alpha \dfrac{\partial \textbf{E}}{\partial \textbf{W}_{ij}}, 0 \leq \alpha \leq 1\) - D.
\(\textbf{W}_{ij}(t+1) = โ \alpha \dfrac{\partial \textbf{E}}{\partial \textbf{W}_{ij}}, 0 \leq \alpha \leq 1\)
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Correct answer: B
Correct update rule: W_ij(t+1) = W_ij(t) - ฮฑ * (โE/โW_ij).
Explanation:
The gradient โE/โW_ij points in the direction of greatest increase of the error E.
Subtracting ฮฑ times the gradient moves the weight opposite to that direction, reducing the error.
W_ij(t) is the current weight; the update is incremental (new = old + step). Do not discard the current weight.
ฮฑ (the learning rate) is a small positive scalar that controls step size. Typical practice is to choose ฮฑ small enough to ensure stable descent.
Summary: The correct weight update for gradient descent uses the previous weight minus the learning rate times the gradient, which ensures movement toward lower error.
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