Let \(W_{ππ}\) represents weight between node \(π\) at layer \(π\) andβ¦
2019
LetΒ \(W_{ππ}\)Β represents weight between nodeΒ \(π\)Β at layerΒ \(π\)Β and nodeΒ \(π\)Β at layerΒ \((πβ1)\)Β 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.
\(\textbf{W}_{ij}(t+1) = β \alpha \dfrac{\partial \textbf{E}}{\partial \textbf{W}_{ij}}, 0 \leq \alpha \leq 1\)
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Correct answer: B
Correct update rule: W_ij(t+1) = W_ij(t) - Ξ± * (βE/βW_ij).
Explanation:
The gradient βE/βW_ij points in the direction of greatest increase of the error E.
Subtracting Ξ± 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.
Ξ± (the learning rate) is a small positive scalar that controls step size. Typical practice is to choose Ξ± 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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