The cost function of a general neural network is defined as J(ŷ,y) 1 m L(VW), y() The loss function L(ỹ(¹), y() is defined by the logistic loss function L(¹),y) = [ylogy) + (1-y)log (1 - ¹)] Please list the stochastic gradient descent update rule, batch gradient descent update rule, and mini-batch gradient descent update rule. Explain the main difference of these three update rules.

Operations Research : Applications and Algorithms
4th Edition
ISBN:9780534380588
Author:Wayne L. Winston
Publisher:Wayne L. Winston
Chapter20: Queuing Theory
Section20.4: The M/m/1/gd/∞/∞ Queuing System And The Queuing Formula L = Λw
Problem 14P
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The cost function of a general neural network is defined as
J(ŷ,y) =
m
// [4 (9(0), y(1)
The loss function L(ŷ), y() is defined by the logistic loss function
Ly, y) = [ylogy) + (1-y)log (1 - ¹)]
Please list the stochastic gradient descent update rule, batch gradient descent update rule, and
mini-batch gradient descent update rule. Explain the main difference of these three update
rules.
Transcribed Image Text:The cost function of a general neural network is defined as J(ŷ,y) = m // [4 (9(0), y(1) The loss function L(ŷ), y() is defined by the logistic loss function Ly, y) = [ylogy) + (1-y)log (1 - ¹)] Please list the stochastic gradient descent update rule, batch gradient descent update rule, and mini-batch gradient descent update rule. Explain the main difference of these three update rules.
Given a neural network, its structure is shown below. z." is the output of the linear part of ith
neuron in layer l; a¹ = g(z) is the output of the activation part of jth neuron in layer I and
g(z) is the activation function.
X₁
x₂
1
Xn
[1]
[1][1]
za
z[¹]|a²²]
Z3
[1] [¹]
a4
XXIS
[2][2]
z₁ a
[2][2]
z₂a₂
[2]
[3][3]
Z₁9₁
Transcribed Image Text:Given a neural network, its structure is shown below. z." is the output of the linear part of ith neuron in layer l; a¹ = g(z) is the output of the activation part of jth neuron in layer I and g(z) is the activation function. X₁ x₂ 1 Xn [1] [1][1] za z[¹]|a²²] Z3 [1] [¹] a4 XXIS [2][2] z₁ a [2][2] z₂a₂ [2] [3][3] Z₁9₁
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