Gradient Descent in ReLU Neural Network
$begingroup$
I’m new to machine learning and recently facing a problem on back propagation of training a neural network using ReLU activation function shown in the figure. My problem is to update the weights matrices in the hidden and output layers.
The cost function is given as:
$J(Theta) = sumlimits_{i=1}^2 frac{1}{2} left(a_i^{(3)} - y_iright)^2$
where $y_i$ is the $i$-th output from output layer.
Using the gradient descent algorithm, the weights matrices can be updated by:
$Theta_{jk}^{(2)} := Theta_{jk}^{(2)} - alphafrac{partial J(Theta)}{partial Theta_{jk}^{(2)}}$
$Theta_{ij}^{(3)} := Theta_{ij}^{(3)} - alphafrac{partial J(Theta)}{partial Theta_{ij}^{(3)}}$
I understand how to update the weight matrix at output layer $Theta_{ij}^{(3)}$, however I don’t know how to update that from the input layer to hidden layer $Theta_{jk}^{(2)}$ involving the ReLU activation units, i.e. not understanding how to get $frac{partial J(Theta)}{partial Theta_{jk}^{(2)}}$.
Can anyone help me understand how to derive the gradient on the cost function...?
neural-network gradient-descent activation-function
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$begingroup$
I’m new to machine learning and recently facing a problem on back propagation of training a neural network using ReLU activation function shown in the figure. My problem is to update the weights matrices in the hidden and output layers.
The cost function is given as:
$J(Theta) = sumlimits_{i=1}^2 frac{1}{2} left(a_i^{(3)} - y_iright)^2$
where $y_i$ is the $i$-th output from output layer.
Using the gradient descent algorithm, the weights matrices can be updated by:
$Theta_{jk}^{(2)} := Theta_{jk}^{(2)} - alphafrac{partial J(Theta)}{partial Theta_{jk}^{(2)}}$
$Theta_{ij}^{(3)} := Theta_{ij}^{(3)} - alphafrac{partial J(Theta)}{partial Theta_{ij}^{(3)}}$
I understand how to update the weight matrix at output layer $Theta_{ij}^{(3)}$, however I don’t know how to update that from the input layer to hidden layer $Theta_{jk}^{(2)}$ involving the ReLU activation units, i.e. not understanding how to get $frac{partial J(Theta)}{partial Theta_{jk}^{(2)}}$.
Can anyone help me understand how to derive the gradient on the cost function...?
neural-network gradient-descent activation-function
asked 4 mins ago
nullnull
1
New contributor
null is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
add a comment |
$begingroup$
I’m new to machine learning and recently facing a problem on back propagation of training a neural network using ReLU activation function shown in the figure. My problem is to update the weights matrices in the hidden and output layers.
The cost function is given as:
$J(Theta) = sumlimits_{i=1}^2 frac{1}{2} left(a_i^{(3)} - y_iright)^2$
where $y_i$ is the $i$-th output from output layer.
Using the gradient descent algorithm, the weights matrices can be updated by:
$Theta_{jk}^{(2)} := Theta_{jk}^{(2)} - alphafrac{partial J(Theta)}{partial Theta_{jk}^{(2)}}$
$Theta_{ij}^{(3)} := Theta_{ij}^{(3)} - alphafrac{partial J(Theta)}{partial Theta_{ij}^{(3)}}$
I understand how to update the weight matrix at output layer $Theta_{ij}^{(3)}$, however I don’t know how to update that from the input layer to hidden layer $Theta_{jk}^{(2)}$ involving the ReLU activation units, i.e. not understanding how to get $frac{partial J(Theta)}{partial Theta_{jk}^{(2)}}$.
Can anyone help me understand how to derive the gradient on the cost function...?
neural-network gradient-descent activation-function
asked 4 mins ago
nullnull
1
New contributor
null is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
I’m new to machine learning and recently facing a problem on back propagation of training a neural network using ReLU activation function shown in the figure. My problem is to update the weights matrices in the hidden and output layers.
The cost function is given as:
$J(Theta) = sumlimits_{i=1}^2 frac{1}{2} left(a_i^{(3)} - y_iright)^2$
where $y_i$ is the $i$-th output from output layer.
Using the gradient descent algorithm, the weights matrices can be updated by:
$Theta_{jk}^{(2)} := Theta_{jk}^{(2)} - alphafrac{partial J(Theta)}{partial Theta_{jk}^{(2)}}$
$Theta_{ij}^{(3)} := Theta_{ij}^{(3)} - alphafrac{partial J(Theta)}{partial Theta_{ij}^{(3)}}$
I understand how to update the weight matrix at output layer $Theta_{ij}^{(3)}$, however I don’t know how to update that from the input layer to hidden layer $Theta_{jk}^{(2)}$ involving the ReLU activation units, i.e. not understanding how to get $frac{partial J(Theta)}{partial Theta_{jk}^{(2)}}$.
Can anyone help me understand how to derive the gradient on the cost function...?
neural-network gradient-descent activation-function
neural-network gradient-descent activation-function
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null is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
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null is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 4 mins ago
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New contributor
null is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 4 mins ago
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asked 4 mins ago
nullnull
1
1
New contributor
null is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
null is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
null is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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