Mixing
Help understanding equation with $nabla_hat{x}$
$begingroup$
I have the following defined:
$hat{x} leftarrow epsilon x + (1-epsilon)tilde{x}$
and then this:
$lambda(||nabla_hat{x}D_w(hat{x})||_2-1)^2$
Now this is something I have to implement into a computer program, and I think I've got most of it, with the exception of $nabla_hat{x}$
All of the different x are vectors
Could someone please help me understand what it means?
Thank you in advance!
Edit for clarifications:
I'm implementing a Wasserstein GAN from the following paper: (https://arxiv.org/abs/1704.00028). Section 4, page 4, equation 3 contains the equation in question
$D_w$ is a neural network ( The discriminator in a GAN )
The second equation is something the authors of the paper have called Gradient Penalty and is supposed to be added to the calculated loss used to train the algorithm.
linear-algebra
asked Jan 17 at 8:13
CoveyCovey
32
$endgroup$
add a comment |
$begingroup$
I have the following defined:
$hat{x} leftarrow epsilon x + (1-epsilon)tilde{x}$
and then this:
$lambda(||nabla_hat{x}D_w(hat{x})||_2-1)^2$
Now this is something I have to implement into a computer program, and I think I've got most of it, with the exception of $nabla_hat{x}$
All of the different x are vectors
Could someone please help me understand what it means?
Thank you in advance!
Edit for clarifications:
I'm implementing a Wasserstein GAN from the following paper: (https://arxiv.org/abs/1704.00028). Section 4, page 4, equation 3 contains the equation in question
$D_w$ is a neural network ( The discriminator in a GAN )
The second equation is something the authors of the paper have called Gradient Penalty and is supposed to be added to the calculated loss used to train the algorithm.
linear-algebra
asked Jan 17 at 8:13
CoveyCovey
32
$endgroup$
$begingroup$
What is w in that expression?
$endgroup$
– I like Serena
Jan 17 at 8:32
$begingroup$
Would you be so kind to give some context? What is the general meaning of the 2nd equation, and what do you mean by implementing a computer program? Do you intend to, for example, solve a differential equation, or calculate the value of some known expression?
$endgroup$
– Aleksejs Fomins
Jan 17 at 8:46
$begingroup$
Edited question to clarify :-)
$endgroup$
– Covey
Jan 17 at 9:28
add a comment |
$begingroup$
I have the following defined:
$hat{x} leftarrow epsilon x + (1-epsilon)tilde{x}$
and then this:
$lambda(||nabla_hat{x}D_w(hat{x})||_2-1)^2$
Now this is something I have to implement into a computer program, and I think I've got most of it, with the exception of $nabla_hat{x}$
All of the different x are vectors
Could someone please help me understand what it means?
Thank you in advance!
Edit for clarifications:
I'm implementing a Wasserstein GAN from the following paper: (https://arxiv.org/abs/1704.00028). Section 4, page 4, equation 3 contains the equation in question
$D_w$ is a neural network ( The discriminator in a GAN )
The second equation is something the authors of the paper have called Gradient Penalty and is supposed to be added to the calculated loss used to train the algorithm.
linear-algebra
asked Jan 17 at 8:13
CoveyCovey
32
$endgroup$
I have the following defined:
$hat{x} leftarrow epsilon x + (1-epsilon)tilde{x}$
and then this:
$lambda(||nabla_hat{x}D_w(hat{x})||_2-1)^2$
Now this is something I have to implement into a computer program, and I think I've got most of it, with the exception of $nabla_hat{x}$
All of the different x are vectors
Could someone please help me understand what it means?
Thank you in advance!
Edit for clarifications:
I'm implementing a Wasserstein GAN from the following paper: (https://arxiv.org/abs/1704.00028). Section 4, page 4, equation 3 contains the equation in question
$D_w$ is a neural network ( The discriminator in a GAN )
The second equation is something the authors of the paper have called Gradient Penalty and is supposed to be added to the calculated loss used to train the algorithm.
linear-algebra
linear-algebra
asked Jan 17 at 8:13
CoveyCovey
32
asked Jan 17 at 8:13
CoveyCovey
32
edited Jan 17 at 13:16
Covey
asked Jan 17 at 8:13
CoveyCovey
32
asked Jan 17 at 8:13
CoveyCovey
32
asked Jan 17 at 8:13
CoveyCovey
32
32
$begingroup$
What is w in that expression?
$endgroup$
– I like Serena
Jan 17 at 8:32
$begingroup$
Would you be so kind to give some context? What is the general meaning of the 2nd equation, and what do you mean by implementing a computer program? Do you intend to, for example, solve a differential equation, or calculate the value of some known expression?
$endgroup$
– Aleksejs Fomins
Jan 17 at 8:46
$begingroup$
Edited question to clarify :-)
$endgroup$
– Covey
Jan 17 at 9:28
add a comment |
$begingroup$
What is w in that expression?
$endgroup$
– I like Serena
Jan 17 at 8:32
$begingroup$
Would you be so kind to give some context? What is the general meaning of the 2nd equation, and what do you mean by implementing a computer program? Do you intend to, for example, solve a differential equation, or calculate the value of some known expression?
$endgroup$
– Aleksejs Fomins
Jan 17 at 8:46
$begingroup$
Edited question to clarify :-)
$endgroup$
– Covey
Jan 17 at 9:28
$begingroup$
What is w in that expression?
$endgroup$
– I like Serena
Jan 17 at 8:32
$begingroup$
What is w in that expression?
$endgroup$
– I like Serena
Jan 17 at 8:32
$begingroup$
Would you be so kind to give some context? What is the general meaning of the 2nd equation, and what do you mean by implementing a computer program? Do you intend to, for example, solve a differential equation, or calculate the value of some known expression?
$endgroup$
– Aleksejs Fomins
Jan 17 at 8:46
$begingroup$
Would you be so kind to give some context? What is the general meaning of the 2nd equation, and what do you mean by implementing a computer program? Do you intend to, for example, solve a differential equation, or calculate the value of some known expression?
$endgroup$
– Aleksejs Fomins
Jan 17 at 8:46
$begingroup$
Edited question to clarify :-)
$endgroup$
– Covey
Jan 17 at 9:28
$begingroup$
Edited question to clarify :-)
$endgroup$
– Covey
Jan 17 at 9:28
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
In Linear Algebra the operator in question is called the Del operator, $nabla$ , and is defined such that:
$nabla = frac{partial}{partial x}mathbf{i} + frac{partial}{partial y}mathbf{j} + frac{partial}{partial z}mathbf{k}$.
The subscript used in your equation is $hat{x}$, but what is the vector in question. From what I can understand you have del acting on this function $D_{w}(hat{x})$ but the subscript might be restricting or changing what coordinate system Del is acting in.
I hope this helps.
answered Jan 17 at 13:38
C_RichmondC_Richmond
863
$endgroup$
$begingroup$
Oh right. Thank you - this definitely helps!
$endgroup$
– Covey
Jan 18 at 9:09
add a comment |
Your Answer
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
In Linear Algebra the operator in question is called the Del operator, $nabla$ , and is defined such that:
$nabla = frac{partial}{partial x}mathbf{i} + frac{partial}{partial y}mathbf{j} + frac{partial}{partial z}mathbf{k}$.
The subscript used in your equation is $hat{x}$, but what is the vector in question. From what I can understand you have del acting on this function $D_{w}(hat{x})$ but the subscript might be restricting or changing what coordinate system Del is acting in.
I hope this helps.
answered Jan 17 at 13:38
C_RichmondC_Richmond
863
$endgroup$
$begingroup$
Oh right. Thank you - this definitely helps!
$endgroup$
– Covey
Jan 18 at 9:09
add a comment |
$begingroup$
In Linear Algebra the operator in question is called the Del operator, $nabla$ , and is defined such that:
$nabla = frac{partial}{partial x}mathbf{i} + frac{partial}{partial y}mathbf{j} + frac{partial}{partial z}mathbf{k}$.
The subscript used in your equation is $hat{x}$, but what is the vector in question. From what I can understand you have del acting on this function $D_{w}(hat{x})$ but the subscript might be restricting or changing what coordinate system Del is acting in.
I hope this helps.
answered Jan 17 at 13:38
C_RichmondC_Richmond
863
$endgroup$
$begingroup$
Oh right. Thank you - this definitely helps!
$endgroup$
– Covey
Jan 18 at 9:09
add a comment |
$begingroup$
In Linear Algebra the operator in question is called the Del operator, $nabla$ , and is defined such that:
$nabla = frac{partial}{partial x}mathbf{i} + frac{partial}{partial y}mathbf{j} + frac{partial}{partial z}mathbf{k}$.
The subscript used in your equation is $hat{x}$, but what is the vector in question. From what I can understand you have del acting on this function $D_{w}(hat{x})$ but the subscript might be restricting or changing what coordinate system Del is acting in.
I hope this helps.
answered Jan 17 at 13:38
C_RichmondC_Richmond
863
$endgroup$
In Linear Algebra the operator in question is called the Del operator, $nabla$ , and is defined such that:
$nabla = frac{partial}{partial x}mathbf{i} + frac{partial}{partial y}mathbf{j} + frac{partial}{partial z}mathbf{k}$.
The subscript used in your equation is $hat{x}$, but what is the vector in question. From what I can understand you have del acting on this function $D_{w}(hat{x})$ but the subscript might be restricting or changing what coordinate system Del is acting in.
I hope this helps.
answered Jan 17 at 13:38
C_RichmondC_Richmond
863
answered Jan 17 at 13:38
C_RichmondC_Richmond
863
answered Jan 17 at 13:38
C_RichmondC_Richmond
863
answered Jan 17 at 13:38
C_RichmondC_Richmond
863
863
$begingroup$
Oh right. Thank you - this definitely helps!
$endgroup$
– Covey
Jan 18 at 9:09
add a comment |
$begingroup$
Oh right. Thank you - this definitely helps!
$endgroup$
– Covey
Jan 18 at 9:09
$begingroup$
Oh right. Thank you - this definitely helps!
$endgroup$
– Covey
Jan 18 at 9:09
$begingroup$
Oh right. Thank you - this definitely helps!
$endgroup$
– Covey
Jan 18 at 9:09
add a comment |
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$begingroup$
What is w in that expression?
$endgroup$
– I like Serena
Jan 17 at 8:32
$begingroup$
Would you be so kind to give some context? What is the general meaning of the 2nd equation, and what do you mean by implementing a computer program? Do you intend to, for example, solve a differential equation, or calculate the value of some known expression?
$endgroup$
– Aleksejs Fomins
Jan 17 at 8:46
$begingroup$
Edited question to clarify :-)
$endgroup$
– Covey
Jan 17 at 9:28