I am reading the paper "Image Style Transfer Using Convolutional Neural Networks". Another paper is A Neural Algorithm of Artistic Style.
I cannot understand part of Fig2 in this paper. The Fig2 is in the following:
I have some questions about the middle part: compute its derivative with respect to the pixel values by error back-propagation.
1, what does $\frac{\partial E_{L}}{\partial F^{L-1}}$ mean in the top-middle part of this figure? How to compute it?
2, How to compute $\frac{\partial L_{total}}{\partial\overrightarrow{x}}$ and $\frac{\partial E_{L}}{\partial\overrightarrow{x}}$ by back propagation?
I guess, $\frac{\partial E_{L}}{\partial\overrightarrow{x}}$=$\frac{\partial E_{L}}{\partial F^{L}}\frac{\partial F^{L}}{\partial F^{L-1}}...\frac{\partial F^{1}}{\partial \overrightarrow{x}}$. And $\frac{\partial F^{l}}{\partial F^{l-1}}$, where $l = 0, 1, ..., L$ is computed by back propagation. Am I right?
3, what are computed by back propagation. I looked into back propagation, but have no idea how back propagation is working in these two papers.
Could someone give more details and explanations? Thanks