# LeCun paper on deeplearning (Nature, 2015)

As I was reading Y. LeCun's paper on Deep Learning (Nature, vol. 521, 2015), I came across a figure (the 1st one in the paper) which was associated to the backward pass during backpropagation through a convolutional network. I understood everything apart from the very last sentence of the legend that accompanied the figure: "Once the $$\frac{∂E}{∂zk}$$ is known, the error-derivative for the weight $$w_{jk}$$ on the connection from unit j in the layer below is just $$y_j\cdot\frac{∂E}{∂zk}$$".

It must be purely mathematical but I can't figure out why the error-derivative mentioned above equal $$y_j$$ times $$\frac{∂E}{∂zk}$$. Can someone explain to me this result?

Thx.

PS : link to the figure mentioned above is https://www.researchgate.net/figure/Multilayer-neural-networks-and-backpropagation-a-A-multi-layer-neural-network-shown-by_fig4_277411157

As far as I understand, in backpropagation, we need to multiply the local gradient of each node by the gradient from the upper level and this is the value that we send back