How to understand the gradient flow in Densenet showed in the article of CSP-Net?

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Hellow,I wonder why the latter layers(which are close to the end of the whole network) in the DenseNet can use the gradient of former layers to update their weights just like the formulas showed in the artical of CSP-Net.I think the opposite is true,i.e.,the former layers can get all gradients of latter layers.Is there something wrong with my understanding of these formulas in CSP-Net.