Confusion about Gradient-based Relevance Computation

[712Zch]

Could you please explain the formula for Gradient-based Relevance Computation in more detail, I notice you have explained in your blog.
Part code:

z = self.layer.forward(a) + self.eps
        s = (r / z).data
        (z * s).sum().backward()
        c = a.grad
        r = (a * c).data

Part formula:

There are some questions:

1. Why wij can represent by
   , and the i' represents what.
   2.sj is also an equation about a, sj is treated as a constant is not correct.
   3.What is the relationship between zj(a; w) and .

[dwil2444]

@kaifishr I have a similar question to @712Zch :
How can we go from $$c_{i} = \sum_{j} w_{ij}s_{j}$$ to the expression containing the composition:

$$ = \sum_{j} s_{j} \frac{\partial}{\partial a_{i}} \left( \sum_{i^{\prime}} a_{i^{\prime}} w_{i^{\prime} j} \right)$$

You mentioned that $c_{i}$ is expressed as an element of a gradient in the space of input activations, a where $s_{j}$ is treated as a constant.

I am not sure that we can do this, since $s_{j}$ is itself a function of the input activations