Good method to understand this is using tensor notations: let b(1,j,....,i) represent superscript 1 and all the following variables be subscripts on tensor b: Then a(1,i) = w(1,j,i)x(0,j) where x(0,j) is the jth input and w(1,j,i) is the j and ith input from weight 1. and a(2,0) = w(2,i)a(1,i) Thus: a(1,i) = w(1,j,i)x(0,j) and a(2,0) = w(2,i)a(1,i) represent everything we need to know. For dimensions of the nth layer weights all we have to do is know that: dimension of current weight = number of nodes in current layer X dimension of previous weight.
Then can we say that the input layer has associated w and b with shapes, respectively, (1,3) and (1,1) and that they are fixed to, respectively, [1,1,1] and 0?
w is a matrix of shape (3,3) where all its elements on the diagonal are 1 and the rest are 0. This is also called a 3-dimensional identity matrix. b is a vector of shape (3,1) where all the elements are 0.
Good method to understand this is using tensor notations:
let b(1,j,....,i) represent superscript 1 and all the following variables be subscripts on tensor b:
Then a(1,i) = w(1,j,i)x(0,j) where x(0,j) is the jth input and w(1,j,i) is the j and ith input from weight 1.
and a(2,0) = w(2,i)a(1,i)
Thus: a(1,i) = w(1,j,i)x(0,j)
and a(2,0) = w(2,i)a(1,i) represent everything we need to know.
For dimensions of the nth layer weights all we have to do is know that:
dimension of current weight = number of nodes in current layer X dimension of previous weight.
0:00 - 0:07 aliens overtake the Video.
This was a helpful visual. Thanks!
Thnx
Then can we say that the input layer has associated w and b with shapes, respectively, (1,3) and (1,1) and that they are fixed to, respectively, [1,1,1] and 0?
w is a matrix of shape (3,3) where all its elements on the diagonal are 1 and the rest are 0. This is also called a 3-dimensional identity matrix. b is a vector of shape (3,1) where all the elements are 0.
很好理解