I am helping a friend with a project involving neural networks and he wants to convert this equation into matrix notation: $$w_{ij} = \sum_{n=1}^N\left[\sum_{i=1}^I(r_{in}-y_{in})v_{ih}\right](1-z_{hn}^2)x_{jn}$$ with $W$ an $H\times J$ matrix, $R,Y$ $N \times I$ matrices, $Z$ an $N\times H$ matrix, $X$ an $N\times J$ matrix, and $V$ an $I\times H$ matrix.

I was able to get the first part, which is $\left(\sum_{n=1}^N\left[\sum_{i=1}^I(r_{in}-y_{in})v_{ih}\right]x_{jn}\right)$ after distributing over $(1-z_{ht}^2)x_{jt}$, to be reduced to what I think is $(R-Y)VX$. The second part I got something involving elementwise products, but I couldn't get any further. I suspect it involves tensors since we need to take the dot product over the index $t$ and the product $z_{ht}^2x_{jt}$ involves two other indices.

Hopefully this is not too much of a mess. If anyone can help that would be great.

  • $\begingroup$ Your initial equation makes no sense as written. The l.h.s. depends on $i$, whereas the r.h.s. is summed over $i$, and therefore doesn't depend on $i$. And how do you know the l.h.s. doesn't depend on $h$? $\endgroup$ Mar 30, 2022 at 14:25


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