You can do broadcasting with a tensor, at least for products and sums. The product is multilinear, and a sum can be in two steps, first step using a tensor to implement fanout. Though I can see the value in representing structure that can be used more efficiently versus just another box for a tensor. Beyond that (softmax?) seems kind of awkward since you're outside the domain of your "domain specific language". I don't know why it's needed to extend the matrix cookbook to tensor diagrams.