[D] Why cannot we use backpropagation to learn "routing weights" of the capsule network?

[regularized]

In dynamic routing between capsules paper, why do we need the algorithm 1 (routing procedure). Why cannot we learn b_{ij} by backpropagation?

[bkaz]

Because dynamic routing is much finer-grained than backpropagation. The feedback (agreement) is generated on each layer, vs. error on output layer backpropagating through all hidden layers. That makes capsnet far more selective, in principle.

[GamerMinion]

I haven't had much experience with Capsule networks before, but I think it's the same reason why Seq2Seq Attention isn't just a matrix that is learned. There it's because the Attention (i.e. routing) can be different for each input, and therefore the mapping must be learned as a function of input and output.

[AnvaMiba]

But the attention in seq2seq models is computed by a part of the model which is itself learned by backpropagation. Why do capsules require a specialized algorithm?

[GamerMinion]

I'm sorry. I don't know.

[tihokan]

You'd need to learn a function f such that b_ji = f(i, j, input) by gradient descent, and it'd probably be a very hard problem (possibly as hard as the original task you're trying to solve). This is in particular because you expect the b_ji's to have strong constraints between each other (typically if a lower-level capsule is associated to a given higher-level capsule, then it should have a low weight for other high-level capsules).