Dynamic routing between capsules is exactly nonlinear gradient descent on the concave objective Ψ(C) = -Σ_j (||U_j C(:,j)|| - arctan ||U_j C(:,j)||), whose value decreases at every routing iteration.
Matrix capsules with em routing,
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The Convergence of Dynamic Routing between Capsules
Dynamic routing between capsules is exactly nonlinear gradient descent on the concave objective Ψ(C) = -Σ_j (||U_j C(:,j)|| - arctan ||U_j C(:,j)||), whose value decreases at every routing iteration.