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We explain why and numerically confirm that there are no barren plateaus inthe energy optimization of isometric tensor network states (TNS) for extensiveHamiltonians with finite-range interactions. Specifically, we consider matrixproduct states, tree tensor network states, and the multiscale entanglementrenormalization ansatz. The variance of the energy gradient, evaluated bytaking the Haar average over the TNS tensors, has a leading system-sizeindependent term and decreases according to a power law in the bond dimension.For a hierarchical TNS with branching ratio $b$, the variance of the gradientwith respect to a tensor in layer $\tau$ scales as $(b\eta)^\tau$, where $\eta$is the second largest eigenvalue of the Haar-average doubled layer-transitionchannel and decreases algebraically with increasing bond dimension. Theobserved scaling properties of the gradient variance bear implications forefficient initialization procedures.

Isometric tensor network optimization for extensive Hamiltonians is free of barren plateaus