Local observable errors from truncating interaction tails in gapped quantum lattice systems

What the math gives to ML

The paper identifies a non-extensive error-control principle for truncating long-range interactions: local observables are governed by the discarded interaction mass incident on each site, not by the global norm of all discarded terms. For power-law interactions, this yields the explicit local error scaling O(R^{-(p-d)}) when p>2d, uniformly in system size provided a spectral gap remains open along the truncation path. A transferable neural-network analogue is adaptive locality in attention or graph message passing: choose the cutoff or sparsity pattern using per-token tail mass, rather than a global discarded-weight budget. The quantum gap assumption is not automatically available in neural networks, so the proposed method should be treated as a sparsification heuristic whose validity is tested by measuring output drift and training stability as the tail is removed.