Universal scaling framework for parameterized quantum evolutions at criticality

What the math gives to ML

The paper contributes a resource-to-correlation scaling criterion rather than merely comparing final variational energies. Its transferable asset is the emergent correlation length \(\xi_D\), which converts an architecture's finite resource budget \(D\) into the maximum scale of structure it can represent, and the exponent \(\kappa\) in \(\xi_D\propto D^\kappa\), which enables architecture comparisons across different parameterizations. A practical neural-network adaptation is to measure how prediction or representation errors grow with dependency distance on controlled long-range tasks, fit an effective \(\xi\) for each model size or depth, and select architectures with larger \(\kappa\) at equal compute rather than relying only on aggregate validation loss.