Quantify the training-data scaling of WCRG with system size

Determine how the number of equilibrium configurations required to train the WCRG conditional energies to a fixed accuracy scales with the linear system size of the frustrated soft-spin BNNNI model, and quantify the resulting contribution to the total computational cost.

Background

The reported logarithmic reconstruction-depth scaling assumes that the conditional energies have already been learned from an available set of equilibrium configurations. For larger systems, achieving a prescribed learning accuracy may require an increasing number of training configurations, which could introduce an additional system-size dependence into the computational cost.

The paper expects this dependence to be weak but does not evaluate it systematically. Establishing the training-data requirement is therefore necessary for assessing the true end-to-end scalability of WCRG, including both model learning and sample generation.

References

To achieve a given accuracy in this learning, one might need to analyze an increasing number of training configurations as their size increases, possibly leading to an additional increase of the computational cost with $L$. We expect this dependence to be rather weak, but a systematic evaluation of this effect for WCRG, remains to be considered and is left for future investigation.

— Overcoming critical slowing down in frustrated spin systems by learned multiscale sampling  (2608.31114 - Bandini et al., 31 Aug 2026) in Section 4, “Conclusion and perspectives,” final paragraph before the Data availability statement