Neural quantum states represent many-body wavefunctions using neural networks — the network takes a spin configuration as input and outputs the wavefunction amplitude. Training these networks requires computing local energy estimators, which involve flipping individual spins and evaluating the network at each new configuration. For a system of N spins, this means N forward passes per training step. For architectures like Vision Transformers, each forward pass costs O(N), making the total cost O(N^2) per step. The computational bottleneck is the local update.
Winter and Nunnenkamp (arXiv:2603.11189, 2026) design DysonNet to eliminate this bottleneck by structuring the architecture around the physics. The network couples strictly local nonlinearities through global linear layers, mirroring a truncated Dyson series — the perturbative expansion where each order of interaction is a scattering event between otherwise free particles. The local nonlinearities are the scattering; the global linear layers are the free propagation between scattering events.
This structure makes single-spin-flip updates constant-time. When one spin is flipped, only the local nonlinearity at that site changes. The global linear layers propagate the change, but because they are linear, the propagation can be precomputed. The ABACUS algorithm exploits this: precompute the global structure once, then update each local flip in O(1). Total cost drops from O(N^2) to O(N log^2 N) in area-law phases.
The structural point: the physical interpretability of the architecture is what enables the speedup. The Dyson series decomposition is not an approximation imposed for computational convenience — it is the physical structure of many-body interactions. Arranging the network to match this structure makes local updates separable from global structure, which is exactly what allows the constant-time trick. The model is fast because it is meaningful, not despite being meaningful.