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For two-dimensional lattice \(\phi^4\), a trained straight-flow teacher is not described by a local force basis alone. After the local transport basis, the residual separates into a zero-mode Binder component and a lowest-shell finite-\(k\) correlator component. The deflated zero-mode polynomial \(P_5(M;t)\) reduces the dominant Binder-tail component, while \(\phi^\perp_{|n|^2=1}\) reduces the finite-\(k\) correlator component; wrong-parity, off-zero-mode, and random controls do not produce the same reductions.
The same projection distinguishes other sampler classes. Diffusion follows the force-resolvent ordering predicted by the free theory, reverse-KL normalizing-flow collapse appears as a forbidden odd zero-mode residual, and gauge-equivariant teachers are resolved by Wilson-loop-force tangent directions. The operator basis is model- and symmetry-dependent, but the test is common: project the trained field-space function and retain sectors that lower held-out residuals and pass the available controls.
| Comments: | 26 pages, 13 figures, 15 tables |
| Subjects: | High Energy Physics - Lattice (hep-lat); Machine Learning (cs.LG) |
| Cite as: | arXiv:2605.11199 [hep-lat] |
| (or arXiv:2605.11199v1 [hep-lat] for this version) | |
| https://doi.org/10.48550/arXiv.2605.11199 arXiv-issued DOI via DataCite (pending registration) |
From: Moxian Qian [view email]
[v1]
Mon, 11 May 2026 20:06:15 UTC (458 KB)
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