Operator Spectroscopy of Trained Lattice Samplers
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866911672287887360 |
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| author | Qian, Moxian |
| author_facet | Qian, Moxian |
| contents | Trained lattice samplers are usually judged by the ensembles they generate. Here we instead analyze the trained field-space function itself: a flow-matching velocity, a diffusion score, or a normalizing-flow action residual. We project these functions onto operator bases fixed before the fit, chosen from symmetry, exact Gaussian path limits, finite-volume modes, and gauge covariance.
For two-dimensional lattice \(ϕ^4\), 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 \(ϕ^\perp_{|n|^2=1}\) 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_11199 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Operator Spectroscopy of Trained Lattice Samplers Qian, Moxian High Energy Physics - Lattice Machine Learning Trained lattice samplers are usually judged by the ensembles they generate. Here we instead analyze the trained field-space function itself: a flow-matching velocity, a diffusion score, or a normalizing-flow action residual. We project these functions onto operator bases fixed before the fit, chosen from symmetry, exact Gaussian path limits, finite-volume modes, and gauge covariance. For two-dimensional lattice \(ϕ^4\), 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 \(ϕ^\perp_{|n|^2=1}\) 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. |
| title | Operator Spectroscopy of Trained Lattice Samplers |
| topic | High Energy Physics - Lattice Machine Learning |
| url | https://arxiv.org/abs/2605.11199 |