Operator Spectroscopy of Trained Lattice Samplers

• URL: http://arxiv.org/abs/2605.11199v1
• Date: Mon, 11 May 2026 20:06:15 GMT
• Title: Operator Spectroscopy of Trained Lattice Samplers
• Abstract summary: We analyze the trained field-space function itself.<n>We project these functions onto operator bases fixed before the fit.<n>The operator basis is model- and symmetry-dependent, but the test is common.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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