Stable size extrapolation in local score models requires the receptive field to cover the quasi-locality range of the Gaussian-smoothed score, formalized via a size-uniform comparison theorem and validated on the new FDLF benchmark.
Georgii, Gibbs Measures and Phase Transitions, 2nd ed., De Gruyter Studies in Mathematics Vol
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Rigorous analysis shows the continuous noncompact model with kernel exp[−(cosh u−1)] fails Bochner positive-definiteness while finite-alphabet discretizations satisfy reflection positivity via uniform diagonal-dominance certificates for selected v0.
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When Do Local Score Models Extrapolate Across Size? A Diagnostic Theory and Benchmark
Stable size extrapolation in local score models requires the receptive field to cover the quasi-locality range of the Gaussian-smoothed score, formalized via a size-uniform comparison theorem and validated on the new FDLF benchmark.
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A Finite-Lattice Model from a Reciprocal Cost Action: Spectral and Reflection-Positivity Properties
Rigorous analysis shows the continuous noncompact model with kernel exp[−(cosh u−1)] fails Bochner positive-definiteness while finite-alphabet discretizations satisfy reflection positivity via uniform diagonal-dominance certificates for selected v0.