Noise-Debiased Thermodynamic Variance for Local Learning Coefficient Probes
Local learning coefficient (LLC) probes offer a singularity-aware view of neural-network training, but mean-energy methods require a local loss baseline that is ambiguous at transient checkpoints. Thermodynamic variance avoids this input; under mini-batch evaluation, however, direct variance mixes cross-state loss fluctuations with same-state noise. We operationalize this route with the \emph{Shift-Invariant Variance Estimator} (SIVE), which estimates and subtracts the latter component using repeated evaluations. Conditional on any fixed retained path, unclipped SIVE is unbiased for noiseless path variance without requiring MCMC stationarity. The finite-scale diagnostic remains indexed by...
| Authors | Yingjia Cai |
|---|---|
| Primary category | cs.LG |
| Published | 21 June 2026 |
| Last updated at source | 21 September 2026 |
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