Field-Theoretic Criteria for Training Dynamics v0.2: The Two-Dimensional Criterion Layer — dL (Trajectory) and R'_eff (Resource)

Abstract

Field-theoretic criteria for training dynamics v0.2 (upgrade of v0.1 dL trajectory criterion). Two-dimensional criterion layer: (1) dL trajectory dimension (retained from v0.1: spectral criterion a<2/lmax identical to SGD condition lr<2/L; toy 5/5 four-decimal match; GPT-2 124M exponential-drift divergence warning; p99 noise calibration). (2) R'_eff resource dimension (new: the heterogeneous-compute metric vacuum — 32x rated span across precisions on one chip, non-comparable sparsity, unpublished domestic official specs; unified force-ratio coordinate R'_eff=E_effective/E_peak, the NPU generalization of MFU; industrial calibration first-hand from MLPerf v6.0 — GB300 measures 0.40, training band 30-45%, no top-tier system passes 55%; caliber self-consistency infers FP4 training). (3) Dual-channel failure classifier (new: dL x R'_eff x eventfulness classifies four failure types — divergence / silent corruption / data stall / normal; detection upgraded to classification, complementing high-sensitivity low-specificity to reduce false alarms). The full form of criterion-layer neutral content: trajectory + resource dimensions. All data open and reproducible (single 3090 GPU). Chinese version is the companion translation.