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The analysis compares four odd window lengths: 5, 11, 21, and 31 observations. Smaller windows preserve more local variation, while larger windows smooth it more strongly. Agreement across these choices is descriptive robustness to smoothing, not independent replication.
Terms & definitions
| Term | Meaning in this source |
|---|---|
| w | Moving-average window length |
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4. Mathematical and analytical methods
4.1 Gradient and loss summaries
Let gt denote the trainer’s recorded gradient norm. Its raw maximum is reported alongside complete-window centered means at widths w∈{5,11,21,31}:
gtw=1wj=−w−1/2w−1/2gt+j.
Centered means use future observations relative to their nominal center. They are descriptive summaries, not online onset detectors. The field is interpreted as the trainer’s reported gradient magnitude, not a direct measurement of electrical energy, accumulated information, or the magnitude of the eventual parameter update. Optimizer state, learning rate, and clipping may distinguish those quantities.
The adjacent windows 161–180 and 181–200 summarize the early episode. Their relative decline is 1001−g181:200/g161:180. This comparison is retrospective and motivated by the already published transition region; it is not a prospectively predicted effect or an estimated causal effect of declaration.Exact original notation
w\in {5,11,21,31}