eq-18a7e538025bcemathematical expression
Read the equation
The average uses a symmetric window of w observations around time t. For odd w, there are (w−1)/2 samples on each side and one center sample. Because future samples enter the window, the smoothed series is a retrospective descriptive summary rather than an immediately available online detector.
Terms & definitions
| Term | Meaning in this source |
|---|---|
| g_t | Recorded gradient norm |
| w | Odd window length |
| g_bar | Smoothed gradient norm |
How it works
Read the definition from its right-hand expression to the quantity on the left. Its surrounding source records the intended input, state, or parameter context. Where the source leaves an operation unspecified, this page preserves that gap.
Assumptions & limits
End-of-record handling must specify whether incomplete windows are omitted or treated differently.
Original context
Read the surrounding source passage
4.4. Training log summaries Let gt denote the recorded gradient norm. I report its raw maximum and centered averages over complete windows of five, 11, 21, and 31 steps. For odd window width w, gt(w)=1wj=−(w−1)/2(w−1)/2gt+j. (4.8) Centered smoothing uses future observations relative to its labeled center. It is a descriptive robustness check, not a real time declaration detector. A gradient norm is also not the size of the actual optimizer update, accumulated information, or electrical energy. To preserve the earlier pilot comparison, I fit two independent lines to the first 300 observations. Each segment must contain at least 20 observations. For 20≤k≤280, the objective is
Exact original notation
{\overline{g}}_{t}^{(w)}=\frac{1}{w}\sum _{j=-(w-1)/2}^{(w-1)/2}{{g}_{t+j}}.Related builds
Sources & provenance
01
JAIC_Manuscript_Joseph_Anady_FINAL.docx
paragraph 132, math 1 · Sep 22, 2026
{\overline{g}}_{t}^{(w)}=\frac{1}{w}\sum _{j=-(w-1)/2}^{(w-1)/2}{{g}_{t+j}}.
02
JAIC_Manuscript_Joseph_Anady_Revised.docx
paragraph 132, math 1 · Sep 22, 2026
{\overline{g}}_{t}^{(w)}=\frac{1}{w}\sum _{j=-(w-1)/2}^{(w-1)/2}{{g}_{t+j}}.
03
JAIC_Manuscript_Joseph_Anady_FINAL.docx
paragraph 132, math 1 · Sep 22, 2026
{\overline{g}}_{t}^{(w)}=\frac{1}{w}\sum _{j=-(w-1)/2}^{(w-1)/2}{{g}_{t+j}}.
04
JAIC_Manuscript_Joseph_Anady_Revised.docx
paragraph 132, math 1 · Sep 22, 2026
{\overline{g}}_{t}^{(w)}=\frac{1}{w}\sum _{j=-(w-1)/2}^{(w-1)/2}{{g}_{t+j}}.