Read the equation
The candidate split is restricted to indices 20 through 280 within the first 300 gradient observations. This leaves at least twenty observations on each side for a two-line fit. The search range is an analysis choice and is not an observed transition interval.
Terms & definitions
| Term | Meaning in this source |
|---|---|
| k | Candidate split index |
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
Source recovery establishes that the expression appears in this record. Its mathematical validity, implementation behavior, and interpretation must be assessed separately. See the linked source and research notes for the checks available for this version.
Original context
Read the surrounding source passage
(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 SSE(k)=minα,β,γ,ζ[t=1k(gt−α−βt)2+t=k+1300(gt−γ−ζt)2]. (4.9) The minimizing k is the last step of the first segment. The fitted lines need not meet at the boundary. This summarizes a rise and decline within the original pilot domain; it does not establish a discontinuity or fit the entire record of 792 observations.
Exact original notation
20\le k\le 280