Read the equation
For each candidate split k, a separate straight line is fitted to the observations on each side, and their squared residuals are added. The preferred split minimizes this combined residual cost. Because the two lines are independently fitted, they need not meet at k; the procedure selects a descriptive fit boundary rather than proving a physical discontinuity.
Terms & definitions
| Term | Meaning in this source |
|---|---|
| SSE | Sum of squared residuals |
| k | Candidate split index |
| g_t | Gradient norm |
| alpha | First line intercept |
| beta | First line slope |
| gamma | Second line intercept |
| zeta | Second line slope |
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
The source fits the first 300 observations; changing the search interval can change the selected split.
Original context
Read the surrounding source passage
4.2 Descriptive split retained from the pilot To verify the earlier result, we retain its two-independent-line fit over the first 300 gradient observations: SSEk=mina,bt≤kgt−a−bt2+minc,dt>kgt−c−dt2. Each segment contains at least 20 observations. The selected k is the last step in the first segment, not the onset of a newly observed physiological process. This fit is kept on its original 300-step domain rather than silently extending its meaning to all 792 steps. It has no independence-based significance test: sequential training observations are autocorrelated and the split is selected after viewing the trajectory. A smooth nonlinear curve can also describe a rise and decline. 4.3 Effective weight update and factorization invariance For a rank-one adapter, let at∈R13824 and bt∈R5120 be the flattened input and output factors. The learned contribution to the layer is
Exact original notation
SSE\left(k\right)={min}_{a,b}\sum _{t\le k}^{}{{\left({g}_{t}-a-bt\right)}^{2}}+{min}_{c,d}\sum _{t>k}^{}{{\left({g}_{t}-c-dt\right)}^{2}}.Related builds
Sources & provenance
SSE\left(k\right)={min}_{a,b}\sum _{t\le k}^{}{{\left({g}_{t}-a-bt\right)}^{2}}+{min}_{c,d}\sum _{t>k}^{}{{\left({g}_{t}-c-dt\right)}^{2}}.
SSE\left(k\right)={min}_{a,b}\sum _{t\le k}^{}{{\left({g}_{t}-a-bt\right)}^{2}}+{min}_{c,d}\sum _{t>k}^{}{{\left({g}_{t}-c-dt\right)}^{2}}.