diff options
Diffstat (limited to 'notes/01_theory_notes.md')
| -rw-r--r-- | notes/01_theory_notes.md | 8 |
1 files changed, 8 insertions, 0 deletions
diff --git a/notes/01_theory_notes.md b/notes/01_theory_notes.md index d524000..7a54374 100644 --- a/notes/01_theory_notes.md +++ b/notes/01_theory_notes.md @@ -357,6 +357,14 @@ d-d_{\mathrm{hard}} \max(0,k-(P-d)). \] +Interpretation: + +- \(P-d\) is the local redundant parameter dimension. +- If \(k\le P-d\), generic alignment constraints can be absorbed by redundant directions without reducing hard local function rank. +- If \(k>P-d\), every additional generic constraint reduces hard local function rank one-for-one. + +This gives the proposed FA/BP functional-gap onset: parameter-volume cost can grow before the model loses hard function rank, but once the alignment burden exhausts redundancy, FA should separate from BP more sharply. + Soft overlap model. Let \(E\) be the alignment constraint subspace and \(S\) be the task-sensitive subspace: \[ |