lin-0158
12.4 Why a joint norm failed
The first registered experiment concatenated task, base, and tangent residuals into one normalized admission score. It preserved the task and reduced base incompatibility, but the held-out tangent block worsened. This is a five-seed synthetic architecture test on a causal edge-local sequence task. It uses the implemented incidence KET route, independently checks automatic-differentiation tangents by finite differences, and evaluates length and perturbation shifts after repair. Its purpose is to isolate the admission mechanism, not to establish language-model scaling.
|
Audit |
Pretrained |
Joint gate |
Change |
Reading |
|---|---|---|---|---|
|
Task RMSE |
\(0.06114\) |
\(0.06129\) |
\(+0.25\% \) |
predictive semantics preserved |
|
Base Kan RMS |
\(0.84982\) |
\(0.78928\) |
\(-7.12\% \) |
finite route agreement improved |
|
Tangent Kan RMS |
\(1.46421\) |
\(1.61963\) |
\(+10.61\% \) |
registered promise failed |
|
Length-7 RMSE |
\(0.12701\) |
\(0.12515\) |
\(-1.46\% \) |
no collapse on this shift |
An equal-weight penalty comparator drove base and tangent residuals down to \(0.0661\) and \(0.1654\), but raised task RMSE from \(0.0611\) to \(0.4477\). It made the two routes agree by destroying their shared predictive meaning.
Small compatibility residuals are not useful when both routes have collapsed to the same bad computation. The task block is not a soft preference; it is part of the semantic identity of the diagram.