lin-0156
12.2 Base and tangent obstructions
At example \(x\), the base route obstruction is
\[ E_0(x) = d_\theta (x) - \rho \, \operatorname {Lan}\, \iota (x). \]
For an admitted input direction \(v\), the tangent obstruction is
\[ E_1(x;v) = Dd_\theta (x)[v] - D(\rho \, \operatorname {Lan}\, \iota )(x)[v]. \]
The task block is evaluated after the shared decoder \(h\). Thus route compatibility and prediction quality are observable separately.
Definition
12.1
LINCS–KET profile
For validation set \(\mathcal V\), define
\[ \Psi _{\mathrm{KET}}(\theta ) = \bigl( L_{\mathrm{task}}, \lVert E_0\rVert _{\mathcal V}, \lVert E_1\rVert _{\mathcal V,\mathcal P}, L_{\mathrm{shift}} \bigr), \]
where \(\mathcal P\) is a fixed multi-probe tangent design and \(L_{\mathrm{shift}}\) contains declared perturbation or length audits.
The fixed probes make before-and-after comparisons meaningful. Resampling one probe per candidate can turn admission noise into apparent improvement.