lin-0173
13.8 Structured extension: LICKET
LICKET separates an adapter into aggregation and restriction pieces,
\[ \Delta _i = \Delta _i^{\mathrm{colim}} + \Delta _i^{\mathrm{lim}}, \]
and penalizes cross-path interference
\[ C_{ij} = [\Delta _i^{\mathrm{colim}},\Delta _j^{\mathrm{lim}}] + [\Delta _i^{\mathrm{lim}},\Delta _j^{\mathrm{colim}}]. \]
The learned split reduces the cross ratio from \(0.422\) to \(0.051\) on WikiText-2 and from \(0.387\) to \(0.062\) on WikiText-103. In the architectural split, cross-bracket reductions exceed \(400\times \) on both corpora with perplexity within \(2\% \) of the matching baseline.
This extension illustrates the benefit of a richer sketch: instead of asking only whether whole adapters commute, it localizes which limit–colimit interaction carries the obstruction.