  We show unconditional parameterized lower bounds in the area of knowledge
compilation, more specifically on the size of circuits in decomposable negation
normal form (DNNF) that encode CNF-formulas restricted by several graph width
measures. In particular, we show that
  - there are CNF formulas of size $n$ and modular incidence treewidth $k$
whose smallest DNNF-encoding has size $n^{\Omega(k)}$, and
  - there are CNF formulas of size $n$ and incidence neighborhood diversity $k$
whose smallest DNNF-encoding has size $n^{\Omega(\sqrt{k})}$.
  These results complement recent upper bounds for compiling CNF into DNNF and
strengthen---quantitatively and qualitatively---known conditional low\-er
bounds for cliquewidth. Moreover, they show that, unlike for many graph
problems, the parameters considered here behave significantly differently from
treewidth.
