This means that spectral algorithms give a natural way for the selection of the number of latent states for each nonterminal a in the grammar.
when the data from which we estimate an L-PCFG model are not drawn from an L-PCFG (the model is "incorrect"), the number of non-zero singular values (or the number of singular values which are large) is no longer sufficient to determine the number of latent states for each nonterminal.