A number of previous studies have argued that individual-level cognitive biases can influence population-level typological patterns. Here, we highlight a recurring pattern among these studies: different types of cognitive biases appear to be most active in particular tasks or contexts. For example, biases which affect the organisation of linguistic items into a wider system are especially active in language learning tasks; biases which influence the expression of individual linguistic items or categories independent of any system tend to be observed in language creation tasks. The contexts in which a cognitive bias applies are important: the more restricted the contexts, the greater the limit placed on that bias to influence language structure. Item-based (or category-specific) biases may only influence behaviour when a language is first created, or when novel items are needed. By contrast, system-wide biases can apply iteratively with each new generation of learners. This study seeks to further examine the apparent contextual restrictions on category-specific biases. We target linguistic tasks that may combine elements of language learning with language innovation---for example contexts which require generalisation to new items. Our goal is to see whether both types of biases emerge in this context. If so, this might supply a missing link, explaining how category-specific biases come to influence typology. Using word order in the noun phrase as a case study, we examine whether category-specific biases favouring postnominal adjectives but prenominal genitives---previously only seen in improvisation tasks---also influence behaviour in a task that involves generalisation.