A current limitation of the connectionist approach to second language acquisition (SLA) research is that it does not, to my knowledge, include complex linguistic representations. This article proposes a partial solution to this limitation by motivating and illustrating specific analyses that utilize the signbased representations developed within Head-driven Phrase Structure Grammar (HPSG). To motivate the proposed representations, the article applies them to an analysis of four types of mappings between form and function: one-to-one, primed redundancy, nonprimed redundancy and polyfunctional. The paper summarizes representative SLA data that indicate how these mappings may appear in second language (L2) production. Key properties of HPSG analyses are discussed, indicating how they are consistent with connectionist assumptions. Sign-based representations of the four types of mappings are then provided, including several modifications to HPSG formalisms. The article concludes with a discussion of future directions.