Abstract: State-of-the-art argument mining studies have advanced the techniques for predicting argument structures. However, the technology for capturing non-tree-structured arguments is still in its infancy. In this paper, we focus on non-tree argument mining with a neural model. We jointly predict proposition types and edges between propositions. Our proposed model incorporates (i) task-specific parameterization (TSP) that effectively encodes a sequence of propositions and (ii) a proposition-level biaffine attention (PLBA) that can predict a non-tree argument consisting of edges. Experimental results show that both TSP and PLBA boost edge prediction performance compared to baselines.