Abstract: In this work, we enhance higher-order graph-based approaches for span-based semantic role labeling (SRL) by means of structured modeling. To decrease the complexity of higher-order modeling, we decompose the edge from predicate word to argument span into three different edges, predicate-to-head (P2H), predicate-to-tail (P2T), and head-to-tail (H2T), where head/tail means the first/last word of the semantic argument span. As such, we use a CRF-based higher-order dependency parser and leverage Mean-Field Variational Inference (MFVI) for higher-order inference. Moreover, since semantic arguments of predicates are often constituents within a constituency parse tree, we can leverage such nice structural property by defining a TreeCRF distribution over all H2T edges, using the idea of partial marginalization to define structural training loss. We further leverage structured MFVI to enhance inference. We experiment on span-based SRL benchmarks, showing the effectiveness of both higher-order and structured modeling and the combination thereof. In addition, we show superior performance of structured MFVI against vanilla MFVI.