Deep learning has been successfully applied to semantic graph parsing in recent years. However, to our best knowledge, all graph-based parsers depend on a strong assumption about the ordering of graph nodes. This work explores a permutation-invariant approach to sentence-to-graph semantic parsing. We present a versatile, cross-framework, and language-independent architecture for universal modeling of semantic structures. To empirically validate our method, we participated in the CoNLL 2020 shared task, Cross- Framework Meaning Representation Parsing (MRP 2020), which evaluated the competing systems on five different frameworks (AMR, DRG, EDS, PTG, and UCCA) across four languages. Our parsing system, called PERIN, was one of the winners of this shared task. Thus, we believe that permutation invariance is a promising new direction in the field of semantic parsing. 1

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