## 1 Introduction  
Semantic dependency parsing (SDP) attempts to identify semantic relationships between words in a sentence by representing the sentence as a labeled directed acyclic graph (DAG), also known as the semantic dependency graph (SDG). In an SDG, not only can semantic predicates have multiple or zero arguments, but also words from the sentence can be attached as arguments to more than one head word (predicate), or they can be outside the SDG (being neither a predicate nor an argument). SDP has been successfully applied in many downstream tasks of natural language processing, including named entity recognition [1], information extraction [2], machine translation [3], sentiment analysis [4], question generation [5], question answering [6], etc. SDP originates from syntactic dependency parsing which aims to represent the syntactic structure of a sentence by means of a labeled tree. Higher-order information is generally helpful for improving the performance of syntactic and semantic dependency parsing [7; 8; 9] because it contains not only the information about the head and modifier tokens but also the information about higher-order parts (head tokens, modifier tokens, and other tokens linked to them together form the higher-order parts). Here is a straightforward example (as in Figure 1). For the sentence _\"They read Mickey Spillane and talk about Groucho and Harpo\"_, its semantic dependency representation is shown in Figure 1a; the higher-order parts that appear in this sentence are shown in Figure 1b. When considering the semantic dependency relationship between _talk_ and _Harpo_ (dotted edge), if we know (1) _Groucho_ and _Harpo_ are included in the second-order part (_siblings_) and (2) there is a dependency edge labeled _PAT-arg_ between _talk_ and _Groucho_ (blue edges), it is obvious that there is also a dependency edge labeled _PAT-arg_ between _talk_ and _Harpo_. Several semantic dependency parsers have been presented in recent years. Most of them are first-order parsers that utilize the information about first-order parts [10; 11; 12; 13; 14]; the rest are second-order parsers that utilize the information about second-order parts [8; 15; 16]. They have demonstrated that second-order information could bring significant accuracy gains in SDP. However, the second-order parts used in these second-order parsers are limited to specific types, including _siblings_, _grandparent_, and _co-parents_. Utilizing more types of higher-order parts (e.g. _tri-siblings_, _great-grandparents_, _grand-tri-siblings_, etc.) in SDP still remains under-explored. The reason for this issue is that modeling higher-order parts is non-trivial [8]. Higher-order parts have been exploited in syntactic dependency parsing [7; 9; 17; 18; 19]. However, algorithms for higher-order syntactic dependency parsing aim to generate a dependency tree rather than a dependency graph, therefore they are not applicable to SDP. Graph neural networks (GNNs) have been demonstrated to be an effective tool for encoding higher-order information in many graph learning tasks [7; 20]. GNNs aggregate higher-order information in a similar incremental manner: One GNN layer encodes information about immediate neighbors and \(K\) layers encode \(K\)-order neighborhoods (i.e., information about nodes at most \(K\) hops away). This study aims to exploit GNNs' powerful ability of representation learning in SDP. Inspired by the success of GNNs, we investigate using GNNs to encode higher-order information to improve the accuracy of SDP. Instead of encoding higher-order information of specific types of higher-order parts extracted from intermediate parsing graphs, we aggregate higher-order information by stacking multiple GNN layers. We extend the biaffine parser [12] and employ it as the vanilla parser to produce an initial adjacency matrix (close to gold) since there is no graph structure available during testing.