Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the expressive power of message-passing neural networks as global
  feature map transformers   We investigate the power of message-passing neural networks (MPNNs) in their
capacity to transform the numerical features stored in the nodes of their input
graphs. Our focus is on global expressive power, uniformly over all input
graphs, or over graphs of bounded degree with features from a bounded domain.
Accordingly, we introduce the notion of a global feature map transformer
(GFMT). As a yardstick for expressiveness, we use a basic language for GFMTs,
which we call MPLang. Every MPNN can be expressed in MPLang, and our results
clarify to which extent the converse inclusion holds. We consider exact versus
approximate expressiveness; the use of arbitrary activation functions; and the
case where only the ReLU activation function is allowed.

22
The categories of this paper are: chao-dyn
34
The categories of this paper are: chem-ph
18
The categories of this paper are: econ
29
The categories of this paper are: funct-an
15
The categories of this paper are: nucl-ex
26
The categories of this paper are: bayes-an
5
The categories of this paper are: gr-qc
12
The categories of this paper are: nucl-th
30
The categories of this paper are: q-alg
21
The categories of this paper are: adap-org
23
The categories of this paper are: solv-int
31
The categories of this paper are: ao-sci
25
The categories of this paper are: patt-sol
20
The categories of this paper are: acc-phys
8
The categories of this paper are: hep-ex
16
The categories of this paper are: stat