Papers › The Self-Loop Paradox: Investigating the Impact of Self-Loops on Graph Neural Networks
The Self-Loop Paradox: Investigating the Impact of Self-Loops on Graph Neural Networks
Moritz Lampert, Ingo Scholtes
Many Graph Neural Networks (GNNs) add self-loops to a graph to include feature information about a node itself at each layer. However, if the GNN consists of more than one layer, this information can return to its origin via cycles in the graph topology. Intuition suggests that this "backflow" of information should be larger in graphs with self-loops compared to graphs without. In this work, we counter this intuition and show that for certain GNN architectures, the information a node gains from itself can be smaller in graphs with self-loops compared to the same graphs without. We adopt an analytical approach for the study of statistical graph ensembles with a given degree sequence and show that this phenomenon, which we call the self-loop paradox, can depend both on the number of GNN layers k and whether k is even or odd. We experimentally validate our theoretical findings in a synthetic node classification task and investigate its practical relevance in 23 real-world graphs.
In Syntology Open this paper in Syntology's Atlas, the map of the papers in Syntology's graph and their citations.
For agents, Syntology's MCP tool lists every function and class Syntology harvested from this paper and whether it ran (how to connect): get_harvested_code_for_paper(arxiv_id="2312.01721")
Code
Syntology Ran 4 of 4 code samples harvested from 1 repository linked to this paper; 0 have no recorded run. Of those that ran: 4 ran with no contract checked.
By repository: official repository: 4 samples from 1 repository, 4 ran. The run record, sample by sample. “Ran” means executed on a synthesized input, not that the code is correct or reproduces the paper.
Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.
Code Syntology ran Syntology
4 samples harvested; 4 ran; 0 honoured the contract we drafted; 0 have no recorded run. Read from Syntology's graph 2026-09-24; that is when this build read the record, not when the samples ran.
Licence: 4 of the 4 samples are pointer only, meaning Syntology does not serve that copy's text. This page shows no code text for any sample; each one links to its file in the repository.
Harvested from m-lampert/self-loop-paradox. “Ran” means the sample executed on a synthesized input. It does not mean the output is correct, and nothing here reproduces the paper's results. “Honoured” and “violated” refer to a contract Syntology drafted from the code itself; “our draft was wrong” and “fixture could not drive it” are failures of Syntology's instrument, not of the code.
Each sample ends with its code_sha256, Syntology's identity for that exact code. An agent fetches the stored sample with Syntology's MCP tool get_code(code_sha256="…") (how to connect); click an identity to copy that call.
Repository labels, per sample. official repository: The archive marks this repository official for the paper. named in the paper: The archive records that the paper mentions this repository; it is not marked official. community (archive-listed): In the archive's code links for this paper, not marked official and not recorded as mentioned in the paper. found in paper text by Syntology: Syntology found this repository in the paper's own text; whether it is the authors' implementation is not asserted. community: Not in the archive's code links for this paper; a community repository Syntology harvested. Samples from a repository marked official are listed first. Licence labels name the repository's licence as recorded at harvest. “Pointer only” means Syntology does not serve that copy's text, for one of four reasons: no licence file was found; the licence was not identified; the licence is recorded as permissive but that copy's record is not marked cleared; or the licence is outside the permissive list Syntology serves text under (MIT, Apache-2.0, BSD and similar). Some licences outside that list permit redistribution, such as WTFPL, and GPL-3.0 under its conditions; they are simply not on the list. Hover a licence label for the reason. File links open the file on GitHub at the default branch, which may have changed since the harvest.
817257ca0e31d6c5 · report
c423e1f8d2fa6c47 · report
95f57114f79a8413 · report
d0af59f2adba3a06 · report
Tasks
Results from the paper archive 2025-07-28
No leaderboard rows for this paper in the archive.
Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections