Papers › CKGConv: General Graph Convolution with Continuous Kernels
CKGConv: General Graph Convolution with Continuous Kernels
Liheng Ma, Soumyasundar Pal, Yitian Zhang, Jiaming Zhou, Yingxue Zhang, Mark Coates
The existing definitions of graph convolution, either from spatial or spectral perspectives, are inflexible and not unified. Defining a general convolution operator in the graph domain is challenging due to the lack of canonical coordinates, the presence of irregular structures, and the properties of graph symmetries. In this work, we propose a novel and general graph convolution framework by parameterizing the kernels as continuous functions of pseudo-coordinates derived via graph positional encoding. We name this Continuous Kernel Graph Convolution (CKGConv). Theoretically, we demonstrate that CKGConv is flexible and expressive. CKGConv encompasses many existing graph convolutions, and exhibits a stronger expressiveness, as powerful as graph transformers in terms of distinguishing non-isomorphic graphs. Empirically, we show that CKGConv-based Networks outperform existing graph convolutional networks and perform comparably to the best graph transformers across a variety of graph datasets. The code and models are publicly available at https://github.com/networkslab/CKGConv.
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="2404.13604")
Code
Syntology Ran 8 of 11 code samples harvested from 1 repository linked to this paper; 3 have no recorded run. Of those that ran: 8 ran with no contract checked.
By repository: official repository: 11 samples from 1 repository, 8 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
11 samples harvested; 8 ran; 0 honoured the contract we drafted; 3 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: 11 of the 11 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 networkslab/CKGConv. “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.
ecf14287d3465c48 · report
9dc78001d467fc9d · report
1bb331bf70a78136 · report
b5c9e7acf599a98a · report
ef96c45530e5a76b · report
309b367fdc9f4994 · report
bdfc097c2a07782f · report
47e492109e6d308f · report
dc82c18c9d42c1c1 · report
d59c374db2cf64ae · report
f1cbbbc857d8b871 · report
Tasks
Results from the paper archive 2025-07-28
| Task | Dataset | Model | Metric | Value | Rank at snapshot | Leaderboard | Report |
|---|---|---|---|---|---|---|---|
| Graph Classification | CIFAR-10 | CKGCN | Accuracy | 72.785 | #1 of 1 | Archive leaderboard | report |
| Graph Classification | MNIST | CKGCN | Accuracy | 98.423 | #5 of 13 | Archive leaderboard | report |
| Graph Classification | Peptides-func | CKGCN | AP | 0.6952 | #15 of 44 | Archive leaderboard | report |
| Graph Regression | Peptides-struct | CKGCN | MAE | 0.2477 | #17 of 39 | Archive leaderboard | report |
| Graph Regression | ZINC | CKGCN | MAE | 0.059 | #6 of 27 | Archive leaderboard | report |
| Graph Regression | ZINC-500k | CKGCN | MAE | 5.9 | #36 of 36 | Archive leaderboard | report |
| Node Classification | CLUSTER | CKGCN | Accuracy | 79.003 | #4 of 12 | Archive leaderboard | report |
| Node Classification | PATTERN | CKGCN | Accuracy | 88.661 | #1 of 11 | Archive leaderboard | report |
Ranks are positions in the archive's leaderboards as they stood at the 2025-07-28 snapshot. Results published since then are not among these rows, so a rank here is not a current standing.
Methods
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