Example title: Higher-order message passing on cell complexes

A. Author^1,*
John Doe^2,*
B. Author^1,2

¹ Example University
² Another Institute

^* Equal contribution

Example Venue 2026

Paper Code BibTeX

On this page

1. Introduction
2. Method
3. Results
Cite
References

Validation accuracy by epoch

Synthetic example data

Data table

Epoch	Model A	Model B	Model C
0	0.440	0.360	0.340
10	0.592	0.477	0.520
20	0.689	0.563	0.620
30	0.751	0.627	0.674
40	0.791	0.674	0.704
50	0.816	0.710	0.720
60	0.832	0.736	0.729
70	0.842	0.755	0.734
80	0.849	0.769	0.737
90	0.853	0.780	0.738
100	0.855	0.788	0.739

Abstract

Example abstract. Message passing networks on graphs aggregate information over pairs of nodes. We extend the aggregation to cells of every dimension through the boundary maps of a cell complex, and show that the resulting layers are as expressive as the cellular Weisfeiler-Lehman test. On three synthetic benchmarks the model improves accuracy at a similar parameter count.

1. Introduction

Graph neural networks pass messages along edges[1]. Cell complexes add faces of higher dimension, so a layer can also pass messages between edges that bound the same face.¹A sidenote sits next to the sentence it explains, in the margin on wide screens.

2. Method

Figure 1.A 2-cell. Its boundary is three edges, each with an orientation.

Definition 2.1 (Boundary matrix). For a cell complex

X

, the boundary matrix

B_k

has one row per

(k-1)

-cell and one column per

k

-cell, with entry

\pm 1

when the row cell lies on the boundary of the column cell.

A layer updates the features $H_k$ on $k$ -cells from both neighboring dimensions:

H_k' = \sigma\left( B_k^{\top} H_{k-1} W_{\downarrow} + H_k W + B_{k+1} H_{k+1} W_{\uparrow} \right)

(1)

Theorem 2.2.With injective aggregation, the layer in equation (1) distinguishes any two cell complexes that the cellular Weisfeiler-Lehman test distinguishes.

Proof.Example proof sketch. Replace with the argument from the paper.

3. Results

Synthetic example. Test accuracy, mean of five seeds.
Model	Task 1	Task 2	Task 3
Model A	0.861	0.774	0.912
Model B	0.809	0.751	0.918
Model C	0.740	0.702	0.880

Cite

BibTeX

@inproceedings{author2026example,
  title     = {Example title: Higher-order message passing on cell complexes},
  author    = {Author, A. and Doe, John and Author, B.},
  booktitle = {Example Venue},
  year      = {2026}
}

References

E. Author, F. Author. Example reference: neural message passing. Example Journal, 2017.