PANDA: Prior-guided Attentional Dual-path Architecture

Rishabh Jain; Federico Belotti; Stefano Coniglio; Pietro Lio; Stefano Fiorini

cs.LGOct 9, 2026

PANDA: Prior-guided Attentional Dual-path Architecture

Authors: Rishabh Jain, Federico Belotti, Stefano Coniglio, Pietro Lio, Stefano Fiorini

Organizations: University of Cambridge, UK · University of Bergamo, Italy · Independent Researcher

Abstract

Hypergraph Neural Networks (HNNs), designed to model higher-order relations beyond pairwise interactions, typically rely either on fixed structural weights or on normalised attention. Fixed weights can propagate misleading information in heterophilic settings, while normalisation makes attention coefficients competitive, in the sense that, in a message-passing framework, increasing the weight of one sender must reduce the weight of others in the same aggregation set. Our main contribution is the introduction of PANDA (Prior-guided AttentioNal Dual-path Architecture), a plug-in for two-stage message passing HNNs applicable to both undirected and directed settings. The main path interpolates between learned receiver-normalised attention and structural incidence priors, while a non-competitive (not normalised) auxiliary path lets each sender contribute its own transformed information. We also show that, with fixed structural coefficients, PANDA recovers a certain complex-valued convolution operator adopted in previous works. Across four HNNs spanning spatial and spectral methods in both directed and undirected settings, plugging PANDA in yields an average improvement of 5.18 percentage points across eight real-world benchmark datasets. The code is available at https://github.com/jainris/panda.

Figures & tables

	Variant	Telegram	Citeseer	Pubmed	Roman-empire	Cornell	Texas	Squirrel	email-Enron
GeDi	VANILLA	80.96 $\pm$ 4.506	76.47 $\pm$ 1.315	89.80 $\pm$ 0.408	84.10 $\pm$ 0.399	74.32 $\pm$ 5.019	82.97 $\pm$ 2.717	42.35 $\pm$ 2.059	53.24 $\pm$ 7.649
	PANDA w/o Prior,Aux	73.27 $\pm$ 6.631	75.89 $\pm$ 0.973	89.68 $\pm$ 0.415	88.65 $\pm$ 0.753	78.65 $\pm$ 3.908	83.51 $\pm$ 4.432	38.62 $\pm$ 1.851	58.11 $\pm$ 7.376
	PANDA w/o Aux	80.00 $\pm$ 4.485	76.20 $\pm$ 0.768	90.04 $\pm$ 0.316	87.98 $\pm$ 0.758	76.22 $\pm$ 3.585	84.05 $\pm$ 6.216	39.62 $\pm$ 2.573	60.81 $\pm$ 9.145
	PANDA	91.15 $\pm$ 3.567	76.12 $\pm$ 0.921	89.32 $\pm$ 0.416	90.11 $\pm$ 0.699	77.03 $\pm$ 4.230	84.05 $\pm$ 4.595	42.76 $\pm$ 1.742	60.27 $\pm$ 8.466
	$\Delta$ (PANDA - Vanilla)	+10.19	-0.35	-0.48	+6.01	+2.71	+1.08	+0.41	+7.03
HGNN	VANILLA	58.08 $\pm$ 6.760	77.49 $\pm$ 1.226	90.08 $\pm$ 0.318	78.84 $\pm$ 0.650	71.35 $\pm$ 4.713	81.89 $\pm$ 5.135	39.08 $\pm$ 2.861	42.43 $\pm$ 4.366

Table 1: Node classification results reporting mean accuracies

\pm

standard deviation across all datasets. We compare our PANDA plug-in and its ablations with different backbone architectures.

	Variant	Telegram	Citeseer	Pubmed	Roman-empire	Cornell	Texas	Squirrel	email-Enron
GCN	VANILLA	90.38 $\pm$ 2.852	77.00 $\pm$ 1.197	89.28 $\pm$ 0.272	75.18 $\pm$ 0.683	52.43 $\pm$ 9.300	67.57 $\pm$ 6.396	43.70 $\pm$ 1.947	62.16 $\pm$ 5.539
	GAT (PANDA w/o Prior,Aux)	82.88 $\pm$ 3.488	76.75 $\pm$ 0.919	89.92 $\pm$ 0.247	85.90 $\pm$ 0.707	53.78 $\pm$ 10.429	68.92 $\pm$ 6.648	39.73 $\pm$ 1.634	68.92 $\pm$ 6.310
	PANDA	91.73 $\pm$ 3.851	76.30 $\pm$ 1.070	88.97 $\pm$ 0.466	86.74 $\pm$ 0.711	73.78 $\pm$ 6.049	80.54 $\pm$ 4.804	42.84 $\pm$ 1.322	64.86 $\pm$ 7.151
	$\Delta$ (PANDA - Vanilla)	+1.37	-0.70	-0.31	+11.55	+21.35	+12.97	-0.86	+2.70

Table 2: Node classification results reporting mean accuracies

\pm

standard deviation across all datasets for GCN, GAT and PANDA on GCN.

Dataset	$\mathcal{H}_{\mathrm{CE}}$	$\Delta$ Acc.	$q_{\mathrm{mis}}$	$q_{\mathrm{help}}/q_{\mathrm{hurt}}$	$q_{\mathrm{nbr\text{-}rescue}}$	$\overline{\Delta}^{\mathrm{nbr}}_{\neq}$
Roman-empire	0.236	$-27.7$	95.68	29.44 / 1.77	2.20	$+5.29$
Telegram	0.285	$-54.0$	81.73	56.54 / 2.50	16.35	$+3.58$
Cornell	0.420	$-4.6$	57.84	5.95 / 1.35	1.08	$+0.09$
Texas	0.505	$+0.0$	47.03	3.24 / 3.24	1.35	$+0.09$
Citeseer	0.795	$-1.0$	23.97	1.84 / 0.82	0.22	$-0.28$

Table 3: Main auxiliary-path analysis across five datasets.

\mathcal{H}_{\mathrm{CE}}

is clique-expansion homophily from Wang et al. (2023b) .

\Delta

Acc. is the accuracy change after shutting off both auxiliary gates,

{\color[rgb]{1,0,0}\hat{g}^{\ell}_{e,v}}

and

{\color[rgb]{0,0,1}\check{g}^{\ell}_{u,e}}

q_{\mathrm{mis}}

is the fraction of test nodes whose clique-expansion neighbour-majority class differs from the true label.

q_{\mathrm{help}}

and

q_{\mathrm{hurt}}

are the fractions of nodes flipped onto or off the true class by the auxiliary path.

q_{\mathrm{nbr\text{-}rescue}}

is the fraction of test nodes rescued specifically from the misleading neighbour-majority class.

\overline{\Delta}^{\mathrm{nbr}}_{\neq}

is the true-vs-neighbour-majority logit-margin shift on misleading-neighbour nodes. All rates are percentages; full definitions are in Appendix F .

Model	Telegram	Citeseer	Pubmed	Roman-empire	Cornell	Texas	Squirrel	email-Enron
GeDi + Norm Aux	75.96 $\pm$ 5.319	76.56 $\pm$ 0.862	89.25 $\pm$ 0.498	89.42 $\pm$ 0.466	75.14 $\pm$ 3.784	80.27 $\pm$ 6.401	40.07 $\pm$ 4.317	52.16 $\pm$ 7.649
GeDi + PANDA	91.15 $\pm$ 3.567	76.12 $\pm$ 0.921	89.32 $\pm$ 0.416	90.11 $\pm$ 0.699	77.03 $\pm$ 4.230	84.05 $\pm$ 4.595	42.76 $\pm$ 1.742	60.27 $\pm$ 8.466
$\Delta$ (PANDA - Norm Aux)	+15.19	-0.44	+0.07	+0.69	+1.89	+3.78	+2.69	+8.11
HGNN + Norm Aux	69.62 $\pm$ 3.922	77.38 $\pm$ 0.648	89.66 $\pm$ 0.379	79.83 $\pm$ 0.621	70.54 $\pm$ 4.265	80.54 $\pm$ 2.911	38.78 $\pm$ 2.902	51.62 $\pm$ 3.354
HGNN + PANDA	72.12 $\pm$ 2.885	77.17 $\pm$ 1.125	89.77 $\pm$ 0.368	82.37 $\pm$ 0.511	74.59 $\pm$ 2.162	83.24 $\pm$ 5.644	40.43 $\pm$ 0.999	54.59 $\pm$ 8.090
$\Delta$ (PANDA - Norm Aux)	+2.50	-0.21	+0.11	+2.54	+4.05	+2.70	+1.65	+2.97

Table 4: Node classification results reporting mean accuracies

\pm

standard deviation across all datasets. We compare our PANDA plug-in with the Norm Aux variant on different backbone architectures.

Appendix figures & tables17 assets

Supplementary material from the paper’s appendix.

Appendix

Dataset	# Nodes	# Features	# Hyperedges	# Classes	avg $\|e\|$	avg $\|v\|$	CE Hom.	Node Hom.	Hyperedge Hom.
Roman-empire	22,662	300	22,662	18	2.73	2.73	0.2363	0.0582	0.0582
Squirrel	2,223	2,089	2,060	5	23.81	22.07	0.2448	0.2081	0.2152
Telegram	245	1	183	4	49.70	37.12	0.2854	0.3459	0.3784
email-Enron	143	–	139	7	19.58	19.03	0.3251	0.4163	0.4314
Cornell	183	1,703	96	5	4.07	2.14	0.4200	0.4674	0.4534
Texas	183	1,703	110	5	3.81	2.29	0.5049	0.5076	0.3172

Appendix

Table 5: Statistics of the datasets used in our experiments. Reported are the number of nodes, features, hyperedges, and classes, as well as the average hyperedge size (

\lvert e\rvert

), the average node degree (

\lvert v\rvert

), the clique-expansion (CE) homophily computed as in Wang et al. [2023a] , and the node and hyperedge homophily as calculated in Li et al. [2025] .

Model	Telegram	Citeseer	Pubmed	Roman-empire	Cornell	Texas	Squirrel	email-Enron
GeDi (Vanilla)	8.922 M	30.864 M	0.578 M	5.383 M	1.461 M	4.015 M	11.533 M	26.884 M
GeDi + PANDA	0.765 M	35.682 M	6.714 M	0.421 M	8.470 M	0.638 M	1.902 M	5.880 M
HGNN (Vanilla)	0.134 M	13.734 M	1.932 M	1.761 M	10.861 M	3.168 M	3.860 M	0.035 M
HGNN + PANDA	0.163 M	15.720 M	1.400 M	2.590 M	12.358 M	6.638 M	3.366 M	0.139 M
HyperGCN (Vanilla)	0.695 M	3.154 M	0.059 M	0.046 M	0.051 M	0.026 M	0.579 M	0.396 M
HyperGCN + PANDA	0.027 M	1.933 M	0.060 M	0.138 M	0.225 M	0.060 M	0.275 M	0.052 M

Appendix

Table 6: Parameter counts for PANDA and the vanilla models across different datasets and different backbone architectures.

Model	Telegram	Citeseer	Pubmed	Roman-empire	Cornell	Texas	Squirrel	email-Enron
GeDi (Vanilla)	20.3 $\pm$ 0.1 ms	50.9 $\pm$ 1.9 ms	24.8 $\pm$ 0.2 ms	203.8 $\pm$ 1.1 ms	7.2 $\pm$ 0.0 ms	5.5 $\pm$ 0.1 ms	41.2 $\pm$ 0.9 ms	12.8 $\pm$ 0.1 ms
GeDi + PANDA	10.9 $\pm$ 0.0 ms	122.6 $\pm$ 0.7 ms	171.7 $\pm$ 1.0 ms	115.9 $\pm$ 1.9 ms	9.7 $\pm$ 0.0 ms	8.2 $\pm$ 0.1 ms	28.4 $\pm$ 0.1 ms	33.2 $\pm$ 0.1 ms
HGNN (Vanilla)	1.2 $\pm$ 0.0 ms	10.5 $\pm$ 0.0 ms	16.8 $\pm$ 0.0 ms	22.1 $\pm$ 0.0 ms	1.9 $\pm$ 0.0 ms	1.3 $\pm$ 0.0 ms	5.9 $\pm$ 0.0 ms	1.4 $\pm$ 0.0 ms
HGNN + PANDA	5.7 $\pm$ 0.2 ms	22.5 $\pm$ 1.4 ms	42.1 $\pm$ 0.4 ms	120.7 $\pm$ 0.5 ms	5.5 $\pm$ 0.0 ms	3.9 $\pm$ 0.0 ms	23.6 $\pm$ 1.1 ms	20.2 $\pm$ 0.0 ms
HyperGCN (Vanilla)	360.9 $\pm$ 69.2 ms	74.3 $\pm$ 1.8 ms	2.5 $\pm$ 0.0 ms	1.3 $\pm$ 0.0 ms	2.8 $\pm$ 0.2 ms	2.7 $\pm$ 0.1 ms	3.5 $\pm$ 0.0 ms	5.9 $\pm$ 0.0 ms
HyperGCN + PANDA	239.0 $\pm$ 5.2 ms	50.8 $\pm$ 0.7 ms	20.4 $\pm$ 0.0 ms	31.1 $\pm$ 0.2 ms	6.8 $\pm$ 0.0 ms	3.6 $\pm$ 0.1 ms	8.5 $\pm$ 0.0 ms	17.1 $\pm$ 0.0 ms

Appendix

Table 7: Wall-clock inference times (mean

\pm

standard deviation) for PANDA and the vanilla models across different datasets and different backbone architectures.

	Variant	Wisconsin	email-EU	Questions
GeDi	Vanilla	87.45 $\pm$ 5.203	53.48 $\pm$ 4.53	78.29 $\pm$ 1.026
	PANDA	87.84 $\pm$ 4.454	52.87 $\pm$ 5.60	79.69 $\pm$ 1.21
	$\Delta$ (PANDA - Vanilla)	+0.39	-0.61	+1.40
HGNN	Vanilla	85.88 $\pm$ 5.173	52.88 $\pm$ 1.83	78.25 $\pm$ 1.122
	PANDA	85.88 $\pm$ 5.462	52.83 $\pm$ 6.80	79.16 $\pm$ 1.126
	$\Delta$ (PANDA - Vanilla)	+0.00	-0.05	+0.91

Appendix

Table 8: Node classification results reporting mean accuracies

\pm

standard deviation for Wisconsin and email-EU . For Questions , we report the percentage AUC-ROC for each method, as this is a highly unbalanced dataset. We compare our PANDA plug-in and the vanilla model with different backbone architectures.

Model	Parameter Count	Inference Time
GeDi (Vanilla)	0.511 M	195.7 $\pm$ 0.8 ms
GeDi + PANDA	0.427 M	72.8 $\pm$ 0.2 ms
HGNN (Vanilla)	1.463 M	53.4 $\pm$ 1.3 ms
HGNN + PANDA	0.108 M	22.2 $\pm$ 0.0 ms
HyperGCN (Vanilla)	0.213 M	9.3 $\pm$ 0.0 ms
HyperGCN + PANDA	0.032 M	13.1 $\pm$ 0.0 ms

Appendix

Table 9: Parameter counts and wall-clock inference times (mean

\pm

standard deviation) for PANDA and the vanilla models across different backbone architectures on Questions dataset.

Model	Telegram	Citeseer	Pubmed	Roman-empire	Cornell	Texas	Squirrel	email-Enron
GeDi (Vanilla)	29.6782	1.0956	0.1784	1.2821	1.1428	1.0881	11.038	1.1938
GeDi + PANDA	61.9474	0.8936	0.9324	1.4452	1.5472	0.4988	1.8974	6.2111

Appendix

Table 10: Average L2 norm growth of the node embeddings across layers for different datasets. A value of 1 means the L2 norm does not change across layers, <1 means the embeddings are contracting, while >1 means that they are expanding.

Model	Telegram	Citeseer	Pubmed	Roman-empire	Cornell	Texas	Squirrel	email-Enron
GeDi (Vanilla)	1.711	1.848	1.430	1.124	1.143	1.462	1.174	1.178
GeDi + PANDA	1.226	1.956	1.663	0.990	1.236	2.324	1.761	0.961

Appendix

Table 11: Average coefficient of variation for the L2 norm growth of the node embeddings across layers for different datasets. A value of 0 means that each node’s L2 norm grows equally, while a high value means that the increase is disproportionate.

Routing variables
$\alpha^{\mathrm{main}},\,\alpha^{\mathrm{aux}}$	Main and auxiliary incidence coefficients ( $\hat{\alpha}$ in $\mathcal{V}{\to}\mathcal{E}$ , $\check{\alpha}$ in $\mathcal{E}{\to}\mathcal{V}$ ).
$\alpha^{\mathrm{gat}}$	Learned GAT component of the main coefficient.
$\beta^{\mathrm{prior}}$	Per-incidence prior gate; large value $\Rightarrow$ structural prior dominates main path.
$g$	Post-sigmoid auxiliary gate.
$\eta_{\mathrm{unif}}^{\mathrm{gat}}$	Fraction of non-singleton receiver groups with effectively uniform $\alpha^{\mathrm{gat}}$ .
$\rho_{s,R},\,\pi_{s,R}$	Aux-to-main norm ratio and aux share of total norm, in stage $s\in\{\mathcal{V}{\to}\mathcal{E},\mathcal{E}{\to}\mathcal{V}\}$ , role $R\in\{H,T\}$ .

Appendix

Table 12: Symbols used in the “Extended Analysis” section.

Dataset

Test acc. mean

\pm

std

|\mathcal{V}|

|\mathcal{E}|

\overline{|e|}

\overline{|\Gamma(v)|}

Stage

Role

\eta_{\mathrm{unif}}^{\mathrm{gat}}

\beta^{\mathrm{prior}}

g

\alpha^{\mathrm{aux}}

\rho_{s,R}

\pi_{s,R}

Citeseer

75.6\pm 1.2

3312

1951

3.35

1.98

\mathcal{V}{\to}\mathcal{E}

0.000{\scriptscriptstyle\pm}0.000

0.863{\scriptscriptstyle\pm}0.045

0.378{\scriptscriptstyle\pm}0.041

0.243{\scriptscriptstyle\pm}0.027

0.320{\scriptscriptstyle\pm}0.047

0.241{\scriptscriptstyle\pm}0.027

0.862{\scriptscriptstyle\pm}0.046

0.395{\scriptscriptstyle\pm}0.040

0.253{\scriptscriptstyle\pm}0.027

0.335{\scriptscriptstyle\pm}0.047

0.250{\scriptscriptstyle\pm}0.027

\mathcal{E}{\to}\mathcal{V}

0.005{\scriptscriptstyle\pm}0.000

0.930{\scriptscriptstyle\pm}0.040

0.390{\scriptscriptstyle\pm}0.052

0.242{\scriptscriptstyle\pm}0.033

0.269{\scriptscriptstyle\pm}0.041

0.211{\scriptscriptstyle\pm}0.025

0.844{\scriptscriptstyle\pm}0.042

0.399{\scriptscriptstyle\pm}0.050

0.247{\scriptscriptstyle\pm}0.032

0.293{\scriptscriptstyle\pm}0.042

0.226{\scriptscriptstyle\pm}0.025

Cornell

74.9\pm 4.8

183

4.07

2.14

\mathcal{V}{\to}\mathcal{E}

0.429{\scriptscriptstyle\pm}0.001

0.368{\scriptscriptstyle\pm}0.100

0.181{\scriptscriptstyle\pm}0.079

0.140{\scriptscriptstyle\pm}0.062

0.294{\scriptscriptstyle\pm}0.131

0.220{\scriptscriptstyle\pm}0.078

0.379{\scriptscriptstyle\pm}0.093

0.207{\scriptscriptstyle\pm}0.090

0.117{\scriptscriptstyle\pm}0.051

0.124{\scriptscriptstyle\pm}0.056

0.108{\scriptscriptstyle\pm}0.044

Appendix

Table 13: Analysis summary of learned incidence routing and the auxiliary path. The accuracy column reports mean

\pm

standard deviation test accuracy in percent over ten saved checkpoints. Dataset statistics are computed on the loaded hypergraphs. Routing values are means

\pm

standard deviations over the same checkpoints, and over layer–checkpoint instances for Roman-empire. The fraction of uniform attention is computed over non-singleton receiver groups, namely

H(e)\cup T(e)

with

|H(e)\cup T(e)|\geq 2

in the

\mathcal{V}{\to}\mathcal{E}

stage and

\Gamma_{H}(u)\cup\Gamma_{T}(u)

with

|\Gamma_{H}(u)\cup\Gamma_{T}(u)|\geq 2

in the

\mathcal{E}{\to}\mathcal{V}

stage.

Stage	norm( $W_{\beta}$ )	norm( $u_{\beta}$ )
$V\rightarrow E$	0.00272 $\pm$ 0.00436	0.07674 $\pm$ 0.14079
$E\rightarrow V$	0.54175 $\pm$ 0.32409	0.41068 $\pm$ 0.23789

Appendix

Table 14: Norms of weight matrices and bias vectors in each stage of message passing for the single layer GeDi + PANDA model for Telegram dataset.

Dataset	Test acc. mean $\pm$ std	Intervention	$\Delta$ Acc. after gate shut-off
Citeseer	$75.6\pm 1.2$	${\color[rgb]{1,0,0}\hat{g}^{(\ell)}_{e,v}}=0$	$-0.5\pm 0.5$
		${\color[rgb]{0,0,1}\check{g}^{(\ell)}_{u,e}}=0$	$-0.5\pm 0.3$
		both gates $=0$	$-1.0\pm 0.6$
Cornell	$74.9\pm 4.8$	${\color[rgb]{1,0,0}\hat{g}^{(\ell)}_{e,v}}=0$	$-4.1\pm 7.9$
		${\color[rgb]{0,0,1}\check{g}^{(\ell)}_{u,e}}=0$	$-0.5\pm 1.1$
		both gates $=0$	$-4.6\pm 9.7$

Appendix

Table 15: Auxiliary-gate shut-off interventions. The intervention column specifies which post-sigmoid auxiliary gate value is forced to zero. Values are mean

\pm

standard deviation test-accuracy changes in percentage points over ten saved checkpoints; baseline accuracy is reported with the same convention. Negative values mean that the intervention decreases accuracy. Note that this measures the dependence of the model on the auxiliary path, not the marginal contribution of this path.

Intervention	Layer(s) off	Test acc. (%)	$\Delta$ Acc. (pp)
LOO	$\{1\}$	$81.8\pm 3.0$	$-7.4\pm 2.8$
LOO	$\{2\}$	$83.3\pm 1.8$	$-5.8\pm 1.5$
LOO	$\{3\}$	$85.1\pm 2.8$	$-4.1\pm 2.4$
LOO	$\{4\}$	$84.9\pm 3.2$	$-4.3\pm 3.4$
Cumulative	$\{1\}$	$81.8\pm 3.0$	$-7.4\pm 2.8$
Cumulative	$\{1,2\}$	$72.5\pm 4.7$	$-16.7\pm 4.7$

Appendix

Table 16: Per-layer auxiliary-gate interventions on Roman-empire (four PANDA layers, ten saved checkpoints). LOO shuts off both per-incidence auxiliary gates only at the named layer; cumulative shuts off both gates at layers

1,\ldots,k

jointly. Values are mean test accuracy

\pm

standard deviation in percent;

\Delta

Acc. is the corresponding accuracy change vs. the full model (

89.2\pm 0.5

) in percentage points.

Dataset	$\mathcal{H}_{\mathrm{CE}}$	$\Delta$ Acc.	$q_{\mathrm{mis}}$	$q_{\mathrm{help}}$	$q_{\mathrm{hurt}}$	$q_{\mathrm{nbr\text{-}rescue}}$	$\overline{\Delta}^{\mathrm{nbr}}_{\neq}$
Citeseer	0.795	$-1.0$	23.97	1.84	0.82	0.22	$-0.28$
Cornell	0.420	$-4.6$	57.84	5.95	1.35	1.08	$+0.09$
Roman-empire	0.236	$-27.7$	95.68	29.44	1.77	2.20	$+5.29$
Telegram	0.285	$-54.0$	81.73	56.54	2.50	16.35	$+3.58$
Texas	0.505	$\phantom{-}0.0$	47.03	3.24	3.24	1.35	$+0.09$

Appendix

Table 17: Neighbour-majority analysis of the auxiliary path.

\mathcal{H}_{\mathrm{CE}}

is the dataset-level clique-expansion homophily reported by Wang et al. [2023b] .

q_{\mathrm{nbr\text{-}rescue}}

is the unconditional fraction of test nodes (over

|\mathcal{T}|

) for which aux-off follows the misleading neighbour-majority class and the full model predicts the true class.

\overline{\Delta}^{\mathrm{nbr}}_{\neq}

is the true-vs-neighbour-majority logit-margin shift on nodes with

y_{u}^{\mathrm{nbr}}\neq y_{u}

	$u\in\mathcal{T}^{\mathrm{aux\text{-}off}}_{\checkmark}$ (aux-off correct)				$u\in\mathcal{T}^{\mathrm{aux\text{-}off}}_{\times}$ (aux-off wrong)
Dataset	$n$	$\overline{\Delta}^{\mathrm{max}}$	$\%>0$	$n_{\mathrm{hurt}}$	$n$	$\overline{\Delta}^{\mathrm{max}}$	$\%>0$	$n_{\mathrm{help}}$
Citeseer	618	$+0.19$	$69.6$	$6.8$	210	$+0.09$	$41.9$	$15.2$
Cornell	26	$+0.75$	$71.7$	$0.5$	11	$+0.58$	$55.3$	$2.2$
Roman-empire	3484	$+2.99$	$83.3$	$100.5$	2182	$+13.97$	$91.1$	$1668.0$
Telegram	18	$+0.14$	$61.5$	$1.3$	34	$+9.39$	$98.5$	$29.4$
Texas	31	$+0.03$	$50.8$	$1.2$	6	$+0.42$	$50.4$	$1.2$

Appendix

Table 18: Conditional split of

\Delta_{u}^{\mathrm{max}}

by aux-off correctness.

n

is the mean subset size per checkpoint;

\%>0

is the fraction of nodes in the subset with positive

\Delta_{u}^{\mathrm{max}}

n_{\mathrm{hurt}}

counts aux-off-correct nodes flipped to wrong by the full model, while

n_{\mathrm{help}}

counts aux-off-wrong nodes flipped to correct. All columns are means over ten saved checkpoints.

		$\mathcal{V}{\to}\mathcal{E}$		$\mathcal{E}{\to}\mathcal{V}$
Dataset	Layer	$\mathrm{Avg.}\;c_{s}^{\mathrm{src}}$ (std)	$\mathrm{Avg.}\;c_{r}^{\mathrm{recv}}$ (std)	$\mathrm{Avg.}\;c_{s}^{\mathrm{src}}$ (std)	$\mathrm{Avg.}\;c_{r}^{\mathrm{recv}}$ (std)
Citeseer	0	$+0.375\,(0.099)$	$+0.300\,(0.094)$	$+0.006\,(0.124)$	$+0.025\,(0.114)$
Cornell	0	$+0.546\,(0.130)$	$+0.190\,(0.091)$	$+0.027\,(0.131)$	$+0.090\,(0.119)$
Texas	0	$+0.490\,(0.145)$	$+0.211\,(0.114)$	$+0.035\,(0.129)$	$+0.086\,(0.094)$
Telegram	0	$+0.138\,(0.113)$	$+0.036\,(0.101)$	$-0.023\,(0.171)$	$-0.044\,(0.166)$
Roman-empire	0	$+0.529\,(0.106)$	$+0.389\,(0.077)$	$+0.125\,(0.114)$	$+0.006\,(0.103)$

Appendix

Table 19: Source-side and receiver-side cosines between the main-path and auxiliary representations, Eqs. ( 37 ), ( 39 ). Source-side means are computed across all sources of the pass (nodes for

\mathcal{V}{\to}\mathcal{E}

, hyperedges for

\mathcal{E}{\to}\mathcal{V}

) and ten saved checkpoints; receiver-side means are computed across all receivers of the pass (hyperedges for

\mathcal{V}{\to}\mathcal{E}

, nodes for

\mathcal{E}{\to}\mathcal{V}

) and ten checkpoints. Standard deviations across pooled source–checkpoint or receiver–checkpoint instances are shown in parentheses. Roman-empire is the only multi-layer configuration in this analysis.

Figure 1: Source-wise distribution of

c_{s}^{(\ell,p)}

(Eq. ( 37 )) across all sources and ten saved checkpoints, overlaid by layer for the multi-layer Roman-empire family. The vertical dashed line marks

c=0

. The

\mathcal{V}{\to}\mathcal{E}

cosine is uniformly positive across families and layers; the

\mathcal{E}{\to}\mathcal{V}

cosine is concentrated near zero on Citeseer, Cornell, Texas, and Telegram, and spreads more widely on Roman-empire (with layer 2 mass clearly to the left of zero).

Figure 2: Receiver-side distribution of

c_{r}^{\mathrm{recv},(\ell,p)}

(Eq. ( 39 )) across all receivers and ten saved checkpoints, overlaid by layer for the multi-layer Roman-empire family. The vertical dashed line marks

c=0

. The

\mathcal{V}{\to}\mathcal{E}

receiver-side cosine is positive throughout but smaller in magnitude than its source-side counterpart; the

\mathcal{E}{\to}\mathcal{V}

receiver-side cosine is concentrated near zero on every dataset and layer, including Roman-empire’s deeper layers, where aggregation tightens the source-side near-orthogonality further.

Hypergraph Neural Networks

Hypergraph neural networks learn from relationships that connect groups of nodes, capturing interactions beyond ordinary pairwise graphs.

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Anchor-guided Hypergraph Condensation with Dual-level Discrimination

Fan Li, Xiaoyang Wang, Chen Chen, Wenjie Zhang

School of Computer Science and Engineering, University of New South Wales, Sydney, Australia · School of Artificial Intelligence, Shenzhen University, Shenzhen, China.

Hypergraph Neural Networks Dataset Condensation

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The increasing prevalence of large-scale hypergraphs poses significant computational challenges for hypergraph neural network (HNN) training. To address this, hypergraph condensation (HGC) distills large real hypergraphs into compact yet informative synthetic ones, beyond graph condensation (GC) methods limited to pairwise relations. However, existing HGC methods rely on decoupled training architectures, where structure generators are pre-trained on the original hypergraph but not jointly optimized with condensed features during refinement, resulting in misaligned structures that degrade downstream utility. Moreover, trajectory-based optimization incurs substantial computational overhead in refinement, limiting condensation efficiency. To tackle these issues, we propose Anchor-guided HyperGraph Condensation with Dual-level Discrimination (AHGCDD), which consists of three key components: (1) a node initialization module based on Heat Kernel PageRank (HKPR) to encode structural knowledge into feature semantics; (2) an anchor-guided hyperedge synthesis strategy for joint optimization of condensed features and structure; (3) a theoretically grounded dual-level discrimination objective for utility-preserving condensation without redundant HNN training. Extensive experiments demonstrate the superior effectiveness and efficiency of AHGCDD.

Abstract

Hypergraph Neural Networks

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