Defining and Discovering Hyper-meta-paths for Heterogeneous Hypergraphs
Authors: Yaming Yang
Ziyu Zheng
Weigang Lu
Zhe Wang
Xinyan Huang
Wei Zhao
Ziyu Guan
Venue: NeurIPS 2025 poster ()
Keywords: Graph Neural Networks
Hypergraph Neural Networks
Hypergraph Representation Learning
Primary area: deep_learning

Abstract: Heterogeneous hypergraph is a kind of structural data that contains multiple types of nodes and multiple types of hyperedges. Each hyperedge type corresponds to a specific multi-ary relation (called hyper-relation) among subsets of nodes, which goes beyond traditional pair-wise relations in simple graphs. Existing representation learning methods for heterogeneous hypergraphs typically learn embeddings for nodes and hyperedges based on graph neural networks. Although achieving promising performance, they are still limited in capturing more complex structural features and richer semantics conveyed by the composition of various hyper-relations. To fill this research gap, in this work, we propose the concept of hyper-meta-path for heterogeneous hypergraphs, which is defined as the composition of a sequence of hyper-relations. Besides, we design an attention-based heterogeneous hypergraph neural network (HHNN) to automatically learn the importance of hyper-meta-paths. By exploiting useful ones, HHNN is able to capture more complex structural features to boost the model's performance, as well as leverage their conveyed semantics to improve the model's interpretability. Extensive experiments show that HHNN can achieve significantly better performance than state-of-the-art baselines, and the discovered hyper-meta-paths bring good interpretability for the model predictions. To facilitate the reproducibility of this work, we provide our dataset as well as anonymized source code at: https://github.com/zhengziyu77/HHNN.

Defining and Discovering Hyper-meta-paths for Heterogeneous Hypergraphs
Yaming Yang', Ziyu Zheng', Weigang Lu², Zhe Wang', Xinyan Huang Wei Zhao', Ziyu Guan School of Computer Science and Technology. Xidian University, China DDepartment of Civil and Environmental Engineering. The Hong Kong University of Science and Technology, Hong Kong, China
Key Laboratory of Intelligent Perception and Image Understanding of Ministry of Education, School of Artificial Intelligence, Xidian University, China tyym@, chengziyu@stuu. @glu@@ stu., zwang @ stu., ywzhao @ mail., zyguan @ Xxidianedu.cn
Abstract
Heterogeneous hypergraph is a kind of structural data that contains multiple types of nodes and multiple types hyperedges. Each hyperedge type corresponds to spe- eific multi-ary relation (called hyper-relation) among subsets of nodes, which goes beyond traditional pair-wise relations simple graphs. Existing representation learning methods for heterogeneous hypergraphs typically learn embeddings for nodes and hyperedges based on graph neural networks. Although achieving promis- ing performance, they are still limited in capturing more complex structural features and richer semantics conveyed by the composition of various reperrrelations. To fill this research gap, in this work, propose the concept of hyper-men meta-path for heterogeneous hypergraphs, which defined as the composition of a sequence hyper-relations. Besides, neural network (HHNN) to automatically learn the importance of hyper-meta-pen paths. By exploiting useful ones, HHNN is able to capture features to boost the model's performance, as well as leverage their conveyed semanties improve the model's interpretability. Extensive experiments show that HHNN can achieve significantly better performance than state-of-the-art baselines, and the discovered hyper-meta-pathe bring good interpretability for the model predictions. To facilitate the reproducibility of this work, we provide our dataset as well source code at: /ttps::/githine com wwwzgziyunngg/////////
design attention-based heterogeneous hypergraph
complex structural
1 Introduction
Graph data a common type of non-independent identically (non-i.i.d.) distributed data in our real- world life, which can be used to describe various complex relations between objects. Representation learning and knowledge mining on graph data are beneficial for many real-world scenarios, such as social networks [29], bioinformatics [42), e-commerce platform
[43] and relational databases [3], etc. In this paper, we categorize the existing graph data into four categories based on their complexity, shown in Figure
Homogeneous Simple Graphs consist of one type of nodes and one type edges, and each edge represents binary (pair-wise) relation between two nodes. Figure ((a)) shows toy homogeneous simple graph, which describes five users and their pairwise friendship relations.
@ Heterogeneous Simple Graphs consist of multiple types of nodes and multiple types of edges, with edges representing various types of binary relations between node pairs. Figure shbws a toy
"Corresponing author
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

---

2
T1
22
U33
22
m
m2
m2
1
5
W1
22
(a) Homogeneous Simple Graph
(b) Heterogeneous Simple Graph
1
U4
U3
m2
m+
U2
U1
U2
T1
U
U
(c) Homogenenus Hypergraph
(d) Heterogenenus Hypergraph
Figure 1: The toy examples of four categories of graph data.
heterogeneous simple graph, which includes four types of nodes: users, movies, tags, and ratings, denoted by different shapes, and four types of binary relations, denoted by different colors of lines.
@ Homogeneous Hypergraphs generalize the binary relations between node pairs to multi-ary (tuple-wise) relations among a set of nodes. The multi-ary relation among set of nodes called hyperedge. In this work, we also refer to the hyperedge type (i.e., the multi-ary relation) as the hyper-relation. Similar to homogeneous simple graphs, homogeneous hypergraphs consist one type of nodes and one type of hyperedges. Figure [(c) shows toy homogeneous hypergraph, which describes social group (i.e., hyperedge) among users U1. U2. and ug, and another social group among U2, U3, and 144-
4 Heterogeneous Hypergraphs consist of multiple types of nodes and multiple types of hyperedges (hyper-relations), which can describe multiple types of hyper-relations among multiple types of nodes. Figure [(d] shows a toy heterogeneous hypergraph, which contains four types of nodes (indicated by different shapes) and two types of hyperedges (indicated by different shapes with different colors). The two hyperedges (u2, m2, (2) and (u), m., 41 belong to the first type of hyper- relation, indicating the semantics that "a user associates movie with a tag". The two hyperedges {u2, m2, r1} and {u, mi, r belong to the second type reper-relation, indicating the semantics that "a user associates movie with rating".
We can observe that for heterogeneous hypergraphs, when the cardinality of their hyperedges is two, or the types of their nodes and hyperedges are one, they can be reduced to the other three categories of graphs, i.e., the latter are three special cases of the former. in this work, we focus on the representation learning of heterogeneous hypergraphs (more than two types of nodes and more than two types of hyperedges) as they are not only the most general but also the most challenging types of graph data.
19 methods, and follow the typical framework of GNNs by first aggregating information from nodes to hyperedges and then aggregating information from hyperedges back to nodes. They have achieved promising performance and have been successfully applied to practical scenarios such as social recommendation [2 26). spatiotemporal activity prediction (25). and complex system analysis [IT. However, these methods fail to capture more complex structural features and richer semantics conveyed by various types of hyperedges. For the example shown in Figure (dd) the two hyperedge types convey two different semantics we have explained in Paragraph O. In addition, the two hyperedge types interact with
At present, several heterogeneous hypergraph representation learning methods 4. 22 26
30 10]
25 [4 have been proposed. They are all graph neural network
each other through the shared node types (users and movies, i.e., the overlapping area of blue circles and brown circles), resulting in more complex semantics.

---

In this work, we aim to capture the rich semantics contained in heterogeneous hypergraphs. To this end. let us first review an important concept in heterogeneous simple graphs. ie.. meta-path, which is defined as sequence of binary relations between nodes [31]. Referring to the example shown in Figure [cb) let us use "R1" to denote the binary relation of "users watch movies", and use "Rz" to denote the binary relation of "movies have tags". Then, we can compose the metapath " "R1 R2". where "o" denotes the composition operator. This meta-path describes the new composite binary relation between users and tags: "users watch movies that have specific tags". Meta-paths are often
represented by node types as well. Here, the meta-path can also be denoted as U Ra, M Rg T, where U, M, and T' denote the node types of users, movies, and tags, respectively. It is noteworthy that this meta-path is very different from the hyper-relation {U, MM T') since from the meta-path, we cannot know who assigned these tags the movie, while the hyper-relation conveys more precise semantics of "users associate movies with specific tags". Meta-path has been proven to be very useful in capturing heterogeneous structural features from heterogeneous simple graphs [3] g 351 40.
Unfortunately, it can only handle heterogeneous simple graphs and cannot be directly applied to heterogeneous hypergraphs due to the challenge of the multi-arity of hyper-relations.
To fill this research gap, we innovatively propose a novel concept called hyper-meta-patt which formally defined as a sequence of hyper-relations, in which each pair of adjacent hyper-relations shares some common node types. It describes the composite relation of these hyper-relations. In this view, hyper-meta-pale
defined in the spirit of the meta-path, with the former being a generalization of the latter. Hence, papper-met-paaan can capture more complex structural features and richer semantic information in heterogeneous hypergraphs.
Further, we develop a GNN-based representation learning model called Heterogencous Hypergraph Neural Network (HHNN), which is able automatically learn the importance of hyper-meta-pone pathss Each model layer goes through three levels of attention aggregation blocks to refine the representations of nodes and hyperedges. Finally, useful hyper-meta- patta-ppthhsss can be discovered based the optimized attention distributions. The merits are twofold. On the one hand, these hyper-meta-paths help the model capture more complex and subtle high-order structural features, boosting the performance of downstream analysis tasks. On the other hand, the rich semantics conveyed by these hyper-meta-patte endow the model with self- interpretabiliiyy That is, these semantics can bring some interesting interpretations to the model's 's predictions.
The main contributions of this work summarized as follows:
We are the first to define the concept of hyper-meta-por -atth for heterogeneous hypergraphs. It describes the composite relation among sequence of hyper-relations, capturing more complex structural features and richer semantics.
We design a novel network architecture called Heterogeneous Hypergraph Neural Network (HHNN), which can automatically learn the importance of hyper-meta-pathe By discovering and exploiting useful hyper- aoper-meta-peeee meta-paths, HHNN is able to achieve higher performance as well as better seff-interpretabblityy
We conduct extensive experiments to study the effectiveness of the proposed concept of hyper- meta-path and the proposed HHNN model. It turns out that HHNN can achieve significantly better performance than state-of-the-ar baselines, and the discovered hyper-meta-paue -ptths bring good interpretability for the model predictions.
2 Related Work
Homogeneous Hypergraph Neural Networks. Inspired by the graph convolutional network (GCN) (24] for homogeneous simple graphs, HGNN [12) is the first work to define the spectral convolution on hypergraphs based on the hypergraph Laplacian, effectively extending GCN ho- mogeneous hypergraphs. HyperGCN [38] approximates each hyperedge by a set of pairwise edges that connect the nodes in the hyperedge. Inspired by the graph attention network (GAT) (33] for homogeneous simple graphs, Hyper- [4]] develops a self-attention based on the hypergraph neural network to deal with hypergraphs with variable hyperedge size. Inspired by the GraphSAGE model [17] for homogeneous simple graphs, HyperSAGE, [2] proposes an inductive hypergraph learning framework that can capture the intra-relations (within a hyperedge) as well as inter-relations (across hyperedges). HNHN [7] introduces generalized normalization aggregation scheme of GNN,
3

---

which weights the contributions of nodes/hyperedges by a power of their degrees, depending real-valued parameter. UniGNN [2T] is proposed as unified hypergraph learning framework, which generalizes several classic GNNs, such as GCN 224] GAT 133 GIN 37 and GraphSAGE [17] to hypergraphs. AllSet [6] implements hypergraph neural network layers as compositions of two multiset functions. ED-HNN [4]] is hypergraph neural network that can approximate any continu- ous equivariant hypergraph diffusion operators, and thus it can model a wide range of higher-order relations. These methods can effectively address the high-order structural features of hypergraphs, but they have limitations in capturing the heterogeneity of heterogeneous hypergraphs, since there may be multiple types of nodes as well as multiple types of hyperedges.
Heterogeneous Hypergraph Neural Networks. At present, there exists series of heterogeneous hypergraph neural network methods 4
18 36 and the representative ones introduced as follows. HHNE 4 is GCN-based hypergraph neural network that can consider the heterogeneity of nodes by projecting different types of node features into a common feature space. HWNN (30) transforms heterogeneous simple graphs into series of hypergraph snapshots based on a set of user-specified meta-paths. Then it conducts hypergraph convolution based on the Wavelet basis. HGNN+ [4] extends HGNN 12 to heterogeneous hypergraphs by introducing four ways to generate different types of hyperedges. DisenHCN [25] disentangles the user representations into different aspects (location-awarl aware, time- and activity-aware) and aggregates corresponding aspects' features on the constructed hypergraph. These methods not only can capture high-order structural features of hypergraphs but also can address the heterogeneity of nodes and hyperedges by various strategies. However, as we analyzed previously, they fail to capture the complex structural features and rich semantics conveyed by typer-meta-pante
30 14
25
26
10
22
19
5
Preliminaries
In this section, we first define some basic notations and concepts about heterogencous hypergraphs. Then, give the formal definition of our proposed concept of net-neewwwwwhheeeeeeeeee and hyper- meta-path, as illustrated by Figure
Four types of nodes
Two types of hyperedges
M
M
Movies
Tags
R1
(U, M, T3
R
"users associate movies with tags"
Users
R
Ratings
R
(U, R)
"users associate movies with ratings"
R1 (b) Hyper-meta-path
R₂
(a) Hyper-nettonk--shhenna
Figure 2: The illustration of hyper-network- schema and typer-meta-pait of the toy heterogeneous hypergraph shown in Figure T(d) Note that we use "R" to denote node type "Ratings", and use "R," to denote hyperedge type x, i.e., hyper-relation ...
Heterogeneous Hypergraphs. A hypergraph is defined g (V, E, H, W, o v)) where V is set of nodes, & is set of hyperedges, and H (0, 1| is incidence matrix that describes the belonging relations between node and hyperedges, with the entry H.,- = 1 indicating that node i is in the hyperedge j. The diagonal matrix W E [| stores the weights of hyperedges, de - A is node type mapping function, and t:: + is hyperedge type mapping function, with |A| + [ 2. Let v, and e, denote the representation vectors of node and hyperedge j. respectively. Each hyperedge type R& E R conveys specific multi-ary relation among all the associated, and thus we also call it hyper-relation R
tuple A. >, describing the types of the nodes and the types of the hyperedges in a hypergraph, respectively.
Hyper-nettwork-schemm. We define the concept of hyper- www.-nnttwok-chheeeeee
A hypergraph G is homogeneous when = = 1 as well |R| = 1. In this work, we particularly focus on a more challenging setting by considering heterogeneous hypergraphs with |A] > as well as [ > 1, i.e., both the nodes and the hyperedges are heterogeneous.

---

In Figure 2(a) we show the hyper-networt scheea of the toy heterogeneous hypergraph that is previously shown Figure We can clearly see that there are four types of nodes, and two types of hyperedges, i.e., two hyper-relations in the heterogeneous hypergraph.
Hyper-meta-ppahh For each hyper-relation Rs (the hyperedge type is k), we can denote it as its associated node types, i.e., R2 {o(i) = 1, ()) k, vi E V, Vj E &, k E Rj to denote all the associated node types. Then, a hyper-meta-pan patt with length / is defined as a sequence of hyper- relations: P = Ri o R2 o...o o Rt where denotes the composition operator between hyper-relations, and two hyper-relations RS and Rg can be composed if and only if: Rg n R +
In Figure 2(b we intuitively show a hyper-meta path R1 o R2 according to the see, the hyper- -eet--etaaa-aa---- path describes more complex hyper-relation by compositing the two hyper-relations R₁ and R2, since they share the same node types, i.e., Rí n R2 (M,U) Besides, according the semanties of R1 and R2, the hyper-meta-pan conveys a richer semantics of "users associate specific movies with specific tags and specific ratings".
network-schente
shown in Figure [[a) As
Methodology
The aggregation scheme of HHNN is shown in Figure 3 Firstly, it projects node features into hyperedge-specifii feature space, and leverages the a-Attention aggregate features from nodes to hyperedges. Then, it projects hyperedge features back to node-specific feature space, and leverages the 3-Attention and 7-Attention to respectively perform sura-hyperedge-yyp aggregation and inter- hyperedge-type aggregation, resulting in the updated node features.
Node2Edge Projections
Qe-Attention
(1) 3
6
(2)
Edge2Node Projections
m
8-Attention
m 5
Y AtAteention
Figure 3: The aggregation scheme of HHNN.
4.1 Aggregation from Nodes to Hyperedges
Each hyperedge contains multiple nodes, and we define describe all the nodes contained in hyperedge j:
N² = 1,i L,i
In heterogeneous hypergraph, the nodes in N? may have various types. To aggregate the features of these nodes, we need to first project them into a common feature space through parameter matrices, and these projection parameter matrices are specific to both the involved node type o(1) and hyperedge type (i). Then, we leverage the attention mechanism to aggregate the projected node features together, resulting in the updated feature of hyperedge j. which is formally described as follows:
Σ ag.a WVG)+ . IENY
ej =
where o(())= is learnable parameter matrix and its superseript "*() o())" denotes pro- jecting features from nodes of type Φ(i) to hyperedges of type (f)),, aj, is the attention aggregation weight from node to hyperedge which is described follows:
a = Attentiong (1 ((W00)=00)) vv v Hexy)
(3)
where (a()) contains the learnable parameters of the attention function, which are specific to hyper- edge type v'(j) and serve as the attention query. The projected node representations can be mapped into the attention keys and attention values based on different projection parameter matrices.
5

---

4.2 Aggregation from Hyperedges to Nodes
In heterogeneous hypergraph, node may belong to multiple hyperedges various types. For the toy example in Figure [(d] node my belongs to one hyperedge with "blue" type, and one hyperedge with "brown" type. Node 71 belongs to two hyperedges with "brown" type. To this end, in the hyperedge-to-noce aggregation phase, different from most previous approaches, we decompose the aggregation process into two levels, i.e., intra-type aggregation and inter-type aggregation. In the following, we describe the procedures by taking node i as an example.
4.2.1 Intra-type Aggregation
For node assuming that participates in multiple hyperedges of type k, we define set to describe these hyperedges:
N ( H = 1,i V,j E E, (() k}
Then, we leverage the feature projection and the attention mechanism again to aggregate the features of the hyperedges in N,tx, resulting in a temporary representation for node
Σ Bis w ej
(5)
JEN
where W6())+() is projection parameter matrix, and the superseript "Ø(i) < v()" denotes pro- jecting features from hyperedges of type (j) to nodes of type @(i). Big is the attention aggregation weight from hyperedge j to node i, which is calculated as follows:
: Attentiong (cc) (fw00- es jEN
(6)
where (0))) are the attention parameters specific to node type ((1). Like the previous attention function, the attention parameters (o(s) serve as attention query, and the inputs of the function, i.e, the projected hyperedge features, are mapped into attention keys and values.
Similar aggregation processes conducted for all the possible hyperedge types that node par- ticipates in. Finally, we can obtain a set of temporary representations for node i, denoted as [V + 0, vk E RJ. and abbreviated as ( }. Its element v reflects the property of node i from the aspect of hyper-relation Rg.
4.2.2 Inter-type Aggregation
To obtain more comprehensive representation for node i, we use the attention mechanism once more to fuse the temporary representations of node from all the involved hyper-relations:
where N.k, Vk are the attention coefficients that are computed by attention function follows:
7i Attention 2aco
(8)
where Wa(s) the attention parameters specific to node type ((i), and serve as the attention query. The inputs of the attention function, i.c., the obtained temporary node representations, mapped into the attention keys and values.
M
81
In this way, we conduct this three-level attention aggregation in each model layer to update the node representations and the hyperedge represen- tations. Figure 4 shows the overall architecture of HHNN. We can obtain the final node embed- dings (v. E V}. and the final hyperedge em- beddings (e, Vjj f3 from the last layer.
U
Rg
R
R
R
R
Figure The architecture of HHNN.

---

4.3 Training Loss
By obtaining the embeddings nodes and hyperedges, we can implement the loss function according to the task at hand. For example, for the comi-supervised node classification task, we utilize the cross-entropy loss as follows:
L L
Ey: In(C-v.)) kEY
(9)
where v; and y; denote the extracted embedding and the ground-truth label of node i, respectively, y denotes the set node indices that have labels, and C denotes the parameter matrix of the classifier.
In Appendix D we show the overall algorithm of HHNN. In Appendix E. we theoretically show that HHNN can automatically discover the most important hyper-meta-pant for each node, which helps interpret the model's prediction. In Section 5.3 we verify this ability of HHNN through case studies.
4.4 Time Complexity Analysis
The time complexity of HHNN is analyzed as follows. For each layer, the main cost comes from the three-level attention aggregation operations. The c-attention aggregation involves projecting and attending to nodes within each hyperedge, costing [[EE - d, Jo . r), where |E| is the number of hyperedges, da and fa. are the dimensionalities of the input and output features, respectively, and denotes the average number of nodes per hyperedge. In the B-attention aggregation phase, each node aggregates its connected hyperedges of each type, costing ((VVI dg fo -t) where [V] is the number of nodes, d3 and fa are the feature dimensionalities, and denotes the average number of hyperedges of each type that node participates in. In the y-attention aggregation phase, each node fuses its representations across different hyperedge types, costing [[IV] d, f4 k), where d,, and f- are the feature dimensionalities, and is the average number of hyperedge types. Assuming the model has layers, the total time complexity becomes: O( dn So -r--n- + In practical scenarios, da, Sa, [ dly Sy. ; L, ki, to |V] and [ Therefore, the total time complexity of HHNN is equal to: O(V) + [&)), which is linear the size of the hypergraph.
+/|++ |VI S 1//---v 1-n++ [V -dy f k k.n.. usually much smaller constants compared
Experiment
In this section, conduct comprehensive experiments on two real-world datasets. Please see Appendix A for dataset details, see Appendix B for the details of the used baseline methods, and see Appendix for the detailed experimental settings.
5.1 Performance Comparison
Following most previous related studies 12
we compare the performance of all the methods by conducting node classification for the target nodes that are associated with ground-truth labels. The final experimental results are reported Table [ and Table
38 7
As we can see, our proposed HHNN shows the best performance in all cases. This is due to the fact that HHNN able to capture more complex and higher-order structural features that are conveyed by the discovered useful hyper-meta- paths. For all the methods, the performance is significantly better when the training ratio higher, indicating that they can effectively exploit the supervision information. HGNN+ significantly outperforms HGNN in all cases because the former addresses hyperedge heterogeneity
a more nuanced manner. AllSerTsfm performs slightly better than AllDeepSets in most cases, which is also consistent with the similar finding reported in their original paper [6) For most baselines as well as our HHNN, the experimental results on the Olist dataset are better than those the Movielens dataset, which is because the target (Product) nodes in Olist are casier to distinguish, and the structural features conveyed by the three types hyperedges are more informative.
5.2 Ablation Study
As described by Section 4 the key process HHNN lies in three levels of attention aggregation blocks. As illustrated in the left part of Figure 2(a) the a-Attention block performs node-level

---

Table I: Performance comparison on Movielens.
Metrics
Micro
Macro
AUC
Training Ratio
20%
40%
20%
40%
20%
40%
CE-GCN
55,4640.90
57.31
21.99+4.32
26.53
67.86
71.264+1.08
HNHN
52.53+0.79
54,42=1.33
15.67
17.36+3.00
64.61
42.9922.72
HyperGCN
48.53
49.83
16.55
18.05 22222
57.8941.06
59.87 1.99
Sets
52.39+1.13
55,46=1.67
15.72+22.18
23.13
65.47
70.94
AllSetTsfm
53.39+1.84
57.40
18.01 :5.52
30.32.43.13
66.21
73.63 23.63
UniGNN
52.35+1.08
54.18
16.41+2..2
23.11
65.78+22.66
#1.39
EDHNN
53.41
56.72_1.00
18.74 18.74
32.56
70.07
77.06
HGNN
52.54
1.69
20.48
25.98 14.17
65.25
70.06
HGNN+
23.13.12.21
55,44
1.76
21.62 13.21
26.13 12.70
69.62 12.60
73.77 11.62
HHNN
56.80
60.65 60.65-1.88
26.2443.90
33.33
73.21 12.13
78.72+1.00
Table 2: Performance comparison on Olist.
Metrics
Micro
Macro
AUC
Training Ratio
20%
40%
20%
40%
20%
40%
CE-GCN
40.70
42.97
31.29
42.
70.20
77.7610.21
HNHN
53.96 88
60.39 =0.89
43.40+1..00
59.90
84.7 +
88.05 +0.19
HyperGCN
21.96+0.52
27.96
20.21
25.71
62.08
67.6641.05
AllDeepSets
66.96+0.19
66.
75.89_0.79
66.95+0.46
75,89
90.29
94.44
AllSetTsfim
64.57
75.97 10.68
64.82
76.11
88. 88.7910.55
94.3 1 10025
UniGNN
57.47
68.11 0.66
57.13
1..62
87. 87.20.10.25
92.36 1.228
EDHNN
61.62
70.88
61.35
70.71
89.36
93.47 1.335
HGNN
40.66::061
48.62
40.1 10.60
48.38
76. 76.19 1..51
80.93 20.31
HGNN+
59.03
64.16
59.43
64.63
16.84
89.86110.24
HHNN
72.54 40.54
77.74_0.83
72.8910.55
77.90
93.20+0.32
95.39 20.25
aggregation to update hyperedge representations. The 3-Attention block and 7-Attention block correspond to intra-type hyperedge aggregation and inter-type hyperedge aggregation, respectively. Here, we conduct comprehensive ablation studies to investigate the effectiveness of these three attention blocks. The experimental results are shown Table
use the binary bit "0" or "1" to indicate whether the corresponding attention blocks are activated. When an attention block is deactivated, we replace the attention aggregation with the mean aggregation. By considering all possible combinations of the three blocks, obtain eight variants of HHNN. In the first column of Table we also use three-bit binary numbers to denote different variants.
As we can see, in all the cases, the variant "1 111" achieves the best performance, which corresponds the full version of our HHNN. This indicates that the power HHNN can only be fully unleashed when all three attention blocks are assembled together, which implies that these three attention blocks can enhance each other. Besides, variant "010" performs better than variants "001" and "100". and variant "101" performs worse than variants "01 1" and "1 "1""" indicating that the 8-Attention block very effective. This indicates that the different hyperedges a node belongs to have significantly different levels of importance for it.
5.3 Hyper-meta-path Discovery and Interpretability Study
One of the merits of our HHNN is that can discover useful hyper-meta-pant paths for the concerned task (see Appendix E Here, we show this ability of HHNN by analyzing the learned attention coefficients after finishing the model training. In Figure ((a) and Figure (5b) we show the learned attention weights that associated with the movie node m29931 Movielens, and the product node

---

Table 3: The performance of different variants of our HHNN.
Variants Modes
Movielens Macro
Olist
Micro
AUC
Micro
Macro
AUC
000
55.37
27.87
74.09
71.79=0.87
71.79+0.81
93.33
001
11.70
30.63+5.41
75.60+1.61
68.44_0.09
68.72+0.67
92.17=0.34
010
18.97
34.21
78.44
76.96_0.66
77.03+0.00
95.38
011
60.29+1.42
35.45-14.78
79.28
74.74=0.63
74.89+0.62
94.87=0.22
100
57.34
30.55
75.32+1.75
63.60
64.0244079
90.58
101
59.2642.D0
35.45
77.87+1.88
71.19
71.38++0.1
93.24
110
61.42 #1.63
36.22
80.1242.21
77.28
77.41
95.73=0.18
111
62.95 11.9
39.03
12.32
81.87 11.85
79.82
79.91 10.78
96.32 1.021
P4593 on Olist, respectively. In the figures, the magnitude of the attention weights is reflected by the thickness of the corresponding arrows, and the notations in the figures are described in Table 4
In Figure 5(a) for the target movie node, the most important path can be denoted
R2
0,0009
"T R U R2 M". Referring to
0,2690
U
R1
0
the definition Section 3 in the path, the hyper-relation R, (i.e., hyperedge type (UMT)) and the hyper-relation Rs (i.e., hyperedge type (UMR)) are posited based on the movie node shared between them, forming the hyper-meta- path "R, o RR2". Observing the path again, hyper-meta-pane "R2, R22 connects the leftmost tag node to the rightmost movie (i.e.. target) node. The full semantics con- veyed by "R1 RR2 can be described as: "the leftmost tag node participates (UMT) hyperedge" and "the rightmost movie node participates in a (UMR) hy- peredge" and "the two hyperedges share the same user node", which can serve as the interpretation for the prediction result of the target movie node.
0,9591
0,4596
M
M
R2
0,6115
0,258R
R
(a) Moviclens
R2
0,4529
R1
0,3849
0,314
R
0.1919
R2
6,3531
0.4322
0.3344
0.3325
Rs
(b) Olist
Figure 5: Discovered hyper-meta metar-eetapppe meta--pths by HHNN.
Similarly, in Figure 5(b) the discovered most important hyper-meta-pate can be
denoted "S { C R2 p". In the path, the hyper-relation R₁ (i.c., hyperedge type (CPS)) and the hyper-relation R2 (i.c., hyperedge type (CPR)) are composited based on the customer node shared between them, forming the hyper-meta- path "R, o R2... The semantics of the hyper-meta-path can be described as: "the leftmost seller node participates in (CPS) hyperedge" and "the rightmost product node participates in (CPR) hyperedge" and "the two hyperedges share the same customer node". This semantics can help interpret the prediction result of the target product node.
5.4 Analysis of Different Hyperedges
We investigate the impact of the number of hyperedge types on HHNN performance. In Figure 6(a) and Figure ((d) we show the performance of HHNN by exploiting each single type of hyperedges, well the performance by exploiting all types of hyperedges (marked by "ALL" in the legend).

---

As we can see, on both datasets, HHNN achieves the best performance when exploiting all types of hyperedges, which is due to the fact that HHNN can well handle the heterogeneity of hyperedges an adaptive way, and it can compose more complex structural features by combining these hyperedges.
0.80
0.793
0.818
0.9
0.8
Mar
0.75
Accuracy
0.7
Accuracy
0.70
0.6
0.65
0.637
0.6
0.60
0.5
Mi.0
-
UMT
UMR
ALL
0.4
200
400
600
800
1000
0.4
1
3
Hyperedge Type
Dimensionality
Number of Layers
(a) Moviclens
(b) Moviclens
(c) Moviclens
0.95
0.948
0.9
Mic -a- ACC
0.8
0.80
0.811
0.8
Accuracy
AUC
0.7
0.6
0.65
0.50
0.5
-8 Mi.i
0.2
-a- ALC
CPR
OPDF
CPS
ALL
0.4
200 400 600 800 Dimensionality
1000
3
Hyperedge Type
Number of Layers
(d) Olist
(c) Olist
(f) Olist
Figure 6: Hyper- study on Movielens and Olist.
5.5 Hyper-parameter Study
Our proposed HHNN does not have special dyper-parameen Here, study the sensitivity of the hidden dimensionality and the number of model layers on the two datasets, and the results are shown in Figure 6
Referring to Figure 6(b) and Figure 6(e) the model performance poor when the hidden dimension- ality is too small, which indicates that the model suffers from underfitting. HHNN shows the best results when the dimensionalities are equal to 64 on Movielens and 128 on Olist, respectively. After that, the model's performance gradually decreases the dimensionality increases, which is caused by the overfitting issue.
Referring to Figure 6(c) and Figure 6(t) HHNN achieves its best performance when it has two model layers, and the model maintains strong performance even at 3 layers, with no significant performance drop, indicating robustness against over-smoothing. After that, the model's performance decreases significantly when the model goes deeper, which is caused by the overfitting issue of the hypergraph neural network. Notably, each HHNN layer includes two projection and aggregation steps moode-to-hyperede and back), which actually correspond to two layers in standard GNN models. Therefore, 3-layer HHNN is equivalent to 6-layer standard GNN, making it sufficiently deep to capture complex structural patterns without degradation.
6 Conclusion
In this work, we first define novel concept called aapper-mta-paare for heterogeneous hypergraphs. It not only describes more complex structural features but also conveys richer semantic information. Then, we design a three-level attention-based heterogeneous hypergraph neural network called HHNN to automatically learn the importance of hyper-meta-pathh By discovering and exploiting useful ones, HHNNN can achieve higher performance, and the semantics conveyed by these hyper-meta-paths can enhance the model interpretability of HHNN.
10

---

Acknowledgments
This work was supported in part by the National Natural Science Foundation of China under Grants 62303366, 62425605, and 62133012, in part by the Key Research and Development Program of Shaanxi under Grants 3025CY-YBXM part by the Fundamental Research Funds for the Central Universities under Grants ZYTS25211 and ZYTS25086.
2022ZDL,Y01-10, and D024CY2-GJHX.. and in
References
[1] Alessia Antelmi, Gennaro Cordasco, Mirko Polato, Vittorio Scarano, Carmine Spagnuolo, and Dingqi Yang. A survey on hypergraph representation learning. ACM Compuling Surveys, 56(1):1-38, 2023.
[2] Devanshu Arya, Deepak K Gupta, Stevan Rudinac, and Marcel Worring. Hypersage: Gener- alizing inductive representation learning on hypergraphs. arXiv preprint arXiv:2010.04558, 2020.
[3] Song Bai, Feihu Zhang, and Philip HS Torr. Hypergraph convolution and hypergraph attention. Pattern Recognition, 110: 110:777,37 2021.
[4] Inci M Baytas, Cao Xiao, Fei Wang, Anil K Jain, and Jiayu Zhou, Heterogeneous hyper-network embedding. In 2018 IEEE International Conference on Data Mining (ICDM), pages 875-880. IEEE, 2018.
[5] Rui Bing, Guan Yuan, Yanmei Zhang, Senzhang Wang, Bohan Li, and Yong Zhou. An efficient multi-view heterogeneous hypergraph convolutional network for heterogeneous information network representation learning. IEEE Transactions on Big Data, 2024.
[6] Eli Chien, Chao Pan, Jianhao Peng, and Olgica Milenkovic. You are allset: multiset function framework for hypergraph neural networks. In International Conference Learning Representations, 2022.
[7] Yihe Dong, Will Sawin, and Yoshua Bengio. Hnhn: Hypergraph networks with hyperedge neurons. arXiv preprint arXiv:2006. 12278, 2020.
[8] Yuxiao Dong, Nitesh V Chawla, and Ananthram Swami. metapath2vec: Scalable representation learning for heterogeneous networks. In SIGKDD, pages 135-144. ACM, 2017.
(9] Tulia Duta, Giulia Cassarà, Fabrizio Silvestri, and Pietro Liò. Sheaf hypergraph networks. Advances in Neural Information Processing Systems, 36: 16:11207-12099, 2023.
[10] Haoyi Fan, Fengbin Zhang, Yuxuan Wei, Zuoyong Li, Changqing Zou, Yue Gao, and Qionghai Dai. Heterogeneous hypergraph variational autoencoder for link prediction. IEEE transactions on pattern analysis and machine intelligence, (4(5):4125-4133 2021.
[11] Li Feng, Huiying Gong, Shen Zhang, Xiang Liu, Yu Wang, Jinean Che, Ang Dong, Christo- pher H Griffin, Claudia Gragnoli, Jie Wu, et al. Hypernetwork modeling and topology of high-order interactions for complex systems. Proceedings of the National Academy of Sciences, 121(40):e2412222112 2024.
[12] Yifan Feng, Haoxuan You. Zizhao Zhang, Rongrong Ji, and Yue Gao. Hypergraph neural networks. In Proceedings of the AAAI conference on artificial intelligence. volume 33, pages 1558-3565, 2019.
[13] Matthias Fey, Weihua Hu, Kexin Huang, Jan Eric Lenssen, Rishabh Ranjan, Joshua Robinson, Rex Ying, Jiaxuan You, and Jure Leskovee. Position: Relational deep learning- -raph repre- sentation learning on relational databases. In International Conference on Machine Learning, pages 12592-13607 PMLR, 2024.
[14] Yue Gao, Yifan Feng. Shuyi Ji, and Rongrong Ji. Hgnn+: General hypergraph neural networks. IEEE Transactions on Pattern Analysis and Machine Intelligence, 45(3):181-3119) 2022.
11

---

[15] Yue Gao, Zizhao Zhang, Haojie Lin, Xibin Zhao, Shaoyi Du, and Changqing Zou. Hyper- graph learning: Methods and practices. IEEE Transactions on Pattern Analysis and Machine Intelligence, (4(5):244-2566) 2020.
[16] Xavier Glorot and Yoshua Bengio. Understanding the difficulty of training deep feedforward neural networks. In AISTATS, pages 249-256, 2010.
[17] Will Hamilton, Zhitao Ying. and Jure Leskovec. Inductive representation learning on large graphs. In NeurIPS, pages 1024-1034, 2017.
[18] Malik Khizar Hayat, Shan Xue, Jia Wu, and Jian Yang. Heterogeneous hypergraph embedding for node classification in dynamic networks. IEEE Transactions on Artificial Intelligence, 2024.
[19] Aiping Huang. Zihan Fang, Zhihao Wu, Yanchao Tan, Peng Han, Shiping Wang, and Le Zhang. Multi-view heterogeneous graph learning with compressed hypergraph neural networks. Neural Networks, 179:106562, 2024.
[20] Jie Huang, Xin Liu, and Yangqiu Song. Hyper-pate path- bath-based representation learning for hyper- networks. In Proceedings of the 28th ACM International Conference on Information and Knowledge Management, pages 458, 2019.
[21] Jing Huang and Jie Yang. Unignn: unified framework for graph and hypergraph neural net- works. In Proceedings of the Thirtieth International Joint Conference on Artificial Intelligence. International Joint Conferences on Artificial Intelligence Organization, 2021.
[22] Bilal Khan, Jia Wu, Jian Yang, and Xiaoxiao Ma. Heterogeneous hypergraph neural network for social recommendation using attention network. ACM Transactions on Recommender Systems, 2023.
[23] Sunwoo Kim, Soo Yong Lee, Yue Gao, Alessia Antelmi, Mirko Polato, and Kijung Shin. A survey on hypergraph neural networks: an in-depth and step-by-step guide. In Proceedings of the 30th ACM SIGKDD Conference on Knowledge Discovery and Data Mining, pages 6534 6534-6544, 2024.
[24] Thomas N Kipf and Max Welling. Semi-supervised classification with graph convolutional networks. arXiv preprint arXiv: 1609000900 2016.
[25] Yinfeng Li, Chen Gao, Quanming Yao, Tong Li, Depeng Jin, and Yong Li. Disenhen: Disentan- gled hypergraph convolutional networks for spatiotemporal activity prediction. arXiv preprint arXiv:2208.08 06794, 2022.
[26] Yongkang Li, Zipei Fan, Jixiao Zhang, Dengheng Shi, Tianqi Xu, Du Yin, Jinliang Deng, and Xuan Song. Heterogeneous hypergraph neural network for friend recommendation with human mobility. In Proceedings of the 3t ACM International Conference on Information & Knowledge Management, pages 4209-4213 2022.
[27] Tomas Mikolov, Ilya Sutskever, Kai Chen, Greg S Corrado, and Jeff Dean. Distributed rep- resentations of words and phrases and their compositionality. In NeurIPS, pages 3111-3119, 2013.
[28] Mathilde Papillon, Sophia Sanborn, Mustafa Hajij. and Nina Miolane. Architectures of topolog- ical deep learning: A survey of gressage-passigg topological neural networks. arXiv preprint arXiv:2304. 10031, 2023.
[29] Aravind Sankar, Yozen Liu, Jun Yu, and Neil Shah. Graph neural networks for friend ranking large-scale social platforms. In Proceedings of the Web Conference 2021, pages 2535-25466 2021.
[30] Xiangguo Sun, Hongzhi Yin, Bo Liu, Hongxu Chen, Jiuxin Cao, Yingxia Shao, and Nguyen Quoe Viet Hung. Heterogeneous hypergraph embedding for graph classification. In Proceedings of the 14th ACM international conference on web search and data mining, pages
725-733, 2021.
12

---

[31] Yizhou Sun, Jiawei Han, Xifeng Yan, Philip S Yu, and Tianyi Wu. Pathsim: Meta path based top- k similarity search in heterogeneous information networks. VLDB Endowment, 4(11):992-1003,
2011.
[32] Hao Tian and Reza Zafarani. Higher-order networks representation and learning: A survey. ACM SIGKDD Explorations Newsletter, 26(1):1-18, 2024.
[33] Petar Veličković, Guillem Cucurull, Arantxa Casanova, Adriana Romero, Pietro Lio, and Yoshua Bengio. Graph attention networks. arXiv preprint 1rXiv:1710.10900 2017.
[34] Peihao Wang. Shenghao Yang, Yunyu Liu, Zhangyang Wang, and Pan Li. Equivariant by- pergraph diffusion neural operators. In The Eleventh International Conference on Learning Representations, 2023.
[35] Xiao Wang, Houye Ji, Chuan Shi, Bai Wang, Yanfang Ye, Peng Cui, and Philip S Yu. Het- erogeneous graph attention network. In The World Wide Web Conference, pages 2022-2032, 2019.
[36] Ying Wang, Yingji Li, Yue Wu, and Xin Wang. Exploring multiple hypergraphs for heteroge- neous graph neural networks. Expert Systems with Applications, 236:121230) 2024.
[37] Keyulu Xu, Weihua Hu, Jure Leskovec, and Stefanie Jegelka. How powerful are graph neural networks? arXiv preprint arXiv:1810.00820 2018.
[38] Naganand Yadati, Madhav Nimishakavi, Prateek Yadav, Vikram Nitin, Anand Louis, and Partha Talukdar. Hypergen: A new method for training graph convolutional networks on hypergraphs. Advances neural information processing systems, 32, 2019.
[39] Haoran Yang, Hongxu Chen, Lin Li, S Yu Philip, and Guandong Xu. Hyper meta-path contrastive learning for multi-behavior recommendation. In 2021 IEEE International Conference on Data Mining (ICDM), pages 787-796. IEEE, 2021.
[40] Yaming Yang, Ziyu Guan, Jianxin Li, Wei Zhao, Jiangtao Cui, and Quan Wang. Interpretable and efficient heterogeneous graph convolutional network. TKDE, 2021.
[41] Ruochi Zhang, Yuesong Zou, and Jian Ma. Hyper-sagnn: a self-attention based graph neural network for hypergraphs. arXiv preprint arXiv: 19110261,, 2019.
[42] Xiao-Meng Zhang, Li Liang, Lin Liu, and Ming-Jing Jing Tang. Graph neural networks and their current applications in bioinformatics. Frontiers in genetics, 12:690049, 2021.
[43] Jun Zhao, Zhou Zhou, Ziyu Guan, Wei Zhao, Wei Ning, Guang Qiu, and Xiaofei He. Intentge: scalable graph convolution framework fusing heterogeneous information for recommendation. In Proceedings of the 25th ACM SIGKDD international conference on knowledge discovery & data mining, pages 2347-2357, 2019.
[44] Minhao Zou, Zhongxue Gan, Yutong Wang, Junheng Zhang, Dongyan Sui, Chun Guan, and Siyang Leng. Unig-encoder: A universal feature encoder for graph and hypergraph node classification. Pattern Recognition, 147:110115, 2024.
NeurIPS Paper Checklist
1. Claims
Question: Do the main claims made in the abstract and introduction accurately reflect the paper's contributions and scope?
Answer: [Yes].
Justification:
See the abstract and Section I
Guidelines:
The answer NA means that the abstract and introduction do not include the claims made in the paper.
13

---

The abstract and/or introduction should clearly state the claims made, including the contributions made in the paper and important assumptions and limitations. A No or NA answer to this question will not be perceived well by the reviewers.
The claims made should match theoretical and experimental results, and reflect how much the results can be expected to generalize to other settings.
It fine to include aspirational goals as motivation as long as it clear that these goals not attained by the paper.
2. Limitations
Question: Does the paper discuss the limitations of the work performed by the authors?
Answer:
[Yes].
Justification:
See Appendix
Guidelines:
The answer NA means that the paper has no limitation while the answer No means that the paper has limitations, but those are not discussed in the paper.
The authors are encouraged to create separate "Limitations" section in their paper.
The paper should point out any strong assumptions and how robust the results are to violations of these assumptions (e-g., independence assumptions, noiseless settings, model well-specification, asymptotic approximations only holding locally). The authors should reflect on how these assumptions might be violated in practice and what the implications would be.
The authors should reflect on the scope of the claims made, e.g.. if the approach was only tested on few datasets or with a few runs. In general, empirical results often depend on implicit assumptions, which should be articulated.
The authors should reflect the factors that influence the performance of the approach. For example, a facial recognition algorithm may perform poorly when image resolution is low images taken in low lighting. Or specch-to-text system might not be used reliably to provide closed captions for online lectures because fails to handle technical jargon.
The authors should discuss the computational efficiency of the proposed algorithms and how they scale with dataset size.
If applicable, the authors should discuss possible limitations of their approach to address problems of privacy and fairness.
While the authors might fear that complete honesty about limitations might be used by reviewers grounds for rejection, a worse outcome might be that reviewers discover limitations that aren't 't acknowledged in the paper. The authors should use their best judgment and recognize that individual actions in favor of transparency play important role in developing norms that preserve the integrity of the community. Reviewers will be specifically instructed to not penalize honesty concerning limitations.
3. Theory assumptions and proof's
Question: For each theoretical result, does the paper provide the full set of assumptions and complete (and correct) proof?
Answer: [Yes].
Justification:
See Appendix
Guidelines:
The answer NA means that the paper does not include theoretical results.
All the theorems, formulas, and proofs in the paper should be numbered and cross- referenced.
All assumptions should be clearly stated referenced in the statement of any theorems.
The proofs can either appear the main paper or the supplemental material, but if they appear in the supplemental material, the authors are encouraged to provide a short proof sketch to provide intuition.
Inversely, any informal proof provided in the core of the paper should be complemented by formal proofs provided in appendix supplemental material.
14

---

Theorems and Lemmas that the proof relies upon should be properly referenced.
4. Experimental result reproducibility
Does the paper fully disclose all the information needed to reproduce the main ex- perimental results the paper to the extent that affects the main claims and/or conclusions of the paper (regardless of whether the code and data are provided or not)?
Question:
Answer: [Yes].
Justification: See Appendix and our source code Zhengziyu77/HHMN
https: httpp://ggiii http//ggttuuu....e com/
Guidelines:
The answer NA means that the paper does not include experiments.
If the paper includes experiments, a No answer to this question will not be perceived well by the reviewers: Making the paper reproducible is important, regardless of whether the code and data are provided or not.
If the contribution is dataset and/or model, the authors should describe the steps taken to make their results reproducible or verifiable.
Depending on the contribution, reproducibility can be accomplished in various ways. For example, the contribution a novel architecture, describing the architecture fully might suffice, if the contribution is specific model and empirical evaluation, it may be necessary to either make it possible for others to replicate the model with the same dataset, or provide access to the model. In general. releasing code and data often one good way to accomplish this, but reproducibility can also be provided via detailed instructions for how to replicate the results, access to a hosted model (e.g., in the case of a large language model), releasing of model checkpoint, or other means that are appropriate the research performed.
While NeurIPS does not require releasing code, the conference does require all submis- sions to provide some reasonable avenue for reproducibility, which may depend on the nature of the contribution. For example
(a) If the contribution is primarily new algorithm, the paper should make it clear how to reproduce that algorithm.
(b) If the contribution is primarily a new model architecture, the paper should describe the architecture clearly and fully.
(c) If the contribution is a new model (e.g., large language model), then there should either be a way access this model for reproducing the results or a way reproduce the model (e.g., with an open-source dataset or instructions for how to construct the dataset).
(d) We recognize that reproducibility may be tricky in cases, in which authors are welcome to describe the particular way they provide for reproducibility. In the case of closed-source models, it may be that access the model is limited in some way (e.g., to registered users), but it should be possible for other researchers to have some path to reproducing verifying the results.
5. Open access to data and code
Question: Does the paper provide open access the data and code, with sufficient instruc- tions to faithfully reproduce the main experimental results, as described in supplemental material?
Answer: [Yes].
Justification: See Appendix A. and see our source code at: https://github. com/
Zhengziyu77/HHN
Guidelines:
The answer NA means that paper does not include experiments requiring code.
Please see the NeurIPS code and data submission guidelines (https://nips.cm cc/
for more details.
While we encourage the release of code and data, we understand that this might not be possible, so "No" is an acceptable answer. Papers cannot be rejected simply for not including code, unless this central to the contribution (e.g., for a new open-source benchmark).
15

---

The instructions should contain the exact command and environment needed to run to reproduce the results. See the NeurIPS code and data submission guidelines (https
wtt.ssabbbssiooooooooooooooo.o onpolicy) for more details.
The authors should provide instructions data access and preparation, including how to access the raw data, preprocessed data, intermediate data, and generated data, etc.
The authors should provide scripts to reproduce all experimental results for the new proposed method and baselines. If only a subset of experiments are reproducible, they should state which ones are omitted from the script and why.
At submission time, to preserve anonymity, the authors should release anonymized versions (if applicable).
Providing as much information as possible in supplemental material (appended to the paper) is recommended, but including URLs to data and code is permitted.
6. Experimental setting/details
Question: Does the paper specify all the training and test details (e.g., data splits, hyper- parameters, how they were chosen, type of optimizer, etc.) necessary to understand the results?
Answer: [Yes].
Justification: See Appendix and see our source code at: https://githi: com/ zhengziyu77/HHMN
Guidelines:
The answer NA means that the paper does not include experiments.
The experimental setting should be presented in the core of the paper level of detail that is necessary to appreciate the results and make sense of them.
The full details can be provided either with the code, in appendix, or as supplemental material.
7. Experiment statistical significance
Does the paper report error bars suitably and correctly defined or other appropriate information about the statistical significance of the experiments?
Question:
Answer: [Yes].
Justification:
See the experimental results in Table Table and Table 3
Guidelines:
The answer NA means that the paper does not include experiments.
The authors should answer "Yes" if the results accompanied by error bars, confidence intervals, or statistical significance tests, at least for the experiments that support the main claims of the paper.
The factors of variability that the error bars are capturing should be clearly stated (for example, train/test split, initialization, random drawing of some parameter, overall run with given experimental conditions).
The method for calculating the error bars should be explained (closed form formula, call to library function, bootstrap, etc.)
The assumptions made should be given (e.g., Normally distributed errors).
It should be clear whether the error bar the standard deviation or the standard error of the mean.
It is OK to report 1-sigma error bars, but should state it. The authors should preferably report 2-sigma error bar than state that they have a 96% CI, the hypothesis of Normality of errors is not verified.
For asymmetric distributions, the authors should careful not to show in tables or figures symmetric error bars that would yield results that are out of range (e.g. negative error rates).
If error bars are reported in tables or plots, The authors should explain in the text how they were calculated and reference the corresponding figures or tables in the text.
8. Experiments compute resources
16

---

For each experiment, does the paper provide sufficient information on the com- puter resources (type of compute workers, memory, time of execution) needed reproduce the experiments?
Question:
Answer: [Yes].
Justification: See Appendix
Guidelines:
The answer NA means that the paper does not include experiments.
The paper should indicate the type of compute workers CPU or GPU, internal cluster, or cloud provider, including relevant memory and storage.
The paper should provide the amount of compute required for each of the individual experimental runs as well estimate the total compute.
The paper should disclose whether the full research project required more compute than the experiments reported in the paper (e.g., preliminary failed experiments that didn't 't make into the paper).
9. Code of ethics
Question: Does the research conducted in the paper conform, in every respect, with the NeurIPS Code of Ethics
Answer: [Yes].
Justification: All the experiments of this work conform, in every respect, with the NeurIPS Code of Ethics.
Guidelines:
The answer NA means that the authors have not reviewed the NeurIPS Code of Ethics.
If the authors answer No, they should explain the special circumstances that require deviation from the Code of Ethics.
The authors should make sure to preserve anonymity (e.g., if there is special considera- tion due laws or regulations in their jurisdiction).
Broader impacts
Question: Does the paper discuss both potential positive societal impacts and negative societal impacts of the work performed?
Answer: [Yes].
Justification:
See Appendix
Guidelines:
The answer NA means that there is no societal impact of the work performed.
If the authors answer NA No, they should explain why their work has societal impact or why the paper does not address societal impact.
Examples of negative societal impacts include potential malicious or unintended uses (e.g., disinformation, generating fake profiles, surveillance), faimess considerations (e.g.. deployment of technologies that could make decisions that unfairly impact specific groups), privacy considerations, and security considerations.
The conference expects that many papers will be foundational research and not tied to particular applications, let alone mentoyments. However, there a direct path to any negative applications, the authors should point it out. For example, it is legitimate to point out that an improvement in the quality of generative models could used to generate deepfakes for disinformation. On the other hand, it is not needed to point out that generic algorithm for optimizing neural networks could enable people to train models that generate Deepfakes faster.
The authors should consider possible harms that could arise when the technology being used as intended and functioning correctly, harms that could arise when the technology is being used intended but gives incorrect results, and harms following from (intentional or unintentional) misuse of the technology.
17

---

If there are negative societal impacts, the authors could also discuss possible mitigation strategies (e.g.. gated release of models, providing defenses in addition to attacks, mecha- nisms for monitoring misuse, mechanisms to monitor how system learns from feedback over time, improving the efficiency and accessibility of MI.).
11. Safeguards
Question: Does the paper describe safeguards that have been put in place for responsible release of data or models that have a high risk for misuse (c.g., pretrained language models, image generators, scraped datasets)?
Answer: [NA].
Justification:
The paper poses no such risks.
Guidelines:
The answer NA means that the paper poses no such risks.
Released models that have high risk for misuse or dual-use should be released with necessary safeguards to allow for controlled use of the model, for example by requiring that users adhere to usage guidelines or restrictions to access the model or implementing safety filters.
Datasets that have been scraped from the Internet could pose safety risks. The authors should describe how they avoided releasing unsafe images.
We recognize that providing effective safeguards is challenging, and many papers do not require this, but we encourage authors to take this into account and make best faith effort.
12. Licenses for existing assets
Question: Are the creators or original owners of assets (e.g., code, data, models), used in the paper, properly credited and the license and terms of use explicitly mentioned and properly respected?
Answer: [Yes].
Justification: have properly cited existing assets our paper.
Guidelines:
The answer NA means that the paper does not existing assets.
The authors should cite the original paper that produced the code package or dataset.
The authors should state which version of the asset used and, if possible, include URL.
The name of the license (e.g., CC-BY 4.0) should be included for each asset.
For scraped data from a partieular source (e.g., website), the copyright and terms of service of that source should be provided.
If assets released, the license, copyright information, and terms of use in the package should be provided. For popular datasets, wwpppssiiiteeeeoo thcode. com hat.aetaaeessaaeeaeeomo has curated licenses for some datasets. Their licensing guide can help determine the license of dataset.
For existing datasets that are re-packaged, both the original license and the license of the derived asset (if it has changed) should be provided.
If this information is not available online, the authors are encouraged to reach out to the asset's creators.
13. New assets
Question: Are new assets introduced in the paper well documented and is the documentation provided alongside the assets?
Answer: [Yes].
Justification:
We have provided our well-documented source code at: https://github
com/ conn/hengzzyu777/IIg
Guidelines:
The answer NA means that the paper does not release new assets.
18

---

/LLM) for Researchers should communicate the details of the dataset/code/moodl as part of their submissions via structured templates. This includes details about training, license, limitations, etc.
The paper should discuss whether and how consent was obtained from people whose asset is used.
At submission time, remember anonymize your assets (if applicable). You can either create an anonymized URL or include an anonymized zip file.
14. Crowdsourcing and research with human subjects
Question: For crowdsourcing experiments and research with human subjects, does the paper include the full text of instructions given to participants and screenshots, if applicable, as well as details about compensation (if any)?
Answer: [NA].
Justification:
The paper does not involve crowdsourcing nor research with human subjects.
Guidelines:
The answer NA means that the paper does not involve crowdsourcing nor research with human subjects.
Including this information the supplemental material is fine, but if the main contribution of the paper involves human subjects, then much detail as possible should be included in the main paper.
According to the NeurIPS Code of Ethics, workers involved in data collection, curation, other labor should be paid at least the minimum wage in the country of the data collector.
15. Institutional review board (IRB) approvals or equivalent for research with human subjects
Question: Does the paper describe potential risks incurred by study participants, whether such risks were disclosed to the subjects, and whether Institutional Review Board (IRB) approvals (or an equivalent approval/review based on the requirements of your country or institution) were obtained?
Answer: [NA].
Justification: The paper does not involve crowdsoureing nor research with human subjects.
Guidelines:
The answer NA means that the paper does not involve crowdsourcing research with human subjects.
Depending on the country in which research is conducted, IRB approval (or equivalent) may be required for any human subjects research. If you obtained IRB approval, you should clearly state this in the paper.
We recognize that the procedures for this may vary significantly between institutions and locations, and expect authors to adhere to the NeurIPS Code of Ethics and the guidelines for their institution.
For initial submissions, do not include any information that would break anonymity (if applicable), such the institution conducting the review.
16. Declaration of LLM usage
Question: Does the paper describe the usage of LLMs if it is important, original, or non-standard component of the core methods in this research? Note that if the LLM is used only for writing, editing, formatting purposes and does not impact the core methodology, scientific rigorousness, or originality of the research, declaration is not required.
Answer: [NA].
Justification:
The core method development in this research does not involve LLMs.
Guidelines:
The answer NA means that the core method development in this research does not involve LLMs as any important, original, or non-standard components.
Please refer to our LLM policy what should or should not be described.
19

---

A Datasets
construct their hypergraphs based on Cora, PubMed, and Citeseer, which originally belong to homogeneous simple graphs (as shown in Figure (aa). Several methods [ TO 22 also construct their hypergraphs based DBLP, ACM, MAG, and IMDB, which originally belong to heterogeneous simple graphs (as shown in Figure l(b)). In other words, these hypergraphs are transformed from simple graphs, and they essentially describe binary relations rather than multi-ary relations.
Most previous studies 12
2
18
21
14
38 30
In this work, fully reflect the effectiveness of proposed HHNN in capturing complex structural features conveyed by syper-meta-Pe
we have tried our best to construct two genuine heterogeneous hypergraphs, where there are not only multiple types of nodes but also multiple types of real hyper- relations, as illustrated by Figure [(d]] To this end, we have tried our best to construct two new heterogeneous hypergraph benchmark datasets, and their key statistics listed in Table
Table 4: Dataset statisties.
Datasets
Node Type
Number
Hyperedge Type
Hyperedge Semanties
Number
Movies (M)
3439
"a user tags movie with
UMT (Rt)
9681
User (U)
2106
a specific tag"
Movielens
Tag (T)
3108
UMR (R2)
"a user rates movie"
158897
Rating (R)
10
Customer (C)
54321
customer purchases product from seller"
CPS (R))
55630
Product (P)
18454
Seller (S)
2090
"a customer provides a rat- ing for product"
CPR (R2)
55556
Olist
Rating (R)
5
Origin (0)
489
"an order is shipped from origin to destination with a freight value"
Destination (D)
3477
OPDF (Rs)
55630
Freight (F)
14
MovieLens is a real-world movie dataset, which was originally released by GroupLens a research laboratory at University of Minnesota. Based on the raw dataset, we construct heterogeneous hypergraph that contains four types nodes and two types of hyperedges. As we can see, the two hyperedge types (hyper-relations R₁ and R2) natural ternary relations. Movie nodes associated with ground truth labels, describing their genres, such as comedy, action, animation, etc.
Olist is a real-world e-commercial dataset. It contains the orders of Olist Store, Brazilian e- commerce platform. The raw dataset was originally released at Kaggle a data science competition platform. Based on the raw dataset, we construct heterogeneous hypergraph that contains six types of nodes and three types of hyperedges. As shown in the table, the hyper-relations R₁ and R3 are ternary relations, and the hyper-relation R; is quaternary relation. The product nodes are associated with ground labels that describe their categories, such as perfumery, telephone, automotive, etc.
B Baseelnnes
We select ten representative hypergraph neural network methods as our comparative baselines,
including: (1) CE-GCN; (2) HNHN 7 (3) HyperGCN
38 (4) AllSerTssfm 6): (5) AllDeepSets (
(6) UniGNN 21: (7) ED-HNN
+ (8) HGNN 12: (9) HGNN+ 14
Here, CE-GCN is a naive baseline, which first transforms a hypergraph into a simple graph through clique expansion (Л. where two nodes form an edge if and only if they are in the same hyperedge. Then, the GCN 24 model is utilized to encode the resulting simple graph. For baseline UniGNN, we adopt its most powerful variant, i.e., UniGCNII. Baselines AllSetTsfm (AllSerTransffrmee)) and AllDeepSets are two variants of the AllSet method [
22--222222222 22.
https://www
20

---

C Experimental Settings
We use the Pytorch framework implement our proposed HHNN. The number of model layers is searched in (1, 2, 3, 4, 5}, the dimensionality of hidden node/hyperedge representations is searched in {8, 16, 32, 64, 128], the number of attention heads is searched in (1, 2, 4, 8). We use the Adam optimizer optimize all the trainable model parameters, which are randomly initialized by the Xavier uniform distribution [T6]. For ease of tuning, the optimizer settings are the same for both datasets. Specifically, the learning rate is set to 0.001, the weight decay is set to 0.O, and the attention dropout rate is set to 0.5. For more details about perrmeer settings, please see our source code at: https:/ het/ggithubbb.. thub. com/ zhengziyu77 HHHNN
Regarding baselines, we reproduce the experimental results on the two benchmark datasets, based on their official source codes. For fairness, we also try our best to search for the optimal hyper-parameters for them, starting from the default settings of their code or the settings reported in their papers.
For fairness, some of the settings are shared among all the methods. Firstly, they use the same input features. Secondly, they use the same evaluation metrics of Micro F1 (Micro) score, Macro F1 (Macro) score, and Area Under the Curve (AUC) score. Finally, they use the same training/valldatiinnn/ sets. Specifically, on each dataset, we randomly select 5% ground-truth labels as the training set, and the rest (1 - 7 are divided equally as the validation set and the test set, where T E {20, 40}. We randomly repeat all the evaluation tasks ten times and report the mean results with the standard deviation. All the experiments are conducted on Intel(R) Core(TM) 19-10980XE CPU and NVIDIA TITAN RTX GPU with 24GB GPU memory.
D Algorithm
The overall training process of our proposed HHNN shown in Algorithm I
Algorithm 1:
The training process of HHNN.
Input The heterogeneous hypergraph G - (V, The number of model layers N.
Output: The embeddings of all the nodes and hyperedges.
Randomly initialize all the trainable model parameters;
2 for n I,..., N do
# from nodes to hyperedges; Perform a-Attention aggregation according Eqs. 13
# from hyperedges to nodes;
Perform 3-Attention (intra-type) aggregation according to Eqs.
Perform A-ttenntoon (inter-type) aggregation according to Eqs.
8 end
Compute loss according Eq. (9:
10
Update model parameters by gradient descent;
E Theoretical Analysis of Hyper-meta-paths
The HHNN model introduces hierarchical attention mechanism three levels, i.e., node-to- hyperedge, intra-type hyperedge-to-nodee, and inter-type hyperedge-to-node, which correspond to the a-Attention, the S-Attention, and the --Attention, respectively. Here, we can theoretically show that this attention structure enables the model to automatically discover important syper-meta-ae mera--attss by back-tracing the learned attention coefficients.
E.1 Hyper-meta-path Importance Calculation
Consider a target node i E V, its final embedding is output by the last layer N, which reflects the information that flows through sequence of interconnected nodes and hyperedges across the N layers. Theoretically, the importance is the product of the involved attention weights along this
21

---

sequence. Thus, regarding the syper-meta-pee P = R1 RR .... Ry involved in this sequence, its importance can computed follows:
I(P)
11
11 3 y/1
(10)
A higher value of T(P) indicates that the information that propagates along the hyper-meta-patt P contributes more significantly to the target nodes i's final embedding w.
E.2 Important Hyper- Discovering
By calculating the importance I(P) for all relevant paths that lead to the target node we can identify the most important hyper-meta-path p for node as follows:
n arg max ((P)
(11)
P' represents the most significant hyper-meta-patt for the target node i, as learned by the model.
E.3 Interpretability of Discoverd Hyper-meta-path
The automatically discovered hyper-meta-paie -atttttpphhhttt P carries specific semantic meaning derived from the composition of the involved individual hyper-relations. This semantic interpretation can be used explain the model's prediction for the target node For instance, if the task is node classification, the semantics of pp* can provide insight into why the model assigned a particular class label to the target node
E.4
Discussion and Outlook of Attention-basee based Hyper-meta-paue Discovery
HHNN discovers hypermeta-pathi based on the attention distribution, and this attention-based heuristic reveals correlations rather than causal relationships. In the future work, formalization of causal interpretability is an important direction, and we plan to explore techniques like counterfactual reasoning our future work. Here, also conduct a preliminary experiment of masking information along higght paths and observing the change in the model's prediction, and the results are shown in the Table As we can observe, by masking information along high-weight paths, the model's 's performance drops sharply, which clearly indicates that the high-weight paths identified by the HHNN model are crucial.
Table 5: Comparison between HHNN performance with high-weight paths masked (right) and the original performance (left) under the 20% training ratio.
Movielen
Olist
Micro 56.80+1.65 + +28.63+5.9
72.54
13.244 81
Macro 26.24 13.90 - 11.83 12.80
72.89 10.56 - 6.38 10.73 93.20 -0..13
AUC
73.21 12.13 + +4.004
F
Comparison between HAN and HHNN
We compare our HHNN to HAN, which is based on a two-level attention aggregation mechanism. The results are shown in Table As see, HHNN can achieve higher performance against HAN on both ACM and DBLP, which demonstrates the superiority of our HHNN.
G Experiments on More Datasets
Most existing heterogeneous hypergraph datasets are transformed from simple graphs with binary relations, which lack natural multi-way interactions and cannot fully showcase the advantages of
22

---

Table 6: Dataset statistics.
ACM
DBLP
HAN
85.09
90.02
HENN
87.28
91.29
hypergraph neural networks. In contrast, in our work, have tried our best construct two new real-world datasets from the movie domain and e-commerce domain, both containing multiple types of naturally occurring heterogeneous hyperedges based genuine multi-ary relations. The two datasets are more challenging to fully showcase the power of our HHNN. Here, we also conduct a performance comparison three widely-used hypergraph datasets, i.e., Cora, PuMmed, and DBLP, and the results are shown Table We can observe that since these three datasets do not contain complex and heterogeneous structural features, the three hypergraph methods achieve comparable performance, with our HHNN performing slightly better.
Table 7: The performance comparison between three hypergraph methods on three new hypergraph datasets, under the 20% training ratio.
Cora
PubMed
DBLP
UniGNN
76.93+1.73
84.05 +0.63
90.49=0.18
ED-HNN 77.07+1.22
84.1220.68
90.50
HHNN
77.42
84.14
90.50
Table 8: The performance comparison on Movielens, under the 20% training ratio.
Miero
Macro
AUC
SheafHyperGNN 9
46.59 11224 1..2
18.85 1.74
61.68
UniG-Encoder 44
41.7941.17
16.15
58.6641.32
HHNN
56.80+1.65
26.24
73.21
Table 9: The performance comparison Olist, under the 20% training ratio.
Micro
Macro
AUC
SheafHyperGNN 99
51.71 +1.44
51,56
85. 85.60+1.02
UniG-Encoder 44 HHNN
24.40
23.68 2..4
64.96
72.54 10.54
72.89 0.56
93.20.t0.32
Table 10: The rumning time (seconds of 10 epochs) of HHNN on heterogeneous hypergraphs of different sizes using varying ratios of nodes.
Moviclens
Olist
20%
0.730
2.361
40%
0.763
2.449
60%
1.114
2,839
80%
1.205
2,883
100%
1.231
3.194
H Experiments with More Baselines
compare our HHNN against two recent hypergraph models, i.e., SheafHyperGGNN 9 and UniG- Encoder 44), as the new baselines, and their experimental results are shown in Table and Table 9
23

---

Table 11: The running time (seconds of 10 epochs) of HHNN on heterogeneous hypergraphs of different sizes using varying ratios of hyperedges.
Movielens
Olist
20%
0.653
2.413
40%
0.805
2.528
60%
0.927
2.809
80%
1.111
2.978
100%
1.231
3.194
Table 12: The running time (seconds of epoch) of HHNN in comparison with baselines UniGNN and EDHNN.
HyperGCN
UniGNN
ED-HNN
HHNN
Movielens Olist
81.57
0.13 0.17
0.18
0.15
90.22
0.63
0.19
We that our HHNN significantly outperforms the two hypergraph baseline methods both datasets.
I Efficiency Study
To further verify the efficiency of HHNN, we have added the scalability experiment as well as the running time comparison experiment. The results are shown in Table TO Table [1] and Table [2] As we can see, the running time of HHNN increases approximately linearly with the size of the graph. Besides, the running time of HHNN is par with two baselines, UniGNN and EDHNN, and is much less than the running time of the baseline HyperGCN.
J More Related Work
In the past decade, the representation learning methods on hypergraphs have become research surge. In the recent two years, several surveys [1] [2] 23 (28 have been published to comprehensively review existing hypergraph representation learning methods from different perspectives.
Regarding the heterogeneity of nodes and hyperedges, some of the existing methods, e.g., 44 only consider node heterogeneity, and some methods generally consider the hyperedge heterogeneity based on operations like concatenation (30) and adaptive fusion [14]. RelBench [13) leverages graph neural networks learn directly from relational databases, which can also be viewed as a heterogencous hypergraph neural network. In contrast, HHNN focuses on aaper-meta-pataa to capture more complex structural features.
There are also some other path-related methods. Pathsim B1 is the first work to define the concept of meta-path sequence of binary relations among two nodes, which has shown extraordinary effectiveness in capturing heterogeneous structural features and rich semantics contained in hetero- geneous simple graphs. The subsequent study, metapath2vec (8) leverages set of user-specified meta-paths to guide the random walk on heterogeneous simple graphs, transforming heterogeneous structural features into sequences. Then, develops a word2vec [2k] encoder obtain the node representations. Considering that existing methods need users to specify useful meta-paths, which is practical, ie-HGCN [40] is proposed automatically discover and exploit useful meta-paths in heterogeneous simple graphs. HAN 35 is wnol-knownn GNN method for heterogeneous simple graphs, which based on set of user-specified meta-paths. While our model and HAN both adopt hierarchical attention, they are fundamentally different in scope and purpose. Firstly, HAN operates on heterogeneous simple graphs, where all relations are binary between node pairs, whereas HHNN is designed for heterogeneous hypergraphs that naturally encode multi-ary relations of various types. Moreover, HAN's two-level attention relies on manually specified meta-paths, while HHNN introduces three-level attention mechanism that automatically discovers hyper-meta-patee without

---

manual intervention. HMG-CR [39 proposes the concept of hyper meta- path, which is composition of multiple meta-paths between two specified end nodes heterogeneous simple graph. HPHG [20] defines the concept of hyper-path, which is utilized to preserve the complex information about the indecomposability of hypergraphs.
Different from these existing methods above, in this work, we define novel concept called hyper- meta-path, which describes a complex hyper-relation by compositing a sequence of hyper-relations.
K
Limitations
While the proposed HHNN demonstrates strong performance in modeling heterogeneous hypergraphs and good ability to automatically discover semantically meaningful hyper-meta-patte patts, several limita- tions should be acknowledged: (I) Although the attention- aggregation enhances interpretability, reveals correlations rather than causal relationships; (2) Although the model can learn to ignore some meaningless combinations by the attention optimization, the current definition of hyper-meta- path may be two broad in real-world scenarios, particularly when the shared node type is generic or high-freequ highffreueney; (3) HHNN is particularly designed for complex heterogeneous hypergraphs, and it is most pronounced on hypergraphs with natural multi-ary relations, and its advantages may not be fully realized when such structures not prominent. In future work, would like to further explore alternative definitions and discovery mechanisms for hyper-meta-pant patee,, and the direction of utilizing causality is very promising.
L Broader Impacts
The proposed HHNN model contributes to the broader field of graph representation learning by enabling improved performance and understanding for heterogeneous hypergraphs. This advancement can benefit many applications, such as recommendation systems, bioinformatics, and social network analysis, by simultaneously improving task performance and enhancing model interpretability through the modeling of more complex and higher-order relational patterns.
25


Reviews:
[{"review_id": "GXrdC3tjRK", "reviewer": "Reviewer_H8eL", "summary": "The authors propose Heterogeneous Hypergraph Neural Network (HHNN) to effectively capture complex structural features and richer semantics in heterogeneous hypergraphs by introducing the novel concept of hyper-meta-paths.\n\nAuthors define hyper-meta-paths as sequences of hyper-relations that share common node types, generalizing the meta-path concept from simple graphs to heterogeneous hypergraphs to encode multi-ary relations. To leverage these, authors design HHNN, a graph neural network architecture employing three levels of attention mechanisms: α-attention aggregates node features into hyperedge representations, β-attention aggregates hyperedge features intra-type back to nodes, and γ-attention aggregates across hyperedge types. This design allows HHNN to automatically discover and exploit important hyper-meta-paths, enhancing both performance and interpretability.\n\nAuthors perform extensive experiments on two newly constructed real-world heterogeneous hypergraph datasets (Movielens and Olist), demonstrating that HHNN significantly outperforms state-of-the-art baselines in node classification tasks. Additionally, ablation studies verify the critical role of each attention mechanism in HHNN, and case analyses show that the discovered hyper-meta-paths provide meaningful semantic interpretations for model predictions.", "questions": "- First of all, the proposed approach does not seem very different from apply graph neural networks over the graphs where all the relations are represented as nodes. How can authors compare the HNNN with such concepts? This comparison needs to be addressed and studied.\n- In Figure 3, m_{3}' needs to be m_{5}'.\n- Like Figure 3, 3 different attention layers are proposed. However, one of the most straightforward ways is to use a giant attention over all the neighbor nodes connected through hyperedges. That is, instead of \\alpha, \\beta, and \\gamma, one can think of only one attention over all the neighbors or 2 attentions (1 attention over different types and the other attention for each type's neighbors). What is the rationale of choosing the current architecture?\n- Please include minimal explanation about the experimental datasets, so that at least readers can understand what are hperedges and what each UMT means.\n- Similarly, please explain what 20% and 40% means in Table 1 and 2.\n- Why do authors use different settings for Table 3 from Table 1 and 2? This reduces the interpretability of each ablation case compared to the other methods.\n- Related work is recommended to be included in the main content.", "limitations": "Yes", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 4, "significance": 2, "originality": 3, "strengths_and_weaknesses": "Strengths\n\n- Both heterogeneous hypergraphs and the novel concept of hyper-meta-paths are clearly defined, and are well incorporated into existing graph neural network concepts with 3 attention layers.\n- Authors perform qualitative analyses and ablation studies, which not only help readers understand how the model works but also validate the specific contributions of the multi-level attention mechanisms, lending credibility and interpretability to the proposed method. In particular, the case study clearly shows the role of each attention layer.\n- HHNN achieves consistently superior performance over given real-world datasets. Along with the ablation study, the experimental results demonstrate the practical benefits of introducing hyper-meta-paths and the effectiveness of the attention mechanisms.\n\nWeaknesses\n- As with many graph-based methods, how hyperedges and hyper-meta-paths are defined from raw data significantly influences model performance. However, the paper does not provide guidance, heuristics, or sensitivity analyses for constructing these structures, limiting practical applicability in diverse domains.\n- The authors evaluate HHNN on only two datasets (Movielens and Olist), both drawn from recommendation and e-commerce domains. This narrow empirical scope raises concerns about how well the method generalizes to other domains such as biomedical networks, financial graphs, or knowledge graphs.\n- The high-level idea behind HHNN—modeling multi-entity relationships as hyperedges and learning over their compositions—is conceptually very similar to Relational Deep Learning (RDL), where database tuples are modeled as nodes and joins as edges to enable graph representation learning directly on relational databases. However, the paper does not discuss or compare itself to this relevant body of work, notably missing connections to: Fey, M., et. al., Relational Deep Learning: Graph Representation Learning on Relational Databases. In Proceedings of the 41st International Conference on Machine Learning, ICML 2024.", "was_revised": true, "final_justification": "Authors have addressed various points I raised. My major concerns were in (1) similarity to the heterogeneous flattened graph approach (along with its weakness) and (2) limited experiments. Authors' responses have changed my perspective that the proposed framework is more principled and fundamental even if the underlying deep computational graphs have similarity to the existing approaches that I was concerned about. Also, authors have added more experimental results supporting their arguments.", "rebuttal": "Thanks for your comments. In the following, we respond to your concerns point by point.\n\n---\n\n**Point 1**: *Does not provide guidance, heuristics, or sensitivity analyses for constructing hyper-meta-paths.*\n\n**Reply 1**: Thank you for the comment. Unlike many prior methods that require hand-crafted meta-paths or heuristics, our HHNN automatically discovers useful hyper-meta-paths based on the input heterogeneous hypergraph through a multi-level attention mechanism. Therefore, it does not rely on manual definition or construction rules. This design makes our HHNN eliminate the need for additional guidance or sensitivity analysis in constructing hyper-meta-paths.\n\n---\n\n**Point 2**: *Evaluate HHNN on only two datasets (Movielens and Olist), both drawn from recommendation and e-commerce domains.*\n\n**Reply 2**: Thanks for your comment. Most existing heterogeneous hypergraph datasets are transformed from simple graphs with binary relations, which lack natural multi-way interactions and cannot fully showcase the advantages of hypergraph neural networks. In contrast, we have tried our best to construct two new real-world datasets from the movie domain and e-commerce domain, both containing multiple types of naturally occurring heterogeneous hyperedges based on genuine multi-ary relations. Following your suggestion, we will continue seeking more such datasets, and we would greatly appreciate any specific recommendations about such datasets. Nevertheless, we have added three new hypergraph datasets, i.e., Cora, PuMmed, and DBLP, and the results are shown in the table below.\n\n*Table 1. The performance comparison between three hypergraph methods on three new hypergraph datasets, under the 20% training ratio. We can observe that since these three datasets do not contain complex and heterogeneous structural features, the three hypergraph methods achieve comparable performance, with our HHNN performing slightly better.*\n|            | Cora             | PubMed           | DBLP             |\n| ---------- | ---------------- | ---------------- | ---------------- |\n| UniGNN     | 76.93 ± 1.73     | 84.05 ± 0.63     | 90.49 ± 0.18     |\n| ED-HNN     | 77.07 ± 1.22     | 84.12 ± 0.68     | 90.50 ± 0.21     |\n| **HHNN**   | **77.42 ± 1.67** | **84.14 ± 0.74** | **90.50 ± 0.27** |\n\n---\n\n**Point 3**: *Very similar to Relational Deep Learning (RDL), and missing connections to: Fey, M., et. al., ICML 2024.*\n\n**Reply 3**: Thank you for your insightful suggestion. We are glad to learn about the interesting connection between our work and Relational Deep Learning. Following your advice, we have cited this relevant work in our manuscript and included a discussion to acknowledge the relationship. We will update the paper accordingly when permitted.   \n\n---\n\n**Point 4**: *The difference from applying graph neural networks over the graphs where all the relations are represented as nodes.*\n\n**Reply 4**: Thank you for the question. While modeling relations as nodes can flatten multi-way interactions into binary structures, it fundamentally alters the relational semantics. Our approach explicitly preserves native multi-entity hyperedges without decomposing them, allowing HHNN to capture true high-order structures. Moreover, we introduce hyper-meta-paths, a novel concept that composes multi-relational semantics across heterogeneous hyperedges, which cannot be naturally expressed when all relations are reduced to nodes. This design enables both improved performance and stronger interpretability.\n\n---\n\n**Point 5**: *In Figure 3, m_{3}' needs to be m_{5}.*\n\n**Reply 5**: Thank you very much for carefully pointing out this issue. $m_3$ should indeed be $m_5$. We have corrected Figure 3 accordingly and will update the paper when permitted.\n\n---\n\n**Point 6**: *What is the rationale of choosing the current three-level attention architecture?*\n\n**Reply 6**: Thank you for the thoughtful question. Using a single or two attention layers may seem simpler, but it fails to capture the full complexity of heterogeneous hypergraphs. Our three-level attention explicitly aligns with the structure of heterogeneous hypergraphs. As illustrated by Figure 3, $\\alpha$-attention is used since each hyperedge contains multiple nodes, $\\beta$-attention is used since each node may participate in multiple hyperedges of a specific type, and $\\gamma$-attention is used since each node may participate in multiple types of hyperedges. This modular design allows HHNN to adaptively model type-specific interactions and their composition, which would be blurred or lost in a single unified attention. Empirical results in Table 3 also confirm the effectiveness of this fine-grained architecture.\n\n---\n\n**Point 7**: *Include minimal explanation about the experimental dataset. What does UMT hyperedge mean?*\n\n**Reply 7**: Thank you very much for this helpful comment.\nOn Movielens, each *UMT*-type hyperedge connects a User, a Movie, and a Tag, indicating that ''*a user tags a movie with a specific tag*'', and each *UMR*-type hyperedge indicates that ''*a user gives a rating to a movie*''. On Olist, *CPS*-type hyperedge indicates that ''*a customer purchases a product from a specific seller*'', *CPR*-type hyperedge indicates that ''*a customer gives a rating to a purchased product*'', and *OPDF*-type hyperedge indicates that ''*a product is shipped from an origin to a destination using a specific freight*''. We will add these explanations to the new version of our manuscript.\n\n---\n\n**Point 8**: *What do 20% and 40% mean in Tables 1 and 2?*\n\n**Reply 8**: Thank you for this careful comment. 20% and 40% represent different ratios of training labels, respectively. We will add this explanation to our manuscript.\n\n---\n\n**Point 9**: *Why do authors use different settings for Table 3 from Tables 1 and 2?*\n\n**Reply 9**: We are sorry for leading you to this confusion. Tables 1 and 2 present the comparison results among all the baselines as well as our HHNN, under different training ratios. Table 3 presents an ablation study, comparing the experimental results of different variants of our HHNN. The dimension of training ratios is omitted for saving space. We will make the settings clearer in our new version of the manuscript.\n\n---\n\n**Point 10**: *Related work is recommended to be included in the main content.*\n\n**Reply 10**: Thanks for your kind suggestion. We will condense some non-essential content and move the related work into the main body of the paper."}, {"review_id": "xb9rRwSRsd", "reviewer": "Reviewer_bvBy", "summary": "This paper proposes the concept of hyper-meta-paths, a generalization of meta-paths to heterogeneous hypergraphs, and introduces HHNN, a GNN architecture designed to leverage hyper-meta-path semantics via multi-level attention. The authors claim that this framework captures richer relational structures and improves both performance and interpretability. Experimental results demonstrate improved performance over existing baselines across several datasets.", "questions": "Q1. Can you compare HHNN with any path-based model to clarify the benefit of hyper-meta-paths?\nQ2. How do you deal with the rapid growth of hyper-meta-paths?\nQ3. Is the full three-level attention necessary? Any ablation results?\nQ4. Can you provide an example or visualization to support the interpretability claim?\nQ5. How does HHNN generalize to more complex heterogeneous hypergraphs with increased hyperedge arity and semantic diversity?", "limitations": "The proposed method presents scalability challenges due to the rapid growth of hyper-meta-paths in heterogeneous hypergraphs. The claim of interpretability is not supported by concrete examples or analysis. Furthermore, the evaluation is conducted on relatively simple datasets, limiting insight into the broader applicability of the proposed approach.", "rating": 3, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 3, "significance": 2, "originality": 4, "strengths_and_weaknesses": "Strengths\nS1. The paper introduces the notion of hyper-meta-paths; a generalization of meta-paths for heterogeneous hypergraphs. This is appropriate for modeling multi-relational hypergraph semantics.\nS2. The proposed HHNN model uses a three-level attention aggregation scheme (node -> hyperedge -> node) to capture hyper-relational dependencies. The architecture is intuitive and well-structured.\nS3. HHNN outputs interpretable attention weights over hyper-meta-paths, which provides insight into which relational structures are most influential during prediction; an underexplored property in hypergraph learning.\n\nWeaknesses\nW1. The paper does not provide empirical evidence that hyper-meta-paths are essential. There is no comparison with meta-path-based or path-based baseline hypergraph models, making it unclear whether their modeling improves performance.\nW2. The number of hyper-meta-paths can grow rapidly, but the paper does not discuss how to limit or handle this. This may affect scalability on more complex graphs.\nW3. It is unclear whether all components of the model are necessary. The paper does not test what happens if parts of the attention mechanism are removed or modified.\nW4. The datasets used are relatively simple and may not be sufficient to demonstrate the benefit of modeling complex hyper-relational structures.\nW5. The model claims to offer interpretability, but no example or case study is provided to show that the learned hyper-meta-paths are meaningful.", "was_revised": true, "final_justification": "My rating remains as in the current review, with no additional comments.", "rebuttal": "Thanks for your comments. In the following, we respond to your concerns point by point.\n\n---\n\n**Point 1**: *Provide empirical evidence that hyper-meta-paths are essential. Comparison with meta-path-based baseline models.*\n\n**Reply 1**: We would like to kindly remind the reviewer that we did provide empirical evidence from both the ablation study in Section 4.2 and the case study in Section 4.3. Firstly, as shown in Table 3 of Section 4.2, we compare eight variants of HHNN by selectively disabling the α, β, and γ attention layers, which are responsible for capturing and composing hyper-meta-paths. The full version (variant \"111\") consistently outperforms all others, showing the effectiveness of hyper-meta-path in promoting performance. Secondly, as shown in Figure 5 of Section 4.3, we analyze learned attention weights to identify interpretable hyper-meta-paths contributing to predictions. For example, on Movielens, HHNN discovers that the composed hyper-meta-path T ← {UMT} ⋄ {UMR} → M captures semantics: “*a tag $t$ is linked to a movie $m$ through a user $u$, and the user $u$ associates the tag $t$ to a movie, and gives the movie $m$ a rating*”. This semantics is helpful for interpreting the model's prediction results on the movie node $m$. Prior meta-path-based models (e.g., HAN) are designed for heterogeneous simple graphs and cannot directly handle hypergraphs' multi-ary relations. Nevertheless, according to your kind suggestion, we have compared our HHNN with the meta-path-based baseline, HAN, and the results are shown in the table below.\n\n*Table A. Our HHNN can achieve superior performance against HAN on both ACM and DBLP.*\n|          | ACM            | DBLP           |\n| -------- | -------------- | -------------- |\n| HAN      | 85.09±2.48     | 90.02±0.87     |\n| **HHNN** | **87.28±0.88** | **91.29±0.92** |\n\n---\n\n**Point 2**: *The number of hyper-meta-paths can grow rapidly, which may affect scalability on more complex graphs. How does HHNN generalize to more complex heterogeneous hypergraphs with increased hyperedge arity and semantic diversity?**\n\n**Reply 2**: Thanks for your constructive suggestion. Let us first analyze the theoretical time complexity of HHNN. For each layer, the main cost comes from the three-level attention aggregation operations. The $\\alpha$-attention aggregation involves projecting and attending to nodes within each hyperedge, costing $\\mathcal{O}(|E| \\cdot d_\\alpha \\cdot f_\\alpha \\cdot r)$, where $|E|$ is the number of hyperedges, $d_\\alpha$ and $f_\\alpha$ are the dimensionalities of the input and output features, respectively, and $r$ denotes the average number of nodes per hyperedge. In the $\\beta$-attention aggregation phase, each node aggregates its connected hyperedges of each type, costing $\\mathcal{O}(|V| \\cdot d_\\beta \\cdot f_\\beta \\cdot t)$ where $|V|$ is the number of nodes, $d_\\beta$ and $f_\\beta$ are the feature dimensionalities, and $t$ denotes the average number of hyperedges of each type that a node participates in. In the $\\gamma$-attention aggregation phase, each node fuses its representations across different hyperedge types, costing $\\mathcal{O}(|V| \\cdot d_\\gamma \\cdot f_\\gamma \\cdot k)$, where $d_\\gamma$ and $f_\\gamma$ are the feature dimensionalities, and $k$ is the average number of hyperedge types. Assuming the model has $n$ layers, the total time complexity becomes: $\\mathcal{O}(|E| \\cdot d_\\alpha \\cdot f_\\alpha \\cdot r \\cdot n + |V| \\cdot d_\\beta \\cdot f_\\beta \\cdot t \\cdot n + |V| \\cdot d_\\gamma \\cdot f_\\gamma \\cdot k \\cdot n)$. In practical scenarios, $d_\\alpha, f_\\alpha, d_\\beta, f_\\beta, d_\\gamma, f_\\gamma, r, t, k, n$ are usually much smaller constants compared to $|\\mathcal{V}|$ and $|\\mathcal{E}|$. Therefore, the total time complexity of HHNN is equal to: $\\mathcal{O}(|\\mathcal{V}| + |\\mathcal{E}|)$, which is linear to the size of the hypergraph. Therefore, HHNN can well scale to large heterogeneous hypergraphs with more complex semantics. In addition, to verify the efficiency of HHNN, we have added the scalability experiment as well as the running time comparison experiment. The results are shown in the three tables below.\n\n*Table B. We induce heterogeneous hypergraphs of different sizes using *varying ratios of nodes*, and the running time (seconds of 10 epochs) of HHNN increases approximately linearly with the size of the graph.*\n|      | Movielens | Olist |\n| ---- | --------- | ----- |\n| 20%  | 0.730     | 2.361 |\n| 40%  | 0.763     | 2.449 |\n| 60%  | 1.114     | 2.839 |\n| 80%  | 1.205     | 2.883 |\n| 100% | 1.231     | 3.194 |\n\n*Table C. We induce heterogeneous hypergraphs of different sizes using *varying ratios of hyperedges*, and the running time (seconds of 10 epochs) of HHNN increases approximately linearly with the size of the graph.*\n|      | Movielens | Olist |\n| ---- | --------- | ----- |\n| 20%  | 0.653     | 2.413 |\n| 40%  | 0.805     | 2.528 |\n| 60%  | 0.927     | 2.809 |\n| 80%  | 1.111     | 2.978 |\n| 100% | 1.231     | 3.194 |\n\n*Table D. The running time (seconds of 1 epoch) of HHNN is on par with two baselines, UniGNN and EDHNN, and is much less than the running time of the baseline HyperGCN. Kindly remind that the efficiency is not our main contribution.*\n|           | HyperGCN | UniGNN  | ED-HNN | HNHN |\n| --------- | -------- | ------- | ------ | ---- |\n| Movielens | 81.57    | 0.13    | 0.18   | 0.15 |\n| Olist     | 90.22    | 0.17    | 0.63   | 0.19 |\n\n\n---\n\n**Point 3**: *Whether all the components of the model are necessary? Is the full three-level attention necessary? Any ablation results?*\n\n**Reply 3**: We are sorry for leading you to this misunderstanding. We did provide the ablation study in Section 4.2 to demonstrate the necessity of each module. Please see the experimental results in Table 3, the variant \"111\", which activates all three attention blocks, consistently outperforms all other variants, fully demonstrating that the full three-level attention is very necessary.\n\n---\n\n**Point 4**: *The datasets are relatively simple.*\n\n**Reply 4**: Thank you for the comment. Most existing heterogeneous hypergraph datasets are transformed from simple graphs with binary relations, which lack natural multi-way interactions and cannot fully showcase the advantages of hypergraph neural networks. In contrast, we have tried our best to construct two new real-world datasets from the movie domain and e-commerce domain, both containing multiple types of naturally occurring heterogeneous hyperedges based on genuine multi-ary relations. According to your suggestion, we will continue seeking more such datasets, and we would greatly appreciate any specific recommendations about such datasets. Nevertheless, we have added three new hypergraph datasets, i.e., Cora, PuMmed, and DBLP, and the results are shown in the table below.\n\n*Table E. The performance comparison between three hypergraph methods on three new hypergraph datasets, under the 20% training ratio. We can observe that since these three datasets do not contain complex and heterogeneous structural features, the three hypergraph methods achieve comparable performance, with our HHNN performing slightly better.*\n|            | Cora             | PubMed           | DBLP             |\n| ---------- | ---------------- | ---------------- | ---------------- |\n| UniGNN     | 76.93 ± 1.73     | 84.05 ± 0.63     | 90.49 ± 0.18     |\n| ED-HNN     | 77.07 ± 1.22     | 84.12 ± 0.68     | 90.50 ± 0.21     |\n| **HHNN**   | **77.42 ± 1.67** | **84.14 ± 0.74** | **90.50 ± 0.27** |\n\n\n---\n\n**Point 5**: *No example or case study is provided to show that the learned hyper-meta-paths are meaningful. Provide an example or visualization to support the interpretability claim.*\n\n**Reply 5**: Thank you for the comment. We would like to kindly remind the reviewer that we did provide two case studies in Section 4.3. Please see the visualization examples in Figure 5(a) and Figure 5(b), where we intuitively show the discovered useful hyper-meta-paths on Movielens and Olist, respectively. For example, on Movielens, HHNN discovers that the composed hyper-meta-path T ← {UMT} ⋄ {UMR} → M captures semantics: “*a tag $t$ is linked to a movie $m$ through a user $u$, and the user $u$ associates the tag $t$ to a movie, and gives the movie $m$ a rating*”. The two visualization examples show that the learned hyper-meta-paths are meaningful."}, {"review_id": "cCHtoKRGmc", "reviewer": "Reviewer_FZj8", "summary": "This paper addresses the important problem of capturing complex structural and semantic information in heterogeneous hypergraphs, which arises from the composition of different hyper-relations. To this end, the authors introduce a new concept, the \"hyper-meta-path,\" as a generalization of the well-known \"meta-path\" from heterogeneous simple graphs. Based on this concept, the authors propose a novel model, HHNN (Heterogeneous Hypergraph Neural Network). The core of HHNN is a three-level attention mechanism (node-to-hyperedge, intra-type hyperedge-to-node, and inter-type hyperedge-to-node). This architecture is designed to automatically learn the importance of different hyper-meta-paths without requiring manual specification, thereby aiming to improve both model performance and interpretability. The authors conduct experiments on two self-constructed datasets, showing that HHNN outperforms several baseline methods.", "questions": "1. On the Scope and Rigor of Experimental Evaluation: I strongly advice to benchmark HHNN on widely used public datasets, even if they are derived from simple graphs (e.g., hypergraph versions of Cora, PubMed, DBLP, or a dataset from the TGB suite). \n\n2. On Scalability and Computational Complexity: A three-level attention mechanism is intuitively expensive. Add an experiment that plots the training time (or throughput) as the graph size (nodes/hyperedges) increases. This is a standard and necessary experiment to understand the practical limits of the proposed method.\n\n3. On the Definition of Hyper-meta-path: The current definition for composing hyper-relations (Rx ∩ Ry ≠ ∅) is very broad. It allows for composition as long as any node type is shared. Please discuss the potential limitations of this broad definition. For instance, if two hyper-relations only share a very generic and high-frequency node type (e.g., 'Timestamp' or 'Location'), their composition might be syntactically valid but semantically meaningless. Does your model implicitly learn to down-weight such compositions? A brief discussion of this point would add nuance to your work.\n\n4. Over-smoothing: A standard HHNN layer involves two steps of aggregation (node-to-hyperedge and hyperedge-to-node). Deeper GNN models often suffer from over-smoothing, where node representations become indistinguishable. How does your model, especially when stacked for multiple layers, mitigate this well-known issue?", "limitations": "Yes. The authors have adequately addressed the limitations and potential societal impacts of their work. They have dedicated specific sections in the appendix (Appendix G for Limitations and Appendix H for Broader Impacts) to discuss these aspects.", "rating": 4, "confidence": 2, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 2, "significance": 2, "originality": 2, "strengths_and_weaknesses": "Strengths：\n1. Clear and Valuable Problem Definition: The paper accurately identifies a key limitation in existing representation learning methods for heterogeneous hypergraphs: they often focus on individual hyper-relations while ignoring the richer, composite semantics that emerge from their combinations. The motivation to extend the \"meta-path\" concept to this domain is well-founded and promising.\n2.\tConceptual Contribution: The formal definition of the \"hyper-meta-path\" is a clear contribution of this work. It provides a new and useful theoretical lens for reasoning about and analyzing higher-order, heterogeneous dependencies within hypergraphs.\n\nWeaknesses\n\n1. Limited Methodological Novelty: The HHNN model's core architecture closely mirrors the HAN model's two-level attention mechanism (node-level and semantic-level). While HHNN adapts this for hypergraphs via β-Attention (intra-type) and γ-Attention (inter-type), it lacks fundamental innovation expected for top-tier venues like NeurIPS.  \n\n2. Weak Theoretical Grounding for Path Discovery: The claimed \"path discovery\" mechanism relies on attention weight products (Appendix C, Eq. 10), a heuristic approach common in GNNs but lacking rigorous theoretical justification. Without evidence linking high-weight paths to causal model behavior, the interpretability contribution is weakened.  \n\n3. Narrow Empirical Validation: Experiments are limited to two new datasets, raising concerns about potential bias. Benchmarking on standard hypergraph datasets (e.g., hypergraph Cora/PubMed) would better demonstrate generalizability and superiority over SOTA methods.  \n\n4. Lack of Computational Analysis: The three-level attention mechanism likely incurs high computational costs, yet the paper omits complexity analysis or runtime experiments. A brief mention of overhead (Appendix G) is insufficient, undermining the model's practical scalability.", "was_revised": true, "final_justification": "After reviewing the rebuttal and seeing the authors' carefully proposed revision plan, I believe the paper is a weak accept for the conference, at a confidence of 2.", "rebuttal": "Thanks for your comments. In the following, we respond to your concerns point by point.\n\n---\n\n**Point 1**: *HHNN model's core architecture closely mirrors the HAN model's two-level attention mechanism.*\n\n**Reply 1**: Thank you for the comment. While our model and HAN both adopt hierarchical attention, they are fundamentally different in scope and purpose. Firstly, HAN operates on heterogeneous simple graphs, where all relations are binary between node pairs, whereas HHNN is designed for heterogeneous hypergraphs that naturally encode multi-ary relations of various types. Moreover, HAN’s two-level attention relies on manually specified meta-paths, while HHNN introduces a three-level attention mechanism that automatically discovers hyper-meta-paths without manual intervention. Most importantly, our key contribution lies in defining a new structural pattern, i.e., hyper-meta-paths, on heterogeneous hypergraphs. As supported by our theoretical analysis and extensive experiments, this pattern not only effectively captures rich structural information in heterogeneous hypergraphs but also brings good interpretability for mode predictions. Our work offers a simple yet effective first step toward discovering these patterns, and we remain open and enthusiastic to more advanced methods for hyper-meta-path discovery in future research.\n\n---\n\n**Point 2**: *Lack of theoretical justification, and lack of evidence linking high-weight paths to causal model behavior.*\n\n**Reply 2**: Thanks for your comment. We provided theoretical justification in Appendix C. Specifically, we formally define how the hierarchical attention mechanism ($\\alpha$, $\\beta$, $\\gamma$) induces a distribution over hyper-meta-paths traversed during message passing. In addition, in Section 4.3, we show case studies where high-weight hyper-meta-paths align with human-understandable structural patterns. While this does not prove causal influence in a strict sense, it offers intuitive and evidence-backed interpretability. We acknowledge that further formalization of causal interpretability is an important direction, and we plan to explore techniques like counterfactual reasoning in our future work.\n\n---\n\n**Point 3**: *Experiments are limited to two new datasets. Benchmark HHNN on standard hypergraph datasets, even if they are derived from simple graphs (e.g., hypergraph versions of Cora, PubMed, DBLP, or a dataset from the TGB suite).*\n\n**Reply 3**: Thank you for the comment. Most existing heterogeneous hypergraph datasets are transformed from simple graphs with binary relations, which lack natural multi-way interactions and cannot fully showcase the advantages of hypergraph neural networks. In contrast, we have tried our best to construct two new real-world datasets from the movie domain and e-commerce domain, both containing multiple types of naturally occurring heterogeneous hyperedges based on genuine multi-ary relations. Nevertheless, according to your helpful suggestion, we have added three new hypergraph datasets, i.e., Cora, PuMmed, and DBLP, and the results are shown in the table below.\n\n*Table I. The performance comparison between three hypergraph methods on three new hypergraph datasets, under the 20% training ratio. We can observe that since these three datasets do not contain complex and heterogeneous structural features, the three hypergraph methods achieve comparable performance, with our HHNN performing slightly better.*\n|            | Cora             | PubMed           | DBLP             |\n| ---------- | ---------------- | ---------------- | ---------------- |\n| UniGNN     | 76.93 ± 1.73     | 84.05 ± 0.63     | 90.49 ± 0.18     |\n| ED-HNN     | 77.07 ± 1.22     | 84.12 ± 0.68     | 90.50 ± 0.21     |\n| **HHNN**   | **77.42 ± 1.67** | **84.14 ± 0.74** | **90.50 ± 0.27** |\n\n---\n\n**Point 4**: *Lack of complexity analysis, and lack of scalability experiment.*\n\n**Reply 4**: Thanks for your kind suggestion. The time complexity of HHNN is analyzed as follows. For each layer, the main cost comes from the three-level attention aggregation operations. The $\\alpha$-attention aggregation involves projecting and attending to nodes within each hyperedge, costing $\\mathcal{O}(|E| \\cdot d_\\alpha \\cdot f_\\alpha \\cdot r)$, where $|E|$ is the number of hyperedges, $d_\\alpha$ and $f_\\alpha$ are the dimensionalities of the input and output features, respectively, and $r$ denotes the average number of nodes per hyperedge. In the $\\beta$-attention aggregation phase, each node aggregates its connected hyperedges of each type, costing $\\mathcal{O}(|V| \\cdot d_\\beta \\cdot f_\\beta \\cdot t)$ where $|V|$ is the number of nodes, $d_\\beta$ and $f_\\beta$ are the feature dimensionalities, and $t$ denotes the average number of hyperedges of each type that a node participates in. In the $\\gamma$-attention aggregation phase, each node fuses its representations across different hyperedge types, costing $\\mathcal{O}(|V| \\cdot d_\\gamma \\cdot f_\\gamma \\cdot k)$, where $d_\\gamma$ and $f_\\gamma$ are the feature dimensionalities, and $k$ is the average number of hyperedge types. Assuming the model has $n$ layers, the total time complexity becomes: $\\mathcal{O}(|E| \\cdot d_\\alpha \\cdot f_\\alpha \\cdot r \\cdot n + |V| \\cdot d_\\beta \\cdot f_\\beta \\cdot t \\cdot n + |V| \\cdot d_\\gamma \\cdot f_\\gamma \\cdot k \\cdot n)$. In practical scenarios, $d_\\alpha, f_\\alpha, d_\\beta, f_\\beta, d_\\gamma, f_\\gamma, r, t, k, n$ are usually much smaller constants compared to $|\\mathcal{V}|$ and $|\\mathcal{E}|$. Therefore, the total time complexity of HHNN is equal to: $\\mathcal{O}(|\\mathcal{V}| + |\\mathcal{E}|)$, which is linear to the size of the hypergraph. In addition, to verify the efficiency of HHNN, we have added the scalability experiment as well as the running time comparison experiment. The results are shown in the three tables below.\n\n*Table II. We induce heterogeneous hypergraphs of different sizes using *varying ratios of nodes*, and the running time (seconds of 10 epochs) of HHNN increases approximately linearly with the size of the graph.*\n|      | Movielens | Olist |\n| ---- | --------- | ----- |\n| 20%  | 0.730     | 2.361 |\n| 40%  | 0.763     | 2.449 |\n| 60%  | 1.114     | 2.839 |\n| 80%  | 1.205     | 2.883 |\n| 100% | 1.231     | 3.194 |\n\n*Table III. We induce heterogeneous hypergraphs of different sizes using *varying ratios of hyperedges*, and the running time (seconds of 10 epochs) of HHNN increases approximately linearly with the size of the graph.*\n|      | Movielens | Olist |\n| ---- | --------- | ----- |\n| 20%  | 0.653     | 2.413 |\n| 40%  | 0.805     | 2.528 |\n| 60%  | 0.927     | 2.809 |\n| 80%  | 1.111     | 2.978 |\n| 100% | 1.231     | 3.194 |\n\n*Table IV. The running time (seconds of 1 epoch) of HHNN is on par with two baselines, UniGNN and EDHNN, and is much less than the running time of the baseline HyperGCN. Kindly remind that the efficiency is not our main contribution.*\n|           | HyperGCN | UniGNN  | ED-HNN | HNHN |\n| --------- | -------- | ------- | ------ | ---- |\n| Movielens | 81.57    | 0.13    | 0.18   | 0.15 |\n| Olist     | 90.22    | 0.17    | 0.63   | 0.19 |\n\n---\n\n**Point 5**: *The definition for composing hyper-relations is very broad. If two hyper-relations only share a very generic and high-frequency node type, their composition might be semantically meaningless.*\n\n**Reply 5**: Thank you for this thoughtful observation. We agree that the compositional condition is broad and may include semantically weak or spurious hyper-meta-paths, especially when the shared node type is generic. Nevertheless, HHNN can mitigate this issue through its hierarchical attention mechanism. At the intra-type level ($\\beta$-attention), the model learns to weight different hyperedges based on their contextual importance to each node. At the inter-type level ($\\gamma$-attention), it further aggregates across different hyperedge types, allowing the model to down-weight weak or generic compositions that are less informative for the task. Most importantly, the final influence of a hyper-meta-path is determined by the product of attention weights across all levels (see Eq. (10) in Appendix C), which implicitly suppresses semantically meaningless paths by assigning them a low cumulative weight. This design allows flexible path discovery, and the model learns to emphasize meaningful compositions and ignore noisy ones based on data-driven evidence. We will discuss this point further in the manuscript.\n\n---\n\n**Point 6**: *How does HHNN mitigate the over-smoothing issue, especially when stacked for multiple layers?*\n\n**Reply 6**: Thank you for the comment. HHNN mitigates over-smoothing primarily through its type-aware and structured three-level attention aggregation mechanism, which separates node-to-hyperedge and hyperedge-to-node message passing, and further decomposes the latter into intra-type and inter-type attention aggregation. This design limits the indiscriminate mixing of heterogeneous features and helps preserve type-specific and high-order structural information throughout the network. In addition, as the model depth experiment shown in Figure 6(c) and Figure 6(f), the model maintains strong performance even at 3 layers, with no significant performance drop, indicating robustness against over-smoothing. Notably, each HHNN layer includes two projection and aggregation steps (node-to-hyperedge and back), which actually correspond to two layers in standard GNN models. Therefore, a 3-layer HHNN is equivalent to a 6-layer standard GNN, making it sufficiently deep to capture complex structural patterns without degradation."}, {"review_id": "2Yh3MWnIsX", "reviewer": "Reviewer_qQ4P", "summary": "This study presents a novel concept of hyper-meta-path for heterogeneous hypergraphs where there are multiple types of nodes as well as multiple types of hyperedges. To be more specific, the hyper-meta-path is defined as the composition of a sequence of hyper-relations, and each hyper-relation describes a multi-ary relation, corresponding to one hyperedge type. The hyper-meta-path is expected to capture more complex structural features of heterogeneous hypergraphs. The authors design an attention-based heterogeneous hypergraph neural network to learn the importance of different hyper-meta-paths, and conduct extensive experiments to verify the effectiveness of the proposed concept.", "questions": "My questions are the same as the four weaknesses listed above. Please address those weaknesses.", "limitations": "Yes", "rating": 5, "confidence": 5, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 4, "clarity": 3, "significance": 4, "originality": 4, "strengths_and_weaknesses": "**Strengths**\n\n- The proposed concept of hyper-meta-path is novel and interesting, and is well defined. The authors have carefully analyzed its effectiveness, and verified its effectiveness through extensive experiments.\n\n- At the beginning of Section 1, the review of the existing four categories of graph data is well organized, and the four illustrations are intuitive.\n\n- The proposed model HHNN is clearly described by equations and intuitively described by Figure 3 and Figure 4. Therefore, the technical description of the methodology is highly readable and easy to follow.\n\n- The comparison experiments show that the performance of the proposed method is promising. The ablation study and hyper-meta-path discovery experiment show that the proposed methods can effectively discover useful hyper-meta-paths.\n\n- The authors have provided the source code and the used datasets, and provided much detailed information in the appendix, facilitating good reproducibility of this work.\n\n\n\n**Weaknesses**\n\n- The time complexity of the proposed method could be analyzed.\n\n- More baselines could be considered, and the related work could be further enriched.\n\n- According to the content, it is more appropriate to update the subtitle of Section 4.3 to \"Hyper-meta-path Discovery and Interpretability Study\".\n\n- It seems that there is a minor issue in Line 267. According to Figure 5(a), the {UMT} hyperedge and the {UMR} hyperedge are connected by a user node, instead of a movie node.", "was_revised": true, "final_justification": "After checking the rebuttal, I believe my concerns have been well addressed, thus I vote for acceptance.", "rebuttal": "Thanks for your comments. In the following, we respond to your concerns point by point.\n\n---\n\n**Point 1**: *The time complexity of the proposed method could be analyzed.*\n\n**Reply 1**: Thanks for your kind suggestion. The time complexity of HHNN is analyzed as follows. For each layer, the main cost comes from the three-level attention aggregation operations. The $\\alpha$-attention aggregation involves projecting and attending to nodes within each hyperedge, costing $\\mathcal{O}(|E| \\cdot d_\\alpha \\cdot f_\\alpha \\cdot r)$, where $|E|$ is the number of hyperedges, $d_\\alpha$ and $f_\\alpha$ are the dimensionalities of the input and output features, respectively, and $r$ denotes the average number of nodes per hyperedge. In the $\\beta$-attention aggregation phase, each node aggregates its connected hyperedges of each type, costing $\\mathcal{O}(|V| \\cdot d_\\beta \\cdot f_\\beta \\cdot t)$ where $|V|$ is the number of nodes, $d_\\beta$ and $f_\\beta$ are the feature dimensionalities, and $t$ denotes the average number of hyperedges of each type that a node participates in. In the $\\gamma$-attention aggregation phase, each node fuses its representations across different hyperedge types, costing $\\mathcal{O}(|V| \\cdot d_\\gamma \\cdot f_\\gamma \\cdot k)$, where $d_\\gamma$ and $f_\\gamma$ are the feature dimensionalities, and $k$ is the average number of hyperedge types. Assuming the model has $n$ layers, the total time complexity becomes: $\\mathcal{O}(|E| \\cdot d_\\alpha \\cdot f_\\alpha \\cdot r \\cdot n + |V| \\cdot d_\\beta \\cdot f_\\beta \\cdot t \\cdot n + |V| \\cdot d_\\gamma \\cdot f_\\gamma \\cdot k \\cdot n)$. In practical scenarios, $d_\\alpha, f_\\alpha, d_\\beta, f_\\beta, d_\\gamma, f_\\gamma, r, t, k, n$ are usually much smaller constants compared to $|\\mathcal{V}|$ and $|\\mathcal{E}|$. Therefore, the total time complexity of HHNN is equal to: $\\mathcal{O}(|\\mathcal{V}| + |\\mathcal{E}|)$, which is linear to the size of the hypergraph. In addition, to verify the efficiency of HHNN, we have added the scalability experiment as well as the running time comparison experiment. The results are shown in the three tables below.\n\n*Table (1). We induce heterogeneous hypergraphs of different sizes using *varying ratios of nodes*, and the running time (seconds of 10 epochs) of HHNN increases approximately linearly with the size of the graph.*\n|      | Movielens | Olist |\n| ---- | --------- | ----- |\n| 20%  | 0.730     | 2.361 |\n| 40%  | 0.763     | 2.449 |\n| 60%  | 1.114     | 2.839 |\n| 80%  | 1.205     | 2.883 |\n| 100% | 1.231     | 3.194 |\n\n*Table (2). We induce heterogeneous hypergraphs of different sizes using *varying ratios of hyperedges*, and the running time (seconds of 10 epochs) of HHNN increases approximately linearly with the size of the graph.*\n|      | Movielens | Olist |\n| ---- | --------- | ----- |\n| 20%  | 0.653     | 2.413 |\n| 40%  | 0.805     | 2.528 |\n| 60%  | 0.927     | 2.809 |\n| 80%  | 1.111     | 2.978 |\n| 100% | 1.231     | 3.194 |\n\n*Table (3). The running time (seconds of 1 epoch) of HHNN is on par with two baselines, UniGNN and EDHNN. Kindly remind that the efficiency was not claimed as our main contribution.*\n|           | UniGNN  | ED-HNN | HNHN |\n| --------- | ------- | ------ | ---- |\n| Movielens | 0.13    | 0.18   | 0.15 |\n| Olist     | 0.17    | 0.63   | 0.19 |\n\n\n---\n\n**Point 2**: *More baselines could be considered, and the related work could be further enriched.*\n\n**Reply 2**: Thanks for your kind suggestion. We have added two recent hypergraph models, i.e., SheafHyperGNN [1] and UniG-Encoder [2], as the new baselines, and their experimental results are shown in the two tables below. We can see that our HHNN significantly outperforms the two hypergraph baselines on both datasets. We will also enrich our related work by introducing the two methods, as well as more recent heterogeneous hypergraph neural networks.\n\n*Table (4). The performance comparison on Movielens, under the 20% training ratio.*\n|                   | Micro          | Macro          | AUC            |\n| ----------------- | -------------- | -------------- | ----------     |\n| SheafHyperGNN [1] | 46.59±1.24     | 18.85±1.74     | 61.68±1.48     |\n| UniG-Encoder [2]  | 41.79±1.17     | 16.15±0.96     | 58.66±1.32     |\n| **HHNN**          | **56.80±1.65** | **26.24±3.90** | **73.21±2.13** |\n\nTable (5). The performance comparison on Olist, under the 20% training ratio.\n|                   | Micro          | Macro          | AUC            |\n| ----------------- | -------------- | -------------- | -------------- |\n| SheafHyperGNN [1] | 51.71±1.54     | 51.56±1.38     | 85.60±1.02     |\n| UniG-Encoder [2]  | 24.40±0.39     | 23.68±0.49     | 64.96±0.28     |\n| **HHNN**          | **72.54±0.54** | **72.89±0.56** | **93.20±0.32** |\n\n\n*Refs*:\n\n[1] Duta, Iulia, et al. \"Sheaf hypergraph networks.\" Advances in Neural Information Processing Systems 36 (2023): 12087-12099.\n\n[2] Zou, Minhao, et al. \"Unig-encoder: A universal feature encoder for graph and hypergraph node classification.\" Pattern Recognition 147 (2024): 110115.\n\n---\n\n**Point 3**: *Update the subtitle of Section 4.3 to \"Hyper-meta-path Discovery and Interpretability Study.*\n\n**Reply 3**: Thanks for your helpful suggestion. Section 4.3 conducts an interpretability study based on the useful hyper-meta-paths discovered by HHNN. Therefore, following your suggestion, we will update the subsection title to “Hyper-meta-path Discovery and Interpretability Study”.\n\n---\n\n**Point 4**: *According to Figure 5(a), the {UMT} hyperedge and the {UMR} hyperedge are connected by a user node.*\n\n**Reply 4**: Thank you for your careful review. We are sorry for this typo. Indeed, the {UMT} hyperedge and the {UMR} hyperedge are connected by a shared user node. We will correct this typo in the new version of our manuscript."}]

Author rebuttal:

Meta-review: This authors present a novel concept of hyper-meta-path for heterogeneous hypergraphs. IN a heterogeneous hypergraph,  there are different types of nodes and / or different types of hyperedges. The hyper-meta-path aims to capture complex structural patterns, and the important of different hyper-meta-paths are learned through an attention-based heterogeneous hypergraph neural network. Extensive experiments are conducted to validate the efficacy of proposed approach. 

Strengths:
- Heterogeneous hypergraphs are under-explored area and the notion of hyper-meta-paths are novel.
- The proposed solution is intuitive, sound, and reasonable.
- Superior performance with detailed analysis of results

Weaknesses:
- The number of hyper-meta-path could grow quickly especially on complex hypergraphs with many node/edge types. This raises scalability concern, as well as how they can be defined / selected.
- The proposed approach bears some similarity to the approaches on flattened heterogeneous graph, limiting its novelty if not explained or clarified properly. 
- The experiments could be strengthened by including more complex datasets and stronger baselines

The paper does have scientific merit in terms of its problem, key concept, and experimental results. There are several non-fundamental  weaknesses, most of which have been addressed satisfactorily in the rebuttal, while the rest can be potentially addressed in the camera ready.
Decision: Accept (poster)