HYPER: A Foundation Model for Inductive Link Prediction with Knowledge Hypergraphs
Authors: Xingyue Huang
Mikhail Galkin
Michael M. Bronstein
Ismail Ilkan Ceylan
Venue: ICLR 2026 Poster (2026)
Keywords: Knowledge Hypergraph
Link Prediction
Graph Neural Networks
Foundation Models
Primary area: learning on graphs and other geometries & topologies
TL;DR: We develop the first foundation model over inductive link prediction with knowledge hypergraphs.

Abstract: Inductive link prediction with knowledge hypergraphs is the task of predicting missing hyperedges involving completely *novel entities* (i.e., nodes unseen during training). Existing methods for inductive link prediction with knowledge hypergraphs assume a fixed relational vocabulary and, as a result, cannot generalize to knowledge hypergraphs with *novel relation types* (i.e., relations unseen during training). Inspired by knowledge graph foundation models, we propose HYPER as a foundation model for link prediction, which can generalize to *any knowledge hypergraph*, including novel entities and novel relations. Importantly, HYPER can learn and transfer across different relation types of *varying arities*, by encoding the entities of each hyperedge along with their respective positions in the hyperedge. To evaluate HYPER, we construct 16 new inductive datasets from existing knowledge hypergraphs, covering a diverse range of relation types of varying arities. Empirically, HYPER consistently outperforms all existing methods in both node-only and node-and-relation inductive settings, showing strong generalization to unseen, higher-arity relational structures.

Published as a conference paper at ICLR 2026
HYPER: A FOUNDATION MODEL FOR INDUCTIVE LINK PREDICTION WITH KNOWLEDGE HYPERGRAPHS
Xingyue Huang University of Oxford
Mikhail Galkin Google Research
Michael M. Bronstein
University of Oxford & AITHYRA
ismail Ilkan Ceylan TU Wien & AITHYRA
ABSTRACT
Inductive link prediction with knowledge hypergraphs is the task of predicting missing hyperedges involving completely novel entities (i.e., nodes unseen during training). Existing methods for inductive link prediction with knowledge hyper- graphs assume a fixed relational vocabulary and, as result, cannot generalize to knowledge hypergraphs with novel relation types (i.e., relations unseen during training). Inspired by knowledge graph foundation models, we propose HYPER foundation model for link prediction, which can generalize any knowledge hypergraph, including novel entities and novel relations. Importantly, HYPER can learn and transfer across different relation types of varying arities, by encoding the entities of each hyperedge along with their respective positions in the hyper- edge. To evaluate HYPER, construct 16 new inductive datasets from existing knowledge hypergraphs, covering diverse range of relation types of varying ar- ities. Empirically, HYPER consistently outperforms all existing methods in both node-only and node-and-relatte inductive settings, showing strong generalization to unseen, higher-arity relational structures.
INTRODUCTION
Generalizing knowledge graphs with relations between any num- ber of nodes, knowledge hypergraphs offer flexible means of storing, processing, and managing relational data. Knowl- edge hypergraphs can encode rich relationships between enti- ties; e.g., consider relationship between four entities: "Bengio has a research project on topic ClimateAl in Montreal funded by CIFAR". This relational information a knowledge hypergraph (see Figure [
Sasha AtConference
Bengio ClimasuAl
Research
CIFAR
be represented in via an (ordered) hy- peredge Research(Bengie ClimateAl, Montreal, CIFAR), where Research represents relation of arity four.
lan
2015
Teaches
EthicalAl
NeurlPS
The generality of knowledge hypergraphs motivated body of work for machine learning with knowledge hypergraphs (Guan
al.
202 Fatemi et al. 2020; Yadati 2020; Zhou al. 2023b;
A knowledge hy- pergraph with three hyperedges over distinct relation types.
Figure 1:
Huang et al. 2025b). One of the most prominent learning tasks is inductive link prediction with knowledge hypergraphs, where the goal is to predict missing hyperedges involving completely novel
entities (Yadati) 2020 Zhou et al.) 2023b. Huang et al., (025b). The main shortcoming of existing methods for inductive link prediction with knowledge hypergraphs is that they cannot generalize to knowledge hypergraphs with novel relation types. This constitutes the main motivation of our work: Can design an effective model architecture for inductive link prediction with knowledge hypergraphs, where the predictions can involve both novel entities and novel relations?
depieted in Figure The training hypergraph Giain is over the relations Research, Teaches, and AtConference, while the inference graph G over the novel relations Trading, Sells, and AtFair. The task is predict missing links such as
Example. Consider the knowledge hypergraphs

---

Published as a conference paper at ICLR 2026
Sells(Samsung, Best Buy, Q60D TV) in Gjt- Ideally, the model should learn relation invariants that map Teaches + Sells, Research + Trading, and AtConference + AtFair, as these relation types play analogous structural roles in their respective graphs, even though their labels and entities are entirely different.
Approach. In essence, our study builds on the success of knowledge graph foundation
Sauha
AtConference
CTA
AtFair
models (KGFMs) (Galkin et al. 2024| Mao
Begglo Clinztoii
Montroal
LED
Vezza
et al.] 2024). which have shown remark- able performance in link prediction tasks involving both novel entities and novel re- lations. However, KGFMs can only per- form link prediction using binary relations, which raises the question of how to trans- late the success of KGFMs to fully rela- tional data. To this end, we propose HYPER, class of knowledge hypergraph founda- tion models for inductive link prediction, which can generalize to any knowledge hy- pergraph. The fundamental idea behind our approach is to learn properties of relations that are transferable between different types of relations of varying arity. Consider, for example, the two hyperedges (from Figure
Research
Trading
Diplay
2015
BastBur
2004
Teaches
Sells
PriksiAi
Q60D TV
Ganin
NauriPS
G
Figure 2:
A model is trained on relations like Research, Teaches, and AtConference, and ex- pected to generalize to structurally similar relations TradingDeal, Sells, and AtBusinessFair test time.
AtConference(Sashar Montreal, 2015, EthicalAl, NeurlPS), Research Research(Bengio, ClimateAl, Montreal, CIFAR),
which "intersect" with each other. The entity Montreal appears in the second position of the first hyperedge and the third position of the second hyperedge. Such (pairwise) interactions between relations can be viewed as fundamental relations to learn from: any model learning from relations between relations can transfer this knowledge to novel relation types that have similar interactions.
Furthermore, we can encode such relations between relations in separate relation graph, which can be used to learn from. We illus- trate this on our running example in Figure 3 where the relations appear as nodes; the interactions between relations as edges; and finally, the positions of the interactions as edge weights. our set- ting, a directed edge from relation ri to r2 with edge label j) indicates that "The i-th position of and the j-th position of r2 in- tersect in G", which captures fundamental interaction between and r2. Critically, however, there is no upper bound on the number of such possible interactions. While there are at most actions between an m-ary relation and an n-ary relation, we cannot impose any bound on the arity of the relations since then the model
Research
(1.1)
(3,2)
(2, 3)
(4,3)
Teaches
(3,4)
AtConference
Gun
Figure 3: The relation graph Giel corresponding to the knowledge hypergraph Gurin- would not generalize to all knowledge hypergraphs.
inter-
Contributions. Our main contributions can be summarized follows:
To the best of our knowledge, HYPER is the first foundation model that allows zero-shot generalization to knowledge hypergraphs of arbitrary arity with novel nodes and novel relations at test time.
We evaluate HYPER on 3 existing benchmark datasets and additionally on 16 new bench- mark datasets with varying proportions of test-time tuples involving unseen relations. HYPER consistently outperforms existing hypergraph baselines trained end-to-end, par- ticularly when the proportion of new relations is high.
To assess the performance of KGFMs on hypergraphs. we reify the knowledge hypergraphs into KGs and apply KGFMs on them. Remarkably, HYPER, trained on only 2 hypergraphs and 3KGs, consistently outperforms the popular KGFM model UL.TRA trained on 50 KGs.
We conduct an empirical investigation over the positional interaction encoding scheme within HYPER, demonstrating the critical role of encoding choices.
2

---

Published as a conference paper at ICLR 2026
2 RELATED WORK
Table I: Methods' ability to handle high-arity re- lations (High-arity) and inductively generalize to unseen entities (Ind. e) and relations (Ind. r).
Link Prediction with Knowledge Graphs. Early knowledge graph embedding methods (Bordes et al. 2013; Sun et al. 2019; Trouil-
lon et al. 2016 Balazevic et al., 2019; Abb
boud et al. 2020)
limited to the trans- ductive setup: these methods do not general- ize to unseen entities or to unseen relations. Multi-relational graph neural networks (GNNs) such as RGCN (Schlichtkrull et al. 2018) and CompGCN (Vashishth et al.) 2020) similarly rely on stored entity embeddings, remaining in- herently transductive. To overcome these limitations, Teru et al. (2020) introduced GralL, pio-
Methods
High-arity
Ind. e
Ind. r
HypE, BoxE NBFNet, Net
x
x
X
x
G-MPNN, HCNet ULTRA, KG-ICL
V
/
x
X
/
/
HYPER
neering method enabling iode-inductive link prediction, which is later shown to be form of the labeling trick (Zhang et al., (021). Subsequently, architectures such as NBFNet (Zhu et al.) (021),
A **Net (Zhu et al. (023). RED-GNN (Zhang & Yao 2022], and AdaProp (Zhang et al. (023) lever- aged conditional message passing, significantly enhancing expressivity and performance (Huang) jet al. 2023). However, these methods are not inductive on relations, as they assume a fixed rela- tional vocabulary. KGFMs are specifically tailored for inductive predictions on both unseen nodes and relations. InGram (Lee et al. 2023), RAILD (Gesese et al., (022), and ULTRA (Galkin et al. 2024) introduced new KGFM frameworks. Following these, TRIX (Zhang al., 2024) introduced recursive updating of entity and relation embeddings with provably improved expressiveness over ULTRA. KG-ICL (Cui et al., 2024) employed in-context learning with unified tokenization for en- tities and relations. Additionally, double-equivarian GNNs, like ISDEA (Gao et al.) (023) and MTDEA [Zhou et al., 2023a). emphasized relational equivariance, enhancing robustness to unseen relations. Huang et al. (2025a) proposed MOTIF as a general KGFM framework and formally stud- ied the expressive power of KGFMs. All of these methods are confined to KGs with binary relations, and they do not naturally apply to higher-arity relations, as shown in Table [
Link Prediction with Knowledge Hypergraphs. Knowledge hypergraphs generalize traditional KGs to handle higher-arity relational data. Initial researches such as HypE (Fatemi et al. 2020) and BoxE (Abboud et al. 2020) leveraged shallow embedding models adapted from KG embed- ding frameworks. Later approaches extended graph neural networks to knowledge hypergraphs. G- MPNN (Yadati] 2020) and RD-MPNNs (Zhou et al.) (023b) introduced relational message passing mechanisms explicitly designed for hypergraph settings, incorporating positional entity information critical for high-arity relations. Huang et al. (0055) proposed HCNets as a conditional message- passing approach tailored for inductive hypergraph link prediction and conducted analysis. While these methods can handle knowledge hypergraphs, they are not inductive on re- lations: none of these methods can generalize unseen relations (shown in Table D. Our work on HYPER builds on these foundations by combining the strengths of conditional message passing on knowledge hypergraphs with the powerful inductive generalization techniques explored in re- cent KGFMs (Galkin et al., 2024 Lee et al. 2023 Huang et al.) 2025a) to effectively generalize to knowledge hypergraphs within unseen nodes and relations.
expressivity
Foundation Models on Hypergraphs. Existing foundation models on hypergraphs are tailored to text-attributed hypergraphs. HyperBERT (Bazaga al., (2024) integrates pretrained language mod- els with hypergraph convolution for node classification, while HyperGene (Du et al. 2021) and SPHH (Abubaker et al., 2023) propose self-supervised objectives tailored to local and global hyper- graph structures. More recent works such as Hyper-FM FM (Feng et al., 2025) and IHP (Yang et al.) 2024) introduce multi-domain pretraining and instruction-guis guudded adaptation, respectively, marking the first steps toward generalizable hypergraph models. These methods rely heavily on text attributes for generalization and are predominantly tailored to node classification tasks; they do not support link prediction over knowledge hypergraphs with unseen relations at test time.
PRELIMINARIES
Knowledge Hypergraphs. A knowledge hypergraph G = (V, E) consists of a set of nodes V. hyperedges F. (i.e., facts) of the form e r(u1,...,,u Uk), where R is a relation type,
3

---

Published as a conference paper at ICLR 2026
and u, E V, I i S k are nodes. The arity of relation is given by k = ar(r), where ar R + Nzo- For an hyperedge e, p(e) denotes its relation, and e(i) denotes the node at the i-th position of e. We refer to the knowledge hypergraph with all edges having arity of exactly 2 as a knowledge graph. The set of (l))) {(e,t) e(i) = v,e E, S ar(p(e)))- The positional neighhorhood of hyperedge with respect to a position is: Miee = {(e(t),5) ii,,,, S ar (p(e)))
pairs associated with a node v is defined as:
Link Prediction on Hyperedges. Given a knowledge hypergraph G
and query qui,..., Mp-1. ? u1+1..... u4), the link prediction task involves scoring all possible hyperedges formed by replacing the placeholder "?" with each node v V. We denote a k-tuple of nodes by u u= (u,,..... 2xx) and the tuple excluding position f by ü = (u1...., 11 #1......... 4x.. Thus, we represent a query succinetly as q = (g. u, f). In the fully-inductiive setting for link prediction (i.e., node and celation-inductive link prediction), the goal is to answer queries of the form q = (g. ú, t) on an inference hypergraph Gi = (V' Eint Rint), where both the entity set Vin and the relation set Pint are entirely disjoint from those seen during training. The model is trained on separate training knowledge hypergraph Guain = (Vrain: Eusin. Ruan). with Visinn n Vin = @ and Ruain n Ru = 0, and must learn transferable representations that generalize across both novel entities and unseen relation types of arbitrary arity. At inference time, each hyperedge e = r r(w1,-
ux) E Pint corresponds Rini. and queries involve predicting missing node at position t within such a tuple, using the surrounding nodes ú and relation = p(e). The model must score candidate completions g(u1,.... 11 U, 1e+1...., ug) for each u E Vint-
to fact involving a relation
Reification. To apply the mod- els designed for KGs on knowl- edge hypergraphs, we trans- form an input knowledge hy- pergraph G
(V, E, R) into reification pro- cess, similar to the one pro- posed Fatemi et al. 2020 Specifically. for each hy- peredge r(ug,..., 24k E, we introduce edge_id & V in the KG to represent the hyperedge it- self and add A binary edges r-1(edge_.d) id, ui), r-2(edge id, u2), that each new edge encodes position-specifee relation such as Research-3 or AtConference-5. For instance, Figure D shows the reified KG of our running example in Figure [] This reification procedure encodes the full higher-order structure of the original knowledge hypergraph into a KG.
R:1 Tea R-s
R-b T-1
A-1
A-3
1:3
a KG via a
Bengio
ClimateAI
Montreal
CIFAR
Sasha
2015
EthicalAl
NeurlPS
E node
Figure 4: Reified KG corresponding to the knowledge R-i abbreviates Research-i,
hypergraph Guain from Fig [ similarly for A as AtConference, and T as Teaches.
r-k(edge id, ux), one for each position. Note
Link Prediction over Reified Knowledge Hypergraphs. Given high-arity query of the form q("1,.... M4-1, ?, U.41...., M4) over the original knowledge hypergraph, we perform link predic- tion in the reified KG by encoding the query as a subgraph which is used to augment the testing knowledge graph. Concretely, we add a new node edge_id and binary triples (edge-id, u;) for all i # t. The prediction task is then reduced to a standard tail prediction problem: ranking all candidate entities e V for the fact qı (edge id, v). We evaluate the model performance using standard ranking metrics over the original entity vocabulary. We use superscript (f) to denote models evaluated under this regime.
4 HYPER: A KNOWLEDGE HYPERGRAPH FOUNDATION MODEL
We now present HYPER, general framework for learning foundation models over knowledge hy- pergraphs. Given a knowledge hypergraph G = (V, F, R) and a query q = (g, ú,, HYPER computes link prediction scores through the following steps:
1. Relation encoder: Relations are encoded in three steps:
We also include alternative ways for reification in Appendix G.3
4

---

Published as a conference paper at ICLR 2026
n
11.1)
(3.2)
(2.3)
P3
(4.3)
[3,44
X1,4
Compute
Encyi 81)
Message Passing Git
Input Hypergraph G
Relation Encoder on Gjt
Entity Encoder G
Figure 5: Overall framework of HYPER. HYPER first constructs relation graph Gral based on the observed positional interactions between the relations. EnCpt then computes embeddings for each position pair, which refined via message passing over Gjel- The resulting relation representations are then used for message passing over the original knowledge hypergraph (shown in color).
(a) Relation graph: Build a relation graph G where each node corresponds to a relation R, and edges capture observed positional interactions between relations.
(b) Encoding positional interactions: Use an encoder Encp1 to embed each interacting posi- tion pair (a, from G into fundamental relation representations.
(c) Encoding the relations: Perform conditional message passing over Geel using fundamental relation representations to obtain relation embeddings for all r E R.
2. Entity encoder: Use learned relation representations to conduct conditional message passing over the original knowledge hypergraph G and obtain link probability via decoder Dec.
The overall framework is illustrated in Figure and the detailed architecture is presented in Ap- pendix G.
We now describe each component.
Relation graph. Given a knowledge hypergraph G = (V, E, R). we construct the relation graph G (Vi,,, Exe, R.a)). The set of nodes is given as Vne R, i.e. each node in G corresponds to relation type in the knowledge hypergraph G. The relation types Reel are defined as all ordered pairs (a, b) for (1 < a,b < ), where kmax max (ar(r) E R} denotes the maximum arity among the observed relations. The edge set Esel captures positional interactions between relation types: for each pair of hyperedges E2 E E with relation types T1 = p(e1) and r22 = p(e2). there exists shared entity appearing in position in ej and position j in 62, add directed edge (ri, 72) with relation type (i.j) to Exe- These positional interactions can be computed efficiently via sparse matrix multiplication (see Appendix B and are invariant over the renaming of relations.
Encoding positional interactions. Unlike knowledge graphs, where each fact involves two entities and naturally leads four types of fundamental relations (head-to-head, head-to-tail, tail-to-head, and tail-to-tail) as introduced in Galkin et al. (2024), knowledge hypergraphs allow facts with ar- bitrary arity. This introduces a key challenge: How to build foundation model that can adapt to unseen knowledge hypergraphs with varying and arbitrarily large arities?
The natural extension of the concept of fundamental relations from KGs knowledge hypergraphs results in mn types of positional interactions between an hyperedge of arity m and an hyperedge of arity n. Each of such interaction characterized by pair (a, b). where a and b denote the entity positions involved in the relation. As consequence, a foundation model for knowledge hypergraphs must be capable of encoding positional interactions in a way that generalizes across different arities.
A naive solution would be to associate separate embedding to each (a, b) pair. However, such an approach does not generalize to unseen arities, as it would require pre-training embeddings for all possible (a, b) combinations. To address this, we propose a shared, compositional position in- teraction encoding scheme. Specifically, given positional interaction labeled (a, b), we define a positional interaction encoder Encμ Noo x N + Rd which maps a pair of argument positions to a dense vector representation of dimensions. To be effective in inductive settings, we require the encoder Encpt to satisfy the following requirements:
5

---

Published as a conference paper at ICLR 2026
1. Extrapolation. The encoder should generalize to unseen positions and combinations, allowing the model to operate on arities and interaction patterns not present during training.
2. Injectivity. Distinct position pairs (a, b) and (a', should map to distinct embeddings to preserve the identifiability of positional interactions:
Ya, b, d', b' E N (a. b) + (a',b)
Encei((a, b)) EnCri((a',
In practice, we implement EnGn as a two-layer multilayer perceptron (MLP) over concatenated sinusoidal encodings of the input positions. Let Pa: Ps E Rd denote the sinusoidal positional encod- ings of positions a and b, respectively. Then, the embedding corresponding to the interaction (a, b) is computed as x MLP((p. || pol), where MLP denotes shared two-layer feedforward network with ReLU activations. This produces a dense embedding that captures the interaction between the two positions. Theoretically, we show that our chosen EnGpt satisfies these properties and is also locally smooth. (See Appendix C for formal theorems and proofs.)
Theorem 4.1 (Informal). There exists a set of parameter for HYPER such that EnCpr is injective, has bounded range, and is Lipschitz (and hence locally smooth).
Empirically, we find that this instantiation of Encpy also enables strong generalization across knowl- edge hypergraphs with varying arities and relational structures. When applied to knowledge graphs, our method recovers standard encoding patterns employed
many KGFMs (Galkin et al.] [2024] Lee al. 2023 Zhang et al., 2024 Huang et al., (025a)) In particular, head-to-tall head to- ro-head, tail-to-tail, and tail-to-head interactions correspond to EnCrr((1, ((1,)(())) 2)), Encri((1, 1)), EnCpr ((,, 2)). and (nCpi( (2, 1)), respectively.
Encoding the relations. HYPER uses Hypergraph Conditional Networks (HCNets) (Huang et al., 20256) to encode relations for its strong inductive performance, support for bidirectional message passing, and easy extensibility to higher-order relational patterns (Huang et al. (025a). HCNets produce query-conditioned representations by aggregating messages from neighboring edges with relation and position information. Here, we take Encpn (a, b)) as the computed messages for each typed edges when message-passing over relation graph with positional encoding (a, b).
Entity encoder. Similarly to how encode the relation, HYPER uses variant of HCNet to encode the entities. In the context of the entity encoder, we apply a separate HCNet over the original knowledge hypergraph G (V, E, R). Each node v E V aggregates from its incident hyperedges by first taking the relation embeddings h/1 obtained from the relation encoder as the messages for each typed hyperedges and then transformed by layer-specific MLP. The resulting HYPER instances will preserve equivariance over nodes and relations. (See Appendix Cloo proof.)
EXPERIMENTS
In this section, aim to evaluate the generalization and effectiveness of HYPER across inductive link prediction tasks on both knowledge hypergraphs and knowledge graphs. We focus on answering the following questions:
Q1: How well does HYPER generalize to unseen entities and relation types?
Q2: How does HYPER handle varying proportions of unseen relations in the test set?
Q3: How does HYPER compare KGFMs reified knowledge hypergraphs?
Q4: What is the impact of different variants of pretraining mix on HYPER?
Q5: How does the encoding of positional information impact the model's ability to generalize?
Q6: How well does HYPER perform on standard knowledge graphs (see Appendix ?
Q7: What computational complexity and empirical scalability of HYPER (see Appendix F
5.1 EXPERIMENTAL SETUPS
Models. We evaluate models using the datasets summarized in Table I3 As a supervised learning baseline, include G-MPNN (Yadati 2020) and HCNet node-inductive methods on knowledge

---

Published as a conference paper at ICLR 2026
Table 2: MRR results on node and relation inductive knowledge hypergraph datasets. Superscript means the model is applied over the reification of hypergraphs.
Method
MFB
WP
WD
50
75
25
50
75
100
50
75
25
75
100
End-to-End Inference
G-MPNN
0.006
0.003
0.001
0.002
0.002
0.004 0.007 0.003 0.005 0.002
0.001
0.000
0.001
0.001
0.001
0.001
HCNe
0.111
0.009
0.069
0.028
0.035
0.026 0.016 0.082 0,104
0.050
0,019
0.003
0.086
0.043
0.015
0.007
HYPER
0.202 0.468
0.207
0.198
0,332 0.200 0.135 0.222 0.159 0.143
0.139
0.202
0.215
0.205
0.172
0.205
Zero-shot Inference
(GKG
0.105
0.477
0.168
0.144
0.255
0.235
0.154 0.277
0.039
0.077
0.073
0.078
0.117
0.155
0.116
0.161
HYPER(KK))
0.148 0.297
0.112
0.130
0.248
0.191 0.039 0.276 0.143
0.147
0.186
0.221
0.167
0.158
0.123
0.146
(4KGA)(4KG)
0.011
0.298
0.042
0.082
0.217
0.170
0.043
0.135
0.009
0.006
0.006
0.004
0.027
0.069
0.063
0.065
HYPER(4KG)
0.109 0.065
0.128
0.087
0.116
0.117
0.089
0.148
0.074
0.212
0.175
0.180
0.148
0.111
0.150
0.255
(S0RG)
0.096
0.010
0.001
0.225
0.083
0.001
0.190
0.006
0.009
0.009
0.004
0.008
0.001
0.001
0.001
HYPER(SOKG)
0,056 0.294 0.084
0.111
0.122
0.156
0.126
0.148
0.067
0.198
0.191
0.155
0.073
0.055
0.130
0.088
(LTRA
0.154
0.442
0.175
0.170
0.338
0.236
0.129
0.280
0.091
0.089
0.089
0.076
0,052
0.136
HYPER(4HG)
0.187 0.377 0.188
0.181
0.349
0.244
0.139
0.278
0,075
0.068
0,086
0.168
0.087
0.158
0.057
0.165
ULTRATGKG-2HGG)
0.446
0.187
0.168
0.343
0.128
0,283
0.045
0.086
0.080
0.090
0.183
0.127
0.137
HYPEN6KG-2HG)
0.216 0.455 0.213
0,173
0.363
0.250 0.140 0.299 0,132
0.152
0.192
0.222
0.223
0.200
0.154
0.182
Finetuned Inference
(KGGA)) 0.214 0.438 0.193
0.174 0.351 0.244 0.136 0.291 0.051 0.092 0.086
0.097
0.191
0.189
0.134
0.145
HYPERGKG-2HG) 0,217 0.456 0.209 0.176 0.347 0.243 0.158 0.275
0.169
0.171 0.194 0.210 0.225 0,234
0.166
0.210
hypergraphs, which are representative of the performance methods relying on end-to-end training. These models, by design, cannot generalize to unseen relations since they explicitly store the trained relation embeddings, and thus have to assign a randomly initialized vector for the representation of the unseen relations. For fair comparison, we evaluate HyPER(endZend), HYPER models trained directly on the corresponding train set for each dataset.
include To also evaluate the pretraining paradigm for foundation models, (LTTRAF(KG/KGG/5KKG) from Galkin al. (2024) as baseline KGFM model They pretrained on increasingly large KG corpora and evaluated on reified hypergraphs for tail-only link prediction, following Section 3 To assess the benefits of pretraining on different relational struc- tures, we experimented with four HYPER variants: HYYPER(KK/4KG/SOO
trained only on 3, 4, and 50 knowledge graph datasets with the same pre-training mix as ULTRA / (3KG/4KG/5OKG) from Galkin et al.] (2024). and HYPER(4HG). trained on four knowledge hypergraph datasets (JF17K (Wen et al. 2016). Wikipcople (Guan et al. 2021), FB-AUTO (Fatemi et al. 2020). and M-FB15K (Fatemi al. (020)). We further include H HYPER + 2HG), HYPER model trained on comprehensive mixture of three knowledge graph (FB15k-237, WÑI8RR, Codex Medium) and two knowledge hypergraph datasets (JF17K, Wikipeople), aiming to combine the advantages of both types of data, and fine-tuned this checkpoint over the training sets for each downstream task. For a fair comparison, we additionally pretrain ULTRA over the same pretraining mixture on reified hypergraphs and include ULTRA (4HG) and ULTRA ( (3KG+2HG).
Evaluations. We adopt filtered ranking protocol: for each query g(u1, u.) where k ar(g) and for each position é S k, we replace the 1-th position by all other entities such that the resulting hyperedges does not appear in training, validation, or testing knowledge hypergraphs. We report Mean Reciprocal Rank (MRR) and provide averaged results for three runs for the experiments. We report the standard deviation along with the full tables in Tables 19 and 20 and Table 21 The codebase is provided in httptss/////.....t /github..../.. com/ wwtp///ySoootttuuroooooo /HYPER See computation resources used in Appendix and further experimental details in Appendix G
5.2 RODE-RELATION INDUCTIVE LINK PREDICTION OVER KNOWLEDGE HYPERGRAPHS
Dataset construction and task settings. To evaluate the transferability and generalization capa- bilities of HYPER, we follow the methodology proposed in InGram (Lee al., 2023) to construct new datasets with varying proportions of unseen relations. We derive these datasets from three
We also include additional haseline results for other reification method KGFM in Appendices G.2 and G.3
7

---

Published as a conference paper at ICLR 2026
hypergraph datasets: JF17K (Wen et al. 2016) (JF), Wikipeople (Guan et al. 2021 (WP), and M- FBISK (Fatemi et al. 2020 (MFB). We also include WD50K (WD) (Galknn et al. 2020), originally hyper-relational KG, which convert into a knowledge hypergraph by hashing the main relation and predicates in canonical order. For each source dataset, we create four variants with different percentages of test tuples containing previously unseen relations: 25% 50%, 75%, and 100%. For instance, JF-25 includes 25% test tuples with unseen relations, while JF-100 contains only entirely unseen relations. This setup" allows us systematically evaluate how models perform under in- creasingly challenging inductive scenarios. We present all the details in Appendix A
Overall performances of HYPER (Q1). We report model performance across each dataset in Table 2 Note that HYPER and its vari- ants drastically outperform HCNet in node and relation-inductive settings. HCNet re- lies on learnable embeddings for each rela- tion type and struggles with unseen relations, leading to sharp performance drops under in- ductive settings. In contrast, HYPER lever- ages pretrained relation encoder, enabling strong generalization and robust performance even with entirely unseen relations. Note that fine-tuning HYPER(3KG+2HG) further boosts results, often matching or surpassing HYPER trained from end-to-end. This demonstrates the strong transferability of HYPER'S representa- tions and shows that lightweight finetuning small task-specific datasets can approach end- to-end performance without full retraining.
Table 3: MRR results on node-inductive datasets.
$ means the model is applied after reification.
Method
JF-IND WP-IND MFB-IND
End-to-End Inference
HGNN
0.102
0.072
0.121
HyperGCN G-MPNN RD-MPNN
0.099
0.075
0.118
0.219
0.177
0.124
0.402
0.304
0.122
HCNet
0.435
0.414
0.368
HYPER(endZend)
0.422
0.435
0.427
Zero-shot Inference
ULTRAF(3KG)
0.321
0.305
0.277
HYPER(3KG)
0.263
0.259
0.184
ULTRA
0.065
0.123
0.096
HYPER(4KG)
0.266
0.231
0.120
Impact on the ratio of known relations (Q2). We experiment with multiple relation-split set- tings that vary the proportion of test triplets involving unseen relations, ranging from 25% to 100%. While node-inductive baselines such HCNet already perform poorly under low rela- tional shift (e.g., 25%), their performance de- grades substantially as the proportion of un- seen relations increases (c.g.. 100%), reflect- ing the difficulty of generalizing to novel rela- tion types. In contrast, HYPER maintains con- sistently strong performance across all splits, demonstrating its robustness and ability to generalize effectively under increased proportion of unseen relations.
ULTKA"(5OKG)
0.007
0.029
0.026
HYPER(5OKG)
0.302
0.253
0.248
ULTRA
0.397
0.319
0.264
HYPER(4HG)
0.403
0.375
0.497
ULTRA=(KKG+HHG)
0.410
0.341
0.294
HYPER(3KG + 2HG)
0.459
0.415
0.404
Finetuned Inference
(LG+2 0.421
0.349 0.446
0.303
HYPER(3KG + 2HG) 0.463
0.455
HYPER vs. ULTRRA on reified knowledge hypergraph (Q3). Across all datasets, HYPER con- sistently outperforms KGFMs like ULTRA* on reified hypergraphs. While KGFMs can in prin- ciple generalize to binary relations, reified hypergraphs form atypical structures, e.g., tripartite graphs with auxiliary edge nodes, which is not commonly seen in pretraining corpora. Notably, UITTR*(50KG), trained on 50 knowledge graphs, performs much worse than the version trained on just 3, and remains substantially behind HYPER(3KG 2HG). This suggests that increasing the number of training graphs does not close the gap introduced by the lack of explicit hypergraph modeling. Moreover, (4TG) and (3KGGHG) also underperform compared with HYPER(4HG) and HYPER(3KG + 2HG), which are trained on the same pretraining mix contain- ing hypergraph datasets, respectively. While reification makes knowledge hypergraphs compatible with KGFMs, it can hinder generalization: auxiliary edge nodes increase hop distances, inverse re- lations are modeled ineffectively, and the resulting structures deviate from standard KG pre-training distributions. Together, this leads to inefficient reasoning and weaker performance.
These percentages are meaningful only in the end-to-end evaluation setting. In the zero-shot setting, all relation types are unobserved.
8

---

Published as a conference paper at ICLR 2026
Table Averaged zero-shot performance of HYPER(3KG 2HG) with different po- sitional interaction encoders.
Original
Comppted
Total Avg (19 hypergraphs)
MAR
0.3
0.265
Model
MRR
Hits @
All-one
0.236
0.262
0.1
Random
0.213
0.239
Magnitude
0.227
0.251
0.0
JF-50
Overall Average
Sinusoidal
0.285
0.281
Figure 6:
Zero-shot performance of HYPER(3KG 2HG) over original and corrupted datasets.
Impact of different pretraining datasets (Q4). The composition pretraining data has a notice- able impact generalization. While HYPER(4HG), pretrained hypergraph datasets, performs strongly on JF and MFB, both of which contain a large proportion of higher-arity relations, it strug- gles on WP, which primarily consists of binary edges. Conversely, WP benefits more from pretrain- ing on binary relational graphs, as seen with HYPER(3KG). The best overall performance comes from HYPER(3KG 2HG), which combines both binary and hypergraph pretraining sources. This suggests that pretraining on diverse relation structures and thus the underlying distribution improves generalization across tasks with varying arities.
5.3 NODE INDUCTIVE LINK PREDICTION OVER KNOWLEDGE HYPERGRAPHS
Settings. To further assess the applicability of node-inductive link prediction tasks with knowl- edge hypergraphs, we follow Yadati (2020) and Huang et al. (0225)), and experiment on three existing datasets: JF-IND, WP-IND, and MFB-IND. We compare our models with several existing approaches for inductive link prediction on knowledge hypergraphs. These include HGNN (Feng al. 2018)) and HyperGCN (Yadati et al., 2019). which were originally designed for simple hyper- graphs and adapted to knowledge hypergraphs by ignoring relations (Yadat) 2020).
We also compare with G-MPNN (Yadati 2020) and RD-MPNN (Zhou et al., 2023b), which were modified for inductive settings by replacing learned entity embeddings with uniform vector, and HCNet (Huang et al. 2025b). We also include the zero-shot performance of standard KGFM UL- TRA on the reification of hypergraphs.
Results and discussion. Table 3 presents the performance of all models across the node-inductive datasets. We continue to observe that HYPER significantly outperforms prior node-inductive base- lines such as HCNet, G-MPNN, and RD-MPNN in the zero-shot setting. Among HYPER variants, without fine-tuning, pretrained HYPER models achieve strong results. Fine-tuned HYPER fur- ther improves performance, achieving the best MRR on JF-IND and WP-IND, and competitive re- sults MFB-IND compared with HYPER trained end-to-end. Notably, HYPER consistently outper- forms ULTRA, which struggles to generalize to the distinct structure of reified hypergraphs. These results confirm HYPER'S robust generalization across variety of datasets.
5.4 IMPACT OF POSITIONAL INTERACTION ENCODERS
To evaluate the importance of design choices in the positional interaction encoder Encpi (Q5), we compare HYPER to three alternatives Endp equipped with different positional encoding schemes: (i) all-one encoding (p. 1d) which collapses all positions and violates injectivity; (ii) random encoding (p.. (0, Ia)). which lacks structure and hinders generalization; and (iii magnitude encoding (pa = a1d), which is unbounded and thus unsuitable for MLPs. In contrast, HYPER uses sinusoidal encoding. which is both injective and bounded, enabling effective extrapolation and robust zero-shot performance. As shown Table 4 sinusoidal encoding yields the best overall performance across 19 hypergraphs, significantly outperforming other schemes in both MRR and Hits@ 3. This highlights the critical property of injectivity and extrapolation of Encp in achieving robust zero-shot generalization.

---

Published as a conference paper at ICLR 2026
5.5 CORRUPTION OVER ARGUMENT POSITION
To validate the significance of ordered information in knowledge hypergraphs (Q5), we conduct an ablation study corrupt positional information. Specifically, for each of 16 newly proposed datasets, we take the most frequent relation type in each test graph and randomly and inconsistently permuted the argument positions for 50% of its hyperedges, making the semantic role of each argu- ment position ambiguous. For instance, a hyperedge r(a, b, c) might become r(b, c). We evaluate our HYPER(3KG 2HG) model in the zero-shot setting on these corrupted datasets. Empirically, observe that when we permute those relations that explicitly stored ordered information, such as cvg.musical gamu lwrgggammmooooo wongsooonnrsssee relationnti in JF-50, the performance drops dramatically, as shown in Figure 6 This is because each argument position carries a distinct semantic role (e.g.. musical, game, song), and HYPER relies on implicitly learning these roles to generalize. Corrupting this positional structure prevents HYPER from inferring roles for unseen relations, leading to dramatic decline in performance.
6 CONCLUSION
In this work, we introduced HYPER, the first foundation model for inductive link prediction over knowledge hypergraphs with arbitrary arity, capable of generalizing both unseen entities and unseen relations. Through extensive experiments on 16 newly constructed and 3 existing induc- tive benchmarks, we demonstrate that HYPER consistently outperforms tfte-offthhear knowledge hypergraph baselines and KGFMs applied to reified hypergraphs, demonstrating its strong general- ization across varied domains and relational structures. One limitation HYPER lies its com- putational complexity of relation arity: the number of positional interactions grows quadratically with the arity of each hyperedge. Future work may explore scalable approximations to mitigate the cost. Additionally, KGFMs, such ULTRA, generally performs better on standard knowledge graph tasks (See Appendix E). Future work may explore bridging the performance gap between higher-order and binary settings.
ACKNOWLEDGMENT
Bronstein is supported by EPSRC Turing AI World-Leading Research Fellowship No. EP/X040062/1 and EPSRC AI Hub on Mathematical Foundations of Intelligence: An "Erlangen Programme" for AI No. EP/Y028872/1.
ETHICS STATEMENT
This work proposes a foundation model for inductive reasoning over knowledge hypergraphs, which may benefit applications in scientific discovery, query answering, and recommendation systems by improving generalization across relational contexts. However, the same capabilities could also be misused for generating reinforeing biased spurious inferences when applied to real-world knowledge bases that contain noise, imbalance, or socially sensitive information. Future applications should therefore include safeguards for interpretability and error auditing, especially in domains with fairness or safety considerations. We acknowledge and adhere to the ICLR Code of Ethics
REPRODUCIBILITY STATEMENT
We ensure the reproducibility of our results. A complete description of dataset construction pro- cedures, including inductive splits with varying proportions of unseen relations, is provided in Ap- pendix A Details of the model architecture, training objectives, and optimization are presented in Section and Appendix G We further describe efficient implementation details and computa- release anonymous codebase with all scripts for data preprocessing, model training, and evaluation at https:: /tttps://github. com/ HlxyScotchuang/ huwphhhuungg/HHRRRRREe HYPER A detailed method of relation graph constructions is included in Ap- pendix B Together, these materials provide all the necessary information to reproduce the experi- ments and results reported in this paper.
tional resources in Appendix D To facilitate verification,
10

---

Published as a conference paper at ICLR 2026
REFERENCES
Ralph Abboud, ismail Ilkan Ceylan, Thomas Lukasiewicz, and Tommaso Salvatori. Boxe: A box embedding model for knowledge base completion. In NeurIPS, 2020.
Abdalgader Abubaker, Takanori Maehara, Madhav Nimishakavi, and Vassilis Plachouras. Self- supervised pretraining for heterogeneous hypergraph neural networks. arXiv preprint arXiv:2311. 1368, 2023.
Ivana Balazevic, Carl Allen, and Timothy Hospedales. Tucker: Tensor factorization for knowledge graph completion. In EMNLP-IJCNLP, 2019.
Adrián Bazaga, Pietro Liò, and Gos Micklem. Hyperbert: Mixing hypergraph-aware layers with language models for node classification on text-attributed hypergraphs. EMNLP, 2024.
Antoine Bordes, Nicolas Usumier, Alberto Garcia-Duran, Jason Weston, and Oksana Yakhnenko. Translating embeddings for modeling multi-relational data. In NIPS, 2013.
Yuanning Cui, Zequn Sun, and Wei Hu. A prompt-based knowledge graph foundation model for universal in-context reasoning. In NeurlPS, 2024.
Boxin Du, Changhe Yuan, Robert Barton, Tal Neiman, and Hanghang Tong. Hypergraph pre- training with graph neural networks. arXiv preprint arXiv:2105. 10862, 2021.
Bahare Fatemi, Perouz Taslakian, David Vazquez, and David Poole. Knowledge hypergraphs: Pre- diction beyond binary relations. In IJCAI, 2020.
Yifan Feng, Haoxuan You, Zizhao Zhang, Rongrong Ji, and Yue Gao. Hypergraph neural networks. In AAAI, 2018.
Yifan Feng, Shiquan Liu, Xiangmin Han, Shaoyi Du, Zongze Wu, Han Hu, and Yue Gao. Hyper- graph foundation model. arXiv preprint arXiv:2503.0120 2025.
Matthias Fey and Jan E. Lenssen. Fast graph representation learning with PyTorch Geometric. In ICLR Workshop Representation Learning Graphs and Manifolds, 2019.
Luis Antonio Galárraga, Christina Teflioudi, Katja Hose, and Fabian Suchanek. AMIE: Association rule mining under incomplete evidence in ontological knowledge bases. Www, 2013.
Mikhail Galkin, Priyansh Trivedi, Gauray Maheshwari, Ricardo Usbeck, and Jens Lehmann. Mes- sage passing for hyper-relational knowledge graphs. In EMNLP, 2020.
Mikhail Galkin, Etienne Denis, Jiapeng Wu, and William L. Hamilton. Nodepiece: Compositional and parameter-efffcient representations of large knowledge graphs. In ICLR, 2022.
Mikhail Galkin, Xinyu Yuan, Hesham Mostafa, Jian Tang, and Zhaocheng Zhu. Towards foundation models for knowledge graph reasoning. In ICLR, 2024.
Jianfei Gao, Yangze Zhou, Jincheng Zhou, and Bruno Ribeiro. Double equivariance for inductive link prediction for both new nodes and new relation types. In arXiv, 2023.
Genet Asefa Gesese, Harald Sack, and Mehwish Alam. Raild: Towards leveraging relation features for inductive link prediction in knowledge graphs. In Proceedings of the 11th international joint conference on knowledge graphs, 2022.
Saiping Guan, Xiaolong Jin, Jiafeng Guo, Yuanzhuo Wang, and Xueqi Cheng. Link prediction on n-ary relational data based on relatedness evaluation. IEEE Transactions on Knowledge and Data Engineering, 2021.
Xingyue Huang, Miguel Romero Orth, ismail Îlkan Ceylan, and Pablo Barceló. A theory of link prediction via relational weisfeiler-leman on knowledge graphs. In NeurIPS, 2023.
Xingyue Huang, Pablo Barceló. Michael M. Bronstein, ismail ilkan Ceylan, Mikhail Galkin, Juan L Reutter, and Miguel Romero Orth. How expressive are knowledge graph foundation models? In ICMI,, 2025a.
11

---

Published as a conference paper at ICLR 2026
Xingyue Huang, Miguel A. Romero Orth, Pablo Barceló, Michael M. Bronstein, and Ismail Ilkan Ceylan. Link prediction with relational hypergraphs. TMLR, 2025b.
Jaejun Lee, Chanyoung Chung, and Joyce Jiyoung Whang. Ingram: Inductive knowledge graph embedding via relation graphs. In ICML, 2023.
Shuwen Liu, Bernardo Grau, Ian Horrocks, and Egor Kostylev. Indigo: Gnn-based inductive knowl- edge graph completion using pair-wise encoding. In NeurIPS, 2021.
Haitao Mao, Zhikai Chen, Wenzhuo Tang, Jianan Zhao, Yao Ma, Tong Zhao, Neil Shah, Mikhail Galkin, and Jiliang Tang. Position: Graph foundation models are already here. In ICML, 2024.
Michael Sejr Schlichtkrull, Thomas N. Kipf, Peter Bloem, Rianne van den Berg, Ivan Titov, and Max Welling. Modeling relational data with graph convolutional networks. In ESWC, 2018.
Zhiqing Sun, Zhi-Hong Deng, Jian- Yun Nie, and Jian Tang. Rotate: Knowledge graph embedding by relational rotation in complex space. In ICLR, 2019.
Komal K. Teru, Etienne G. Denis, and William L. Hamilton. Inductive relation prediction by sub- graph reasoning. In ICML, 2020.
Théo Trouillon, Johannes Welbl, Sebastian Riedel, Éric Gaussier, and Guillaume Bouchard. Com- plex embeddings for simple link prediction. In ICML, pp. 2071-2080. PMLR, 2016.
Shikhar Vashishth, Soumya Sanyal, Vikram Nitin, and Partha Talukdar. Composition-based multi- relational graph convolutional networks. In ICLR, 2020.
Jianfeng Wen, Jianxin Li, Yongyi Mao, Shini Chen, and Richong Zhang. On the representation and embedding of knowledge bases beyond binary relations. In IJCAI, 2016.
Naganand Yadati. Neural message passing for multi-relational ordered and recursive hypergraphs. In NeurlPS, 2020.
Naganand Yadati, Madhay Nimishakavi, Prateek Yadav, Vikram Nitin, Anand Louis, and Partha Talukdar. Hypergen: A new method for training graph convolutional networks on hypergraphs. In NewrlPS, 2019.
Mingdai Yang, Zhiwei Liu, Liangwei Yang, Xiaolong Liu, Chen Wang, Hao Peng, and Philip S Yu. Instruction- based hypergraph pretraining. SIGIR, 2024.
Muhan Zhang, Pan Li, Yinglong Xia, Kai Wang, and Long Jin. Labeling trick: A theory of using graph neural networks for multi-node representation learning. In NeurIPS, 2021.
Yongqi Zhang and Quanming Yao. Knowledge graph reasoning with relational digraph. In WebConf, 2022.
Yongqi Zhang, Zhanke Zhou, Quanming Yao, Xiaowen Chu, and Bo Han. Adaprop: Learning adaptive propagation for graph neural network based knowledge graph reasoning. In KDD, 2023.
Yucheng Zhang, Beatrice Bevilacqua, Mikhail Galkin, and Bruno Ribeiro. TRIX: A more expressive model for zero-shot domain transfer in knowledge graphs. In LoG, 2024.
Jincheng Zhou, Beatrice Bevilacqua, and Bruno Ribeiro. A multi-task perspective for link prediction with new relation types and nodes. In NeurlPS GLFrontiers, 2023a.
Xue Zhou, Bei Hui, Ilana Zeira, Hao Wu, and Ling Tian. Dynamic relation learning for link predic- tion in knowledge hypergraphs. In Appl Intell, 2023b.
Zhaocheng Zhu, Zuobai Zhang, Louis-Pascal Xhonneux, and Jian Tang. Neural bellman-ford net- works: A general graph neural network framework for link prediction. In NeurIPS, 2021.
Zhaocheng Zhu, Xinyu Yuan, Mikhail Galkin, Sophie Xhonneux, Ming Zhang, Maxime Gazeau, and Jian Tang. nett A scalable path-based reasoning approach for knowledge graphs. In NewrIPS, 2023.
12

---

Published as a conference paper at ICLR 2026
A DATASET GENERATION DETAILS
A.1 GENERATING DATASETS FOR NODE AND RELATION-INDUCTIVE LINK PREDICTION
To evaluate models in an inductive setting, created multiple dataset variants with different proportions of unseen relations. Our dataset generation process, following InGram (Lee et al. 2023). detailed in Algorithm | This process creates training and inference hypergraphs with controlled percentages of unseen relations in the test set.
Algorithm Generating Datasets for Node and Relation-inductive Link Prediction
Require: Source knowledge hypergraph
(V, E, R), number of training entities Thaiin number of inference entities nea relation percentage Pret. tuple percentage Ptn. seed value
Ensure: Training knowledge hypergraph Girain = irain Furann Rurin) and Inference knowledge
hypergraph Ginr (Vinf, Eint, Rine)
1: G - Giant connected component of G
2: Randomly split R into Raain and Rar such that RRaiin Rinrl = (1 Pret) Prel
3: Uniformly sample Rarrin entities from V and form Vurain by taking the sampled entities and their neighbors
4: Farain == {r(v1, 02,-.., Un |/ E Virain: r E Rumiin r(U1, U2, U2...., vn.) E F)
5: Farain +- Hyperedges in the giant connected component of Exrain
6: Vinain f- Entities involved in Errain
7: Rmain + Relations involved Ewain
8: Let G' be the subgraph of G where the entities in Virain are removed
9: In G', uniformly sample nhest entities and form Vint by taking the sampled entities and their
neighbors
Fint == X UUY such that |X| Vint, E Ruain, r(11, ....... Up) Rint, r(11, U2..... ..) E E}
Y (1 Pir) Pii where X = (r(v), v2,... "n, un)le E
E F} and Y == (r(v1, ma)le; Vnn,
11: Ens Hyperedges in the giant connected component of Ennt
12: Vint < Entities involved in Ent
13: Rint Relations involved in Ens
14: Split Enn into auxiliary. validation, and test sets with a ratio of 3:1:1
The parameter Pui controls the percentage of test tuples containing unseen relations. For example, when Pri = 0.25, approximately 25% of the tuples in the inference hypergraph contain relations not seen during training. This allows systematically evaluate how models perform under increas- ingly challenging inductive scenarios.
After generating the inference hypergraph, we split into three disjoint sets: auxiliary (for training), validation, and test sets with a ratio of 3:1:1. For a fair comparison, these sets are fixed and provided all models.
A.2 DATASET STATISTICS
Table and Table 6 summarize the statisties of our constructed datasets and the hyperparameters used to generate them, respectively. Additionally, Table the arity distribution across these datasets. Together, these tables illustrate that our benchmarks vary significantly in terms of arity, density, and number of relation types, ensuring diverse and comprehensive evaluation setting.
B SPARSE MATRIX MULTIPLICAATION FOR COMPUTING POSITIONAL INTERACTION
In this section, we describe the procedure to generalize sparse matrix multiplication to effi- ciently construct knowledge hypergraphs from hyperedges of arbitrary arity. Unlike knowledge graphs (Galkin et al. 2024), where only two positions (head and tail) exist per relation, resulting in only 4 fundamental relations (head-to-head, head-to-tail, tail-to-head, tail-to-tail). knowledge hy-
13

---

Published as a conference paper at ICLR 2026
Table Statistics of datasets for inductive hypergraph completion. Max arity is shown for training graph and inference graph, respectively.
Train
Inference
Test
Dataset
Max Arity
V
R
[E]
[V]
[R]
EE
[V
[R]
JF-25
2,616
41
3,371
1,159
36
1,056
209
15
103
5/4
JF-50
2,859
3,524
1,102
37
1,292
157
5
109
5
JF-75
3,129
67
4,287
1,488
38
1,697
225
11
131
5
JF-100
2,123
2,449
1,696
35
2,159
52
5
25
5
WP-25
6,378
128
7,453
2,784
66
4,794
830
19
959
6/4
WP-50
7,586
155
9,536
3,608
87
4,390
531
29
413
7/6
WP-75
7,787
118
9,271
4,737
101
6,221
629
27
459
6
WP-100
7,787
118
9,271
4,891
63
7,516
275
155
6
WD-25
4,533
239
5,482
3,008
191
3,106
250
37
148
22/5
WD-50
3,796
162
4,147
2,303
188
2,353
145
30
91
19/6
WD-75
6,518
243
6,305
5,194
244
5,831
547
57
385
22/5
WD-100
6,798
237
7,271
3,576
105
3,951
385
29
282
19/4
MFB-25
1,266
8,182
1,929
12
2,802
146
87
3/5
MFB-50
1,415
11
8,409
1,528
13
2,426
472
10
486
3/5
MFB-75
2,225
5,271
1,363
16
4,008
675
803
3/4
MFB-100
2,013
19
11,658
2,406
5
4,514
808
5
904
3/5
Table Hyperparameters used to create fully inductive knowledge hypergraph datasets.
HP
JF-25
JF-50
JF-75
JF-100
WP-25
WP-50
WP-75
WP-100
Uraain
1000
1000
1200
1200
900
800
1000
1000
Tosst
900
800
1200
1200
800
1000
1000
1000
Piet
0.4
0.5
0.4
0.5
0.4
0.3
0.5
0.5
Pus
0.25
0.5
0.75
1.0
0.25
0.5
0.75
1.0
HP
WD-25
WD-50
WD-75
WD-100
MFB-25
MFB-50
MFB-75 MFB-100
Trraii
700
1000
10000
10000
100
100
80
120
Peet
1200
1000
8000
8000
95
85
80
100
Piet
0.25
0.5
0.5
0.5
0.5
0.6
0.5
0.5
Pin
0.25
0.5
0.75
1.0
0.25
0.5
0.75
1.0
pergraphs involve & positions per hyperedges, leading to h2 types possible positional interactions total.
Given a knowledge hypergraph G EV, E, R) with n [V] nodes, m = | relations, and maxi- mum arity k. we by representing the knowledge hypergraph via sparse tensors: the edge index E [ and corresponding edge types e El Each column of E lists the l participating nodes for a hyperedge, with each edge associated with its relation type.
To encode positional interactions between relations, perform sparse matrix multiplication in the following steps:
1. For each position E [1,...,k)) ,k), we construct sparse matrices E, E Raxm where each nonzero entry indicates the presence of an entity at position for given relation type.
2. For each pair positions (a, b) {1...., "l..,,,k) ,k] x {1,... ,k}, we compute a sparse matrix multiplication:
Anz = spmm ET E.) mm
Here, (Anz));; is nonzero there exists an entity that simultaneously plays position a in hyperedge of relation and position b in hyperedge of relation j.
14

---

Published as a conference paper at ICLR 2026
This operation systematically captures all intersections between hyperedges that share at least one common node, generalized across different positions.
C
PROOF
We first define isomorphisms and invariants of knowledge hypergraphs. following Huang et al. 2025b a.. The detailed architecture used in the experiments is shown in Appendix G.4
C.I ISOMORPIISMS AND LINK INVARIANTS OF KNOWLEDGE HYYPERGRAPIS
Isomorphisms. An (node-relation) isomorphism from a knowledge hypergraph G (V. E, R) to knowledge hypergraph G' = (V', RR') is a pair of bijections (T, Φ), where π : V + V' and ø R R', such that every fact r(u,, 2gg is in G if and only if the fact (TT))) ... (ux)) is in G". Two graphs are isomorphic if there is an isomorphism between them.
Invariants. For k 2 1, k-ary relation invariant is function associating to each knowledge hypergraph G = (V, E, R) a function {(G) with domain R² such that for every pair of isomorphic knowledge hypergraphs and G², every isomorphism (T, σ), and every tuple Re of relations in G, we have
{()) = ((G))
A (link) invariant a function w assigning to each knowledge hypergraph G (V, LE, Rt) function (() with domain R x V* such that for every pair of isomorphic knowledge hypergraphs G and G", every isomorphism (T, o), and every hyperedge r(u ux) in G, we have
w (r(u),..... ..)) = (df)))
For query q (g, ú, G. where q R is the relation type, (ui..... Up- Me+1,..., ux) are the observed arguments, and is the masked position, we define its image under (T, Φ)
(τ) q (o(a), (T(1),, ...., . (ur- (w:+1)) (ux)), t).
That is, the relation symbol mapped via & and each entity argument via m, while the masked position & (and thus the argument order) is preserved.
C.2 EQUIVARIANCE
We show that HYPER indeed computes link invariant on knowledge hypergraphs.
Proposition C.1 (invariance). Let G (V, , R) and G' (V', E², R') be knowledge hyper- graphs, and let (T,, Φ) be a (node-relation) isomorphism from G to G'. Then, the HYPER ar- chitecture with T layer relation encoders and L layer entity encoders computes link invariant on knowledge hypergraphs, i.e,, for every query (g, ū, f) in G and every candidate E V,
HYPER(G)((Uu...... .x) HYPER (C)()))))))))) T(x)))
Proof. We show that each stage of HYPER is invariant under the action (T,, 6).
Relation graph construction. By definition, Grel = Erel, Riel) has Viel R and contains directed edge (ri, with edge label (i,j) whenever there exist hyperedges e E. with p(e1) T1, p(e2) F2 and a node x E V such that & occurs at position in ea and at position j in e2. Under an isomorphism map ()) given G (Vigt- E'e R(a)), ø bijection between R and Ri', and π is bijection between V to V", Thus, the isomorphism map preserves membership and positional indices inside hyperedges. It holds that
r2 (i.5) E Frel = (o(r1),((12)) (i.j)) E Fial
In particular, the construction invariant to renaming of relations and respects the same positional labels (.. Thus, Gret and G isomorphic via ø with the same edge labels (i.j).
15

---

Published as a conference paper at ICLR 2026
Positional-interaction encoder. By design, Encp No0 x N>0 - R' maps position pair (a, b) to Va.b = MLP((Pe) [Po||Ppl). where Pa- Pb are the sinusoidal encodings of and b. Since MLP is shared across all position pairs, Fa,h depends only (a, b). Because edge labels in Grel and G are the same pairs (a, b) under Φ. we have a label-consistent edge feature assignment: for every edge (r1: 22, (a, b)) in Gret and the corresponding (((r)),((a)) (a,b) in Gz the edge message features coincide, i.c., Lo,b = L'a.b'
Relation encoder. Let h denote the hidden state of the relation node E Vrel computed by the HCNet relation encoder at the t-th layer, conditioned on query relation g. We prove by induction on t that for any isomorphism (TT, の) between G and G',
h
(+) (()))ot)) (Cia)) h (Grol)
Vr R,
Base case: The initialization function INITaa assigns the same parameters to all relations, depending only whether q. Because the query relation maps to (()) under the isomorphism, and all other relations share the same initialization, we have
(0) (rr))())) ( h ( (Grel).
Inductive step: Assume the inductive hypothesis holds for layer t. We remind that each update of the relation encoder is defined 4
h ((+1) r/u = up h rl0 AGG MSG ((h)))) () (e), 2) ( E)
Under the isomorphism Φ. the neighborhood of each relation node is preserved: for every (e, i) e Erst in Grei there exists unique (e', Ey (ő(r) in Gren- and (e).((e) corresponds bijectively to :ee).."") Moreover, for each positional label (a, 6). the corresponding fundamental relation em- bedding Xa,s is identical in both graphs since it depends only on (a, b). By the inductive hypothesis,
(o(4)) (Crat) h( (Gra) for all r'. Because MSGp(e), AGGrel, and (P are all shared, differentiable functions applied pointwise across nodes and edges, and AGG,e is commutatooninvariant The resulting updates are preserved under the action of 6z
the neighboring states satisfy h (e)
((+1) h ((r)ld()) (Gte)) = rlg
(1+1) (Gre)).
Entity encoder. This encoder applies an HCNet over the original knowledge hypergraph G (V, F, R), where each node v E V represents an entity and each hyperedge e = r(u1,..., Uk) E E connects entities according to their argument positions in relation p(e) r.
We prove by induction on that for any isomorphism (T,, Φ) between G and G²,
h (8) ((m))((m.)) (G') h
(1) h/ (G)
YOEV,
Base case: The initialization INIT is shared and depends only on whether the entity participates in the query q and at which position. Since both participation and positional roles are preserved under (T,
h (0) (T))) (G')
h h (G).
(U)
Inductive step: Assume the inductive hypothesis holds for layer é. Under (M. (π, each inci- dent pair i) E E(v) in G corresponds bijectively to (e',2) E E'(x(v)) in G", where e' =
(F (.o......,(),) (ux)) preserves both arity and argument order. The neighborhood mapping
Ni(e) between (c(())) ( is therefore bijective. For every positional index the sinusoidal encoding
Pj is fixed and identical across graphs. The message computation depends on (i)
p(e))q² which
(I)
equals h (T) (1 by relation-encoder cquivariance, (ii) the neighboring states h byg which
(2)
'Note that h (++1) h (++1) since the position and entity information in query q has been dropped in relation encoder, and thus enough write (6() rather than ( Φ) q.
rlg
16

---

Published as a conference paper at ICLR 2026
match h (2) MS)) AGG, and UP are shared differentiable functions and AGG permutation-invarian the up- dates are preserved under (T, Ø):
(x)))))) by the inductive hypothesis, and (iii) the fixed positional encodings Py- Since
(++1) h
((vI)(X.)))) (G') = hoig
(2+1) (G).
Decoder. The unary decoder is a shared map Dec Rd(()) - [0, 1] applied to (())) score the
candidate for the masked position in q. We have (L)
(G') = (L) (G), hence
*(v))(x,,))
Dec (h ( (L) (7.0)) (G')) Dec (4) (G)).
C.3 REQUIREMENTS OF POSITIONAL INTERACTION ENCODERS
In this section, justify our choice of positional interaction encoder MLP((Pa || ps)) by showing that it satisfies the two key properties: extrapolation and injectivity. We further show that the en- coder exhibits smooth dependence on positional indices.
In practice, we implement Enīpr as a two-layer multilayer perceptron (MLP) applied to the concate- nation of sinusoidal encodings of the two input positions. Let Pa: Pb Rd denote the sinusoidal encodings of positions b E N. defined componentwise by
(p=)2. = sin 1000025/4
(pa)2s+1 = cos 1000023/4 for = 0, ,,..,,, 1,
and analogously for Ps- The concatenated positional pair is E(a, b) [pallpb] 1-, 112d and the positional-interaction encoder outputs aa,b MLP b)).
Theorem C.2 (Properties of the positional-interrationn encoder). Assume d and 108/d is irrational (i.e., d & {2, 4, 8)). Let Pa. Ps E 1R be the sinusoidal positional encodings of positions a, E N400 and E'(a, b) [P pallpss] E [-1, 1]2d as above. Then there exists choice of parameters of MLP such that the positional interaction encoder Encr1 No. - IRm satisfies:
1. Injectivity. For all distinct (a, b), (a', (') E No.
(a, + (d',b')
Encer(a, b) # Enoei(a', 8').
2. Boundedness of the range. There exists a compact set C I"" such that Encer(a, K for all (a, N2 2D
3. Lipschitz continuity, smoothness. There exists constant L > such that for all (a, (d', (d',b') e R R?.
Encer b) Encpi(a', < L(aa d'1 +61)6bb'])
Proof. Injectivity. First we show that map Pa is injective. Let wi == 10000 21/d, Suppose
Pa = Ps- Then for each index there exists k; E Z such that
w
2Tk,
Taking /' -i+ +i++.. applying the same argument and dividing the two equalities gives
Wi
k;
Q
Wi+1
But by construction w = 10 8/d which is irrational whenever d & (2,4,8). This is contradic- tion unless = b. Hence b, and the map is injective.
Wis1
Now we show that the concatenation E(a, b) = [pa [ps] E [[11, 1 itself is injective. Suppose F(((ab)) F((a', B)). By definition of concatenation, the first d dimension coordinates give
17

---

Published as a conference paper at ICLR 2026
Pa Pa' and the last d dimension give pa Pv: By the previous part, a' and b = b'. Thus (a. b) (a', (d), ),, so E' is injective.
Finally, show that there exists parameterization of MLP(x) W W b1) b2 that injective. Choose W1 E IRax2d and by R" so that W + b 0 coordinatewise for all E 1,,, Then is the identity the entire domain, and
f(x) W2(W1a + b1) b2 (W2W1) (Web1 + b2)
is an affine map. With n 2 2d we can pick W to have full column rank 2d, and with m 2 2d we can pick W₂ so that W := W2W1 also has rank 2d. Hence æ + Ww + c injective on R2d thus on 1| Therefore, the class contains injective functions.
compaet. Observe that MLP((((pll))) pt)) MLP([-1,1] 1]2d), since sinusoidal encodings are bounded within [-1,1] and the concatenation given by E only affeets the dimensionality of the embedding. MLP continuous function
Boundedness of the range. We need to show that the range of (LP(F((p.lpp.)
a compact domain [-1, 1]2d, and result, its range compact. Consequently, even for unseen arity indices (a, b), the resulting positional representations remain within the same bounded set those observed during training.
Lipschitz continuity (smoothness). Set
Cpcs
w/,
LMPP |/Wll | L =CoosLMPP
For any v,y R and > 0, the mean value theorem gives sin(wz) - sin(wy)] S w|r y and | cos(wzr) cos(wy)) < w|x yl (as sin and cos are all 1-Lipschitz). Hence, with w. 10000 25/d have that
Ip. - 1 (sin(w;a) sin sin(w;;'))
(cos(wra) cos(w,a'))
2
Σ w la 2²12.
1=0
Thus |pp - Po' 112 I Cpos la a'), and similarly Ilpo - 1po-polla 1 Cpool b1.. By triangle inequality
on the concatenation,
[[(aa,)) E(d', .2)12 = Ilpa - P Ipb Po ]||
< Pa Pa ||2 + pps p
< Pec (la a'l + |b 6' b'l).
MLP(x) = Wo + b1) + b is Lipschitz with constant Lip(MLP) < W2lle Lip(a) || LMLP since ReLU is 1-Lipschitz (a RELU, Lip(a) 1). There- fore, by compositions of Lipschitz function,
||Encpr(a,) b) Encri(d',b))
= |MLP(EE(a, b)) MLP(E(dd,
LMIP [[((,,)) B(aa'8'))1
$ LMLP Cpos (la a'l + |b b().
D COMPUTATIONAL RESOURCES
All the pretraining experiments is carried out on a single NVIDIA H100 80GB, and the rest of the experiments carried out using NVIDIA A10 24GB. Pretraining of HYPER over single H100 with parameter specified in Appendix G takes days, while fine-tuning and end-to-end training typically require less than 3 hours.
18

---

Published as a conference paper at ICLR 2026
HYPER is implemented primarily using PyTorch and PyTorch Geometric (Fey & Lenssen 2019
with its core hypergraph message passing implemented via a custom-built Triton kerne This optimization approximately halves the training time and reduces memory consumption by factor of five on average. Instead of explicitly materializing all hyperedge messages, as is done in Py PyTorch Geometric, we directly write neighboring features the corresponding memory locations during aggregation. While the naive materialization approach incurs (l) memory complexity, where k denotes the maximum arity and | the number of hyperedges, our Triton-base based approach achieves O(VV)) memory complexity, depending only on the number of nodes, which enables efficient and scalable training of HYPER models.
E ADDITIONAL. EXPERIMENTS ON KNOWLEDGE GRAPHS
In addition to the knowledge hypergraph inductive settings, we also evaluate our models on inductive knowledge graph link prediction tasks where both nodes and relations can be unseen during training (Q6). This setting presents the most challenging scenario as it requires models to generalize to entirely new knowledge domains with both unseen entities and relation types. We also include inductive node-only knowledge graph link prediction to further strengthen our point.
Datasets. For inductive on both nodes and relations task, we includes 13 datasets in INGRAM (Lee) et al., 2023): FB-25, FB-50, FB-75, 100, WK-25, WK-50, WK-75, WK-100, NL-0, NL-25, NL- 50, NL-75, NL-100; and 10 datasets in MTDEA (Zhou et al., 2023a): MTI tax, MT1 health, MT2 org, MT2 sci, MT3 art, MT3 infra, MT4 sci, MT4 health, Metafram, FBNELL. We also include inductive link prediction nodes only experiments, containing 12 datasets from GralL (Teru et al. 2020j: WN-v1, WN-v2, WN-v3, WN-v4, FB-v1, FB-v2, FB-v3, FB-v4, NL-v1, NL-v2, NL-v3, NL-v4; 4 datasets from INDIGO (Liu et al.
2021 HM 1k, HM 3k, HM 5k, HM Indigo; and ILPC Small, ILPC Large.
datasets from Nodepiece (Galkin et al. 20222
Baseline. We included the zero-shot version of all the models and also include an existing knowl- edge graph foundation model as baseline, ULTRA (Galkin et al. 2024). shown in Table g Table g Notably, following standard convention, for every triplet ruu v) clude its inverse triplet r- (v, u). where r- denotes a newly introduced relation symbol represent- ing the inverse of r for ULTRA. However, HYPER does not need this procedure as the entity encoder employs a variant of HCNet (Huang et al. 2025b), which uses bi-directional message- pessage-passing and automatically considers the message from the inverse direction.
knowledge graph, we also
Results and Discussion. We observe that ULTRA generally performs better on standard inductive link prediction on knowledge graphs, although HYPER still competitive overall. Across both node- only and node-and-relation inductive benchmarks, HYPER performs on par with ULTRA, and often outperforms it on datasets with higher relational diversity or structure. These results demonstrate that the architectural inductive bias of HYPER, originally designed for knowledge hypergraphs, also transfers well to standard knowledge graphs, without compromising generalization ability.
F COMPLEXITY AND SCALABILITY ANALYSIS OF HYPER
To answer Q7, we first examine the theoretical computational complexity of HYPER in Ap- pendix F.I then present its empirical scalability results when applying FB15k-233 Appendix F2
F. THEORETICAL COMPUTATIONAL COMPLEXITY
In this section, we analyze the computational complexity of HYPER. Let G = (V, E, R) denote the input knowledge hypergraph, where n |V] m = L., and [R]] are the number of entities, hyper- edges, and relation types, respectively. Let & be the maximum arity of R, d the hidden dimension, and T the number of pessaag-passinge layers in the relation encoder, and denote L. as the number of message-passing layers in the entity encoder.
Relation Graph Construction The complexity of generating the relation graph in HYPER arises from computing pairwise positional interactions between relation types across hyperedges of
19

---

Published as a conference paper at ICLR 2026
bitrary arity. Unlike knowledge graphs, where each relation involves exactly two fixed positions (head and tail), knowledge hypergraphs induce up to k² positional interaction types for a maxi- mum arity k. For each position E {I....,,k, k), we construct sparse matrices E. R=xm that index entities by their position and relation type. Then, for every pair (a, b), we perform sparse matrix multiplication: spmm( E Eg). Each such multiplication has worst-case complexity of (nnz E. nnz Es)), where n-z(-) denotes the number of nonzero entries. Since there are k2 position pairs, the total time complexity of constructing the relation graph becomes
O max(nnz(()) (nz(),))) (a,b)
In practice, this is significantly accelerated by sparse tensor and batching across position pairs. With- sparse matrix multiplication, the naive construction would require iterating over all hyperedge pairs, resulting in ( 2 complexity, which is infeasible for large-scale datasets.
Additionally, for the positional interaction encoders, associate positional encoding vector EnCer((a, b)) E Rd. This construction requires (k22d) time and space to compute and store.
Relation Encoder The relation encoder in HYPER performs T layers of message passing over the relation graph Gzel (Vies, Eret, Rea),, as constructed before.
There are at most k² position pairs per pair of relation types, where the maximum arity, so the total number of edges is bounded by
Evel x2
In each message passing layer, each relation node aggregates messages from up to &2 neigh- bors, with each edge contributing message via the corresponding positional interaction embedding La.b EnCpi((a, b)) E Rd. Each node then applies an update with cost (dd). Thus, the total complexity of the relation encoder over 7' layers
(T(RR |
Entity Encoder After obtaining relation embeddings from the relation encoder, HYPER applies L layers of conditional message passing over the original knowledge hypergraph G = (V. E, R) using HCNet (Huang al. 2025b). In each layer, every entity v V aggregates messages from its incident hyperedges e E(v), where each hyperedge contributes query codyyccondit message, taking (L E)d), that incorporates its relation embedding h (T))
p[(e]] E Rd. followed by a relation- specific MLP, which takes (LL)))d) Each entity then updates its representation through neural update function with cost (df))
The total complexity of the entity encoder over L layers is thus
O[L(EE [V RR(d)).
F.2 SCALABILITY ANALYSIS
To empirically assess the scalability of HYPER, we compare HYPER with ULTRA, a prominent knowledge graph foundation model, and HCNet, a state-of-the-an node-inductive method on link prediction with knowledge hypergraph. All experiments are conducted on the transductive knowl- edge graph dataset FB F515k-237 using batch size of 64 ensure fair comparison among three methods. We summarize the model parameter size, training/inference times, and GPU memory usage.
Compared with HCNets, HYPER'S training and inference times approximately doubled since HYPER employs two HCNet encoders, one for relations and one for entities. We argue that this over- head represents reasonable trade-off for the substantial performance improvements and stronger inductive generalization demonstrated by HYPER compared with HCNets.
Compared with ULTRA, the main bottleneck of scalability is the complex modeling of knowledge graphs as knowledge hypergraphs. These differences essentially reduce to the difference between HCNet and NBFNets. For detailed discussion, refer the reader to Huang et al. (2025b).
20

---

Published as a conference paper at ICLR 2026
Research
Conffrreece
Redarios
Tys
Type
Bengio
ClimateAI
Montreal
CIFAR
Sasha
2015
EthicalAI
NeurlPS
Benglo
ClimateAl
Montreal
CIFAR
EthicalAI
NearlPS
Figure 7: Two different refferentreifficatooon KG corresponding to the knowledge hypergraph Giaan from Fig On the left figure (t), i abbreviates hasEntity,- On the right figure (1), R-i abbreviates Research-i, similarly for A AtConference, and T as Teaches.
G FURTHER EXPERIMENTAL DETAILS
In this section, provide detailed experimental configurations and dataset statistics. In particular, Table [3] summarizes the training corpora used for each model variant across knowledge graph and knowledge hypergraph settings. Tables [1] and 13 present arity distributions and structural statistics for the node-inductive datasets, while Table 16 reports the corresponding statistics for pretraining datasets. For inductive link prediction involving unseen entities and relations, we provide comprehensive dataset breakdowns in Tables 17 and 18
We also include the complete performance tables together with standard deviation for the node- inductive and node-relation inductive settings shown in Tables 19 21 respectively. Table 22 lists all hyperparameter choices used for pretraining, fine-tuning, and end-to-end training of HYPER. Finally, Table 23 specifies the dataset-specific training schedules for each experimental regime.
G.1 HYPERPARAMETER DETAILS FOR BASELINES
For G-MPNNs, adopt the best best-performing hyperparameters from the original codebase. Specif- ically, we set the input dimension d = 64, hidden dimension h 150, and dropout rate to 0.5. We use training batch size 128, evaluation batch size B 4, and negative sampling ratio ar = 10. The learning rate is set to 0. 0.0005, and models are trained for up to 5000 epochs with validation evaluated every epochs. Aggregation is performed using the max.
For HCNet, we use a 6-layer encoder with an input dimension of 64 and hidden dimension of 64 for all layers. We adopt sum as the aggregation function and enable shortcut connections to facilitate training. Optimization is performed using Adam W with a learning rate of 5 x 10-4. Training conducted with a batch size of 8, using the same number epochs and batches per epoch as HYPeR, with validation performed every 100 steps. The model is trained with 256 adversarial negatives sampled per positive example, and strict negative sampling is enforced to prevent overlap with true triples.
G.2 ADDITIONAL BASELINES FOR KGFMS
To provide more comprehensive evaluation of Knowledge Graph Foundation Models (KGFMs), we expanded our analysis beyond ULTRA, which served as the representative KGFM in the main paper. We additionally evaluated KG-ICL (Cui al. 2024), model that has demonstrated strong performance inductive knowledge graph completion tasks. For KG-ICL, we performed zero- shot experiments across all proposed datasets after reification with 3 variants of KG-ICL using 4 Layer, 5 Layer, and 6 Layer encoders, respectively. We highlight that KG-ICL learns over dif- ferent pretraining mix than ULTRA (FB-v1, NL-v1, and Codex Small). The results, summarized in Table 12, indicate that KG-ICL's performance is substantially lower than that of HYPER, fur- ther supporting the conclusion that existing KGFMs exhibit limited generalization on hypergraph structures.
21

---

Published as a conference paper at ICLR 2026
G.3 IMPACT OF REIFICATION METHODS ON KGFMS
We proposed an alternative reification used in Section 3 where each hyperedge becomes an auxil- iary node with outgoing edges hasEntity_ _i to its arguments and one hasRelationType edge the relation node (left of Fig. 7. noted as (f)). After edge_id node is generated for each edge, we then generate binary edges of the form ( id, u,) for each i [k: to capture the positions of the entities in the relation. Finally, we add the original relation and add an edge hasRela ittiionn onType(eeige.id.r))
node to the KG
Intuitively, i adds two-hop detour (edge_id + hes -> r), unlike which encodes the relation and positional information together at the edge types itself. This generally decreases the performance by over-simplifying the graph structure and disallows KGFM to use different represen- tations for different relations, making the model less efficient. As a result, we opt not to use this in reification in the main experiments.
Table shows two main trends. (i) With KG-only pretraining (3KG/4KG/SOKG) ULTRA is volatile with the relation explosion and we do not observe scaling behavior, while ULTRAÍ is gener- ally more robust to the reified knowledge hypergraphs and shows a more consistent trend as number of pretraining mix grows. (ii) When pretraining includes hypergraphs (4HG), (3KG 2HG), expos- ing role information at the edge type helps a lot: ULTRA+ typically matches or exceeds ULTRA across splits.
Nevertheless, all of the reficiation schemes with ULTTRA underperform compared with HYPER, which avoids reification entirely by design and remains strongest by operating directly on hyper- graph.
G.4 ARCHITECTURE CHOICES OF HYPER
Both the relation and entity encoders in HYPER follow the design based on HCNets (Huang et al., 2025b), with minor variant the relation-specific message functions.
Positional Interactions. In practice, we implement Encrr as a two-layer multilayer perceptron (MLP) over concatenated sinusoidal encodings of the input positions. Let Pa: Ps E Rd denote the sinusoidal positional encodings of positions a and b, respectively. Specifically, let Pa: Ps E Rd denote the sinusoidal positional encodings of positions a, b E N. defined componentwise as
(pa)2 = sin (100000/4)
(
(Pa)2s+1 = cos (100003/4))
a
for = 0.1...., d 1,
and similarly for ps-
Then, the embedding corresponding the interaction (a, is computed X.,6 MLP || Pb)); where MI.P denotes a shared two-layer feedforward network with ReLU activations. This produces dense embedding that captures the interaction between the two positions. Empirically, we find that this instantiation of EnCppt enables strong generalization across knowledge hypergraphs with varying arities and relational structures.
The relation encoder applies an HCNet over the constructed relation graph (Vie Exe, Reg). Here, each node r E Va represents a relation type in G, and an edge captures the induced interactions among relations. For each relation Viel HCNet iteratively updates its representation (1) 1g as:
Relation Encoder.
(0) hr1 INITIel (r, h rrgg
(t+1) UPrel (h AGG
(F's)) e NNar(e)), (e, E ())
where Er((r) the set of edge-position pairs incident to r, and Nias(ee is the positional neigh- borhood of hyperedge at position i. After T layers, we obtain the final relation encoding (T) Here, INIT,el, UPrele AGG and MSGp(e) are differentiable initialization, update, aggregation, and fundamental relation sppecffc message functions, respectively. The initialization function INIT is designed to satisfy generalized target node distinguishability formalized in Huang al. (0255))
22

---

Published as a conference paper at ICLR 2026
Empirically, we initialize the query node Via with all-one vector and all other relation nodes with zero vectors.
In the experiments, adopt the fundamental relation-specific message function MSGr using the fundamental relation embedding Ta,b- Specifically, given a set of neighbor features {(h wig g+
|
(w,j) E (ea)see) for hyperedge and center position i, the message is computed as:
(1)
(w, E eMau(e))) = - j
(O( (n oi + + (1-aa")))p
MSG
+ Xa,b:
where @ is the elemental-wise multiplication, (4) is learnable scalar, Pj is the sinusoidal posi- tional encoding at position j. and Xa, b the fundamental relation embedding computed as described earlier.
Entity Encoder. In the context of the entity encoder, we apply separate HCNet over the original knowledge hypergraph G = (V, F,, R). Each node E V aggregates information from its incident hyperedges, incorporating the relation embeddings h (T) obtained from the relation encoder.
rlq
Given a query (q, ü, (), where û = -u],,.., ux) denotes the entities in the hyperedge and / is the target position, each node V receives initial representation defined
(0) v/a
Σ 1,= ipft
(p. + 1/g
where p: E IRd is the positional encoding position i.
HYPER then iteratively updates the node representations h h/gg as:
(8)
h helg = INIT(U, q), h (++1) UP h (1) oig
1 0/a- AGO ( MSSG (1(h wlg (w, e (e 9) (e, E(t)))
where INIT, UP, AGG, and MSG, are differentiable initialization, update, aggregation, and relation- specific message functions, respectively, with INIT satisfying generalized targets node distinguisha- bility (Huang et al. 2025b). After layers of message passing, we obtain the final entity encoding
h (.) A final unary decoder Dec Rd)) + [0, 1] predicts the score for completing the missing position É in the query q.
Empirically, we select the relation-specifi message function MSGP(e) to be
( + (1-a
MSG, (1(1))) (w,j) E N((e))) = (a
(9) Pbila
(h (T) @ MLP(0) (L
jzi
where additionally MLP(() is a 2-layer MLP with ReLU to transform the relation representation most suitable for each specific layer during message passing.
Update. We summation the aggregation operator for both relation and entity nodes. Each node updates its representation via two-layer MLP applied to the concatenation of its current state and the aggregated message:
((+1) ML.(()) (I. AGGREGATE!()) b/q
where AGGREGATE 5/g denotes the sum of incoming messages to node e under query q at layer f, and represents vector concatenation.
Other. We also apply layer normalization and shorteut connections after aggregation and before the ReLUU activation in both encoders.
23

---

Published as a conference paper at ICLR 2026
G.5 TRAINING OBJECTIVE
Following prior work (Huang et al., 2025b), we train HYPER under the partial completeness as- sumption (Galárraga et al. 2013), where each k-ary fact q(u),.... Ug) is used generate training samples by randomly masking one position S I k. Given a query q = (g. ū, 1), we model filling the missing position p(vlg) (Dec (t)
the conditional probability of entity where Dec is a two-layer MLP and a denotes the sigmoid activation. We optimize the following self-adversariaa negative sampling loss (Sun et al. 2019):
[(wlq) = - log ((vg()))))
Σ Wio log(1 - p(v(l)))
where of are corrupted negative samples, n is the number of negatives per query, a being the adver- sarial temperature, and wio are the importance weights defined by
Wi, Softmax [oog(1 p(v((q)))
To mitigate overfitting, we exclude edges that directly connect query node pairs during training- The best model checkpoint is selected based on validation performance. Following the implementa- tion of ULTRA (Galkin et al. 2024), for pertaining over multiple knowledge graph and knowledge hypergraphs, for each batch, we sample from one of the pretrained (hyper)graphs with probability proportional the number of edges contains.
24

---

Published as a conference paper at ICLR 2026
Table 7: Arity distribution across node-relation inductive datasets.
Datavel
Arily
Training Graph
Inference Graph
Training %
Inforence
266
25.
1441
670
42.75%
63.45%
4
326
120
9.67%
11.36%
25
2
1942
321
55.11%
24.85%
3
1297
692
36,80%
53 33.56%
JF-50
279
2:5
0
0.00%8
000056
K24
3
848
$46
19.78%
49.85%
18-75
4
779
27
18.1988
1.59%
255
2
1349
1637
55,08%5
75.82%
JF-100
159
20,81%
7.36%
25
19
80
0.78%
3.71%
4,331
2,799
79.00%
90.12%
3
612
162
11.16%
5.224
WD-25
1.30%
4355
80.846
20%
067
3
6.99%
0007%
25
0.57%
0.05%
6471
6121
69.00%
98 39%
3
1725
82
18.61%
1.32%
WP-75
25
0.53%
0.08%
1725
91
18.61%
1.21%
1026
11.07%
0.08%
25
0.08%
2
3,680
1.941
87.60%
93.81%
3
114
5.02%
5.51%
WD-25
12
2:5
2
0.74%
0.1056
2,127
WD-30
417
86
10.06%
3.60%
4
438
136
10.56%
5.78%
25
4,500
5,609
37.22%
97.22%
WD-75
22
8.69%
0.38%
25
1.40%
0.00%
5,858
3,631
80.57%
91.90%
006
186
12.46%
4.71%
WD-100
134
5.46%
3.39%
25
137
1555
1.67%
MFR-25
4
0
0.00%
0.00%6
25
416
0.00%
14.8%%
2
149
1400
1.77%
57.71%
3
8260
756
982234
31.10%
MEB-50
0.00%
25
270
9.18%
2497
3639
47.37%
90.79%
1
0.00%
0.00%
25
2
726
3234
6.23%
71.64%
MEB--10
3
10932
370
93.77%
8.20%
2:5
910
0.00%
20.16%
25

---

Published as a conference paper at ICLR 2026
Table Zero-shot experiment results on node and relation inductive knowledge graph datasets
Method
FB-25
FB-50
FB-75
FB-100
WK-25
WK-50
WK-75
WK-100
MRR 11 tO MRR 10 MRR 11GP 10 MRR 11 10 MRR 11 10 MRR 11@ 10 MRR 11@ 10 MRR 11@10
ULTRA(3K))
0.388 0.640 0.338
0.543 0.403
0.61M 0.449
0,642 0.316
0.532 0.166 0.324
0.365
0.537
0.164
0.286
H[YPRR(KK)
0.372
0.373 0.568
0.276
0.334
0.271
HYPER(HHG)
0.277
0.538
0.225
0.427
0,287
0,503
0.336
0.567
0.215
0.422
0.117 0,245 0,280
0.491
0.125 0.247
HYPER(3KG 2HG) 0.382
0.635 0.326 0.535
0,389 0.598 0.434 0.632
0.281 0.428 0.158 0,280 0,365 0.522 0.160 0.280
NL-25
NL-50
NL-75
NI.-100
MT11tax
MT11health MT22org
MT2-scl
Method
MRR H@10 MRR H@10 MRR H 10 MRR 10 MRR H 10 MRR H@10 MRR H MRR H@10
ULTRA(3G)
0,395 0.569 0.407 0.570 0.368 0.547
0.471 0.651 0.224 0,305 0.298 0,374 0.095 0.159 0.258 0.354
HYPER(KK)
0.321 0.550 0.350 0,520 0.320 0.483 0.415 0.627 0.234 0,306 0.361 0,431 0.088 O. 0.142 0.256 0.339
HYPER(4HG)
0.214
0,411 0.226 0.480 0.252 0.455
0.333 0.618 0.200 0.274 0.266 0,358 0.063 0.116
0.195 0.320
HYPER(3KG 2HG) 0.360 0.558 0.376 0.547 0.342 0.540 0.473 0.685 0,204 0.396 0.222 0.399 0.087 0.149 0.258 0.428
Method
MT3-art MT3-infra
MT4-sci
MT4-health
Metafam
FBNELL
NL.0
Avernge
MRR Hθ 10 MRR H@10 MRR Hθ MRR HỘ MRR Hθ MRR H@10 MRR Hθ 10 MRR H@10
ULTRA(3KG)
0.259 0.402
0.274
0.737 0.238
0.652 0.342
0.345
0.513
HYPER(3KG)
0.257 0.402 0.562 0.695 0,259 0.415 0.547 0.723 0.395 0.804 0.447 0.617 0.312 0.501 0.318 0.492
HYPER(HHG)
0.152 0,265 0.363 0.451 0.232 0.412 0,380
0.556
0.191 0.606
0.320
0.537 0.171 0.393
0.228 0.419
HYPER(3KG 2HG) 0,270 0,425 0,573 0,716 0,270 0.441 0.560 0.724
0,457 0.875 0,450
0.639 0,334 0.526
0.336 0,520
Table 9: Zero-shot experiment results node inductive knowledge graph datasets. The best result for each dataset is in bold.
WN-v1
WN-v2
WN-v3
WN-v4
FR-vI
FB-v2
Method
11@10
ULTRA(3KG)
0.648
0.768
0.663
0.765
0.376
0.476
0.611
0.705
0.498
0.656
0.512
0.700
HYPER3KG)
0.703
0.799
0.681
0.788
0.400
0.522
0.644
0.721
0.450
0.622
0.474
0.668
HYPER(4H))
0.533
0.691
0.287
0.392
0.514
0.527
HVYERR(3G + 21GG)
0.702
0.782
0.686
0.785
0.385
0.503
0.640
0.710
0.454
0.648
0.480
0.695
Method
FBBv3
FB-v4
NL.v1
NL.v2
NL..33
NL.v4
MRR H@:0
MRR
H@
10
MRR
H@10
MRR
H@ 10
MRR
H@10
MRR
H@ 10
ULTRAGKG))
0.491
0.654
0.486
0.677
0.785
0.913
0.526
0.707
0.515
0.702
0.479
0.712
HYPER(3K))
0.460
0.653
0.619
0.868
0.514
0.468
0.697
HYPER4HHG)
0,276
0.482
0,280
0.504
0.516
0.863
0.345
0.639
0,340
0.610
0.269
0.582
HYPER/3KG + 2HG)
0.466
0.648
0.460
0.663
0.570
0.719
0.521
0.741
0.509
0.705
0.501
0.728
Method
ILPC Small
ILPC Large
HM 1k
HM 3k
HM
HM Indigo
MRR
11@:10
MRR
11
MRR 11@1
MRR 11
MRR 11@
MRR
110:10
ULTRAGKKÜ
0.302
0.443
0.290
0.424
0.059
0.092
0.037
0.077
0.034
0.071
0.440
0.648
HYPER3KG)
0,291
0.438
0,293
0.412
0.046
0.092
0.036
0.073
0.033
0.069
0.437
0.644
HYPER(4HO)
0.169
0.347
0.183
0.327
0.027
0.075
0.024
0.064
0.024
0.058
0.298
0.484
HYPER + 21G
0.296
0.448
0.289
0.417
0.043
0.106
0.037
0.092
0.034
0.086
0.401
0.614
Table 10: Scalability comparison on FB15k-237 with batch size = 64.
Training Time (s/batch)
Inference Time (s/batch)
Model
# Parameters
GPU Memory (GB)
ULTRA HCNet
168,705
1.19
0.066
12.87
159,297
2.64
0.156
18.03
HYPER
225,409
4.51
0.272
25.30
26

---

Published as a conference paper at ICLR 2026
Table 11: Zero-shot MRR results on node and relation inductive knowledge hypergraph datasets. Superscript & means the model is applied over the reification shown in the main body, and means the model is applied with the alternative reification.
Method
50
75
100
25
50
100
25
75
100
50
75
100
ULTRA SITRA*KKEE (3KG)
0,103
0.437
0.168
0,144
0.255
0.235
0.154
0.277
0.039
0.077
0.073
0.078
0.117
0.155
0.116
0.161
(UTRA*(4KG))
0.011 0.298
0.042
0.082
0.217
0.170
0.043
0.135
0.009
0.006
0.006
0.004
0.027
0.069
0.063
0.065
ULTRA ULTRA*(SOKG) (SOKG)
0.001
0.096
0.010
0.001
0.225
0.083
0.001
0.190
0.006
0.009
0.009
0.004
0.008
0.001
0.001
0.001
ULIRA
0.154
0.442
0.175
0.170
0.338
0.236
0.129
0,280
0.052
0.091
0.089
0.089
0.076
0.175
0.052
0.136
ULTRA "UTRA*(3KG+HHC)
0.209
0.446
0.187
0.168
0.343
0.236
0.128
0.283
0.045
0.086
0.080
0.090
0.183
0.182
0.127
0.137
ULTRA (3KG)
(GKG)
0.119
0.304
0.109
0.091
0.209
0.153
0.062
0.222
0.040
0.070
0,067
0.071
0.171
0.201
0.149
0.176
ULTRA ULTRA'(4KG) (4KG)
0.099 0.325
0.102
0.132
0.343
0.215
0.111
0.274
0.047
0.091
0.089
0.086
0.094
0,141
0.054
0.075
ULTRRA (SOKG)
0.147
0.407
0. 126
0.111
0,310
0.218
0.100
0,262
0.045
0.071
0.045
0.065
0.062
0.124
0.104
0.150
ULTRA
ULTRA (4HG))
0
0.293
0.102
0,113
0.226
0.143
0.065
0.236
0.043
0.069
0.065
0.068
0.147
0.159
0,092
0.089
ULTRA (3KG+2HG)
0,114
0.340
0.121
0.120
0.272
0.197
0,109
0.240
0
0.070
0.052
0.066
0.167
0.117
0.138
HYPER (3KG)
0.148
0.297
0.112
0.130
0.248
0.191
0.039
0.276
0.143
0.147
0.186
0.221
0.167
0.158
0.123
0.146
HYPER(4KG)
0.109
0.065
0.128
0.116
0.148
0.074
0.175
0.180
0.148
0.111
0.150
0.255
HYPER(SOKG)
0.056
0.294
0.084
0,111
0.122
0.156
0.126
0.148
0.067
0.198
0.191
0.155
0.073
0.055
0,130
0.088
HYPER((4H))
HYPER((KG+2HI))
0.216 0.455
0.213
0.173
0.363
0.250
0.140
0.299
0.132
0.152
0.192
0.222
0.223
0.200
0.154 0.182
Table 12: Average zero-shot inference MRR over newly proposed dataset comparison across KG-ICL, ULTRA, and HYPER variants.
Model
Average MRR
KG-ICL Layer))
0.139
KG-ICL(5 Layer)
0.048
KG-ICL(6 Layer)
0.143
ULTRA(3KG)
0.162
ULTRA(4KG)
0.078
ULTRA(50KG)
0.040
ULTRA(4HG)
0.168
ULTRA(3KG+2HG)
0.183
HYPER (3KG)
0.161
HYPER (4KG)
0.135
HYPER (50KG)
0.135
HYPER (4HG)
0.128
HYPER (3KG+2HG)
0.236
Table 13: Training datasets for model variants
Knowledge Hypergraph
Knowledge Graph
Model
JP17K FB-AUTO Wikipoople MFBISK FB15k-237 WNISRR CodEx Medium NELL995 Others(46G)
ULTRA(3KG)
ULTRA(4KG)
ULTRA(5OKG)
ULTRA(3KG 2HG)
4
HYPER(3KG)
V
HYPER(4KG)
HYPER(4IIG)
HYPER(3KG 2HG)
HVPERRend2end))
Trained directly on target dataset's training graph
HCNet
27

---

Published as a conference paper at ICLR 2026
Table 14: Arity distribution across node inductive datasets.
Dataset
Arity
Training Graph
Inference Graph
Training %
Inference %
264
4.28%
2.93%
4586
216
74.36%
70.36%
JF-IND
4
1317
82
21 21.36%
26.71% %
25
0
0
0.00%
0.00%
0
0
0.00%
0.00%
3375
476
81.54%
86.39%
WP-IND
764
75
18.46%
13.61%
25
0
0
0.00%
0.00%
0
0
0.00%
0.00%
336733
7527
100.00%
100.00%
MFB-IND
0
0
0.00%
0.00%
25
0
0.00%
0.00%
Table 15: Dataset statistics of inductive link prediction task with knowledge hypergraph.
Statistic
JF-IND
WP-IND
MFB-IND
# seen vertices
4,685
4,463
3,283
# train hyperedges
6.167
4,139
336,733
# unseen vertices
100
100
500
# relations
31
32
12
# max arity
Table 16: Dataset statistics of pretrained knowledge hypergraphs and knowledge graphs with spective arity.
Dataset
FB-AUTO
WikiPeople
JF17K
MFB15K
FB15k237
WN18RR
CoDEx-M
VV]
3,410
47,765
29,177
10.314
14541
40943
17050
[R]
8
707
327
237
51
train
6,778
305,725
61,104
415,375
272115
86835
185584
valid
2,255
38,223
15,275
39,348
17535
3034
10310
test 2,180
38,281
24,915
38,797 5
20466
3134
10311
max arity
5
9
2
2
# arity= 2
3,786
337,914
56,322
82,247
310,116
93,003
206,205
arity= 3
0
25,820
34,550
400,027
0
0
arity 4
215
15.188
9,509
26
0
arity2 5
7,212
3.307
2,267
11,220
0
28

---

Published as a conference paper at ICLR 2026
Table 17: Dataset statistics for inductive on both node and relation link prediction datasets. Triples are the number of edges given at training, validation, or test graphs, respectively, whereas Valid and Test denote triples to be predicted in the validation and test graphs.
Training Graph
Validation Graph
Test Graph
Dataset
Entifies
Rels
Triples
Entities
Rels
Triples
Valid
Entities
Rels
Triples
Test
FB 25
5190
163
91571
4097
216
17147
5716
4097
216
17147
5716
11636
FB-75
4659
134
62809
2792
186
9316
3106
2792
186
9316
3106
FB-100
4659
134
62809
2624
77
6987
2329
2624
6987
2329
WK-25
12659
47
41873
3228
74
3391
1130
3228
3391
1131
WK-50
12022
72
82481
9328
93
9672
3224
9328
9672
3225
WK-75
6853
52
28741
2722
3430
1143
2722
3430
1144
WK 100
9784
67
49875
12136
37
13487
4496
12136
37
13487
4496
7796
112
2287
2287
NL-25
4396
106
17578
2146
120
2230
743
2146
120
2230
744
NL-50
4396
106
17578
2335
119
2576
859
2335
119
2576
859
NL-75
2607
96
11058
1578
116
1818
606
1578
116
1818
607
NT-1100
12588
55
7832
1709
53
2378
793
1709
2378
793
Metafam
28
13821
1316
13821
590
656
7257
FBNELL
4636
100
10275
4633
100
10275
1055
4752
183
10685
597
Wiki MTT
10000
10
17178
10000
10
17178
1908
10000
16526
1834
Wiki MTI
health
10000
14371
10000
14371
1596
10000
14110
1566
Wiki MT2
10000
10
23233
10000
10
23233
258
10000
21976
2441
Wiki MT2 sci
10000
16
16471
10000
16
16471
1830
10000
16
14852
1650
27262
Wiki MT3 infra
10000
24
21990
10000
24
21990
2443
10000
27
21646
2405
12576
1397
12516
Wiki MT4 bealth
10000
21
15539
10000
21
15539
1725
10000
20
15337
1703
Table 18: Dataset statistics for inductive-e link prediction datasets. Triples are the number of edges given training, validation, test graphs, respectively, whereas Valid and Test denote triples to be predicted in the validation and test graphs.
Training Graph
Validation Graph
Test Graph
Dataset
Rels
Entities
Triples
Entities
Triples
Valid
Entities
Triples
Test
FB-vl
180
1594
4245
1594
4245
489
1093
1993
411
FB-v2
200
2608
9739
2608
9739
1166
1660
4145
947
FB-v3
215
3668
17986
3668
17986
2194
2501
7406
1731
FB-v4
219
4707
27203
4707
27203
3352
3051
11714
2840
WN-v1
9
2746
5410
2746
5410
630
922
1618
373
WN-v2
6954
15262
69554
15262
1838
2757
4011
852
WN-v3
12078
25901
12078
25901
3097
5084
6327
1143
WN-v4
3861
7940
3861
7940
934
7084
12334
2823
NL-vI
14
3103
4687
3103
4687
414
225
833
201
NL-v2
88
2564
8219
2564
8219
922
2086
4586
935
NL-v3
142
4647
16393
4647
16393
1851
3566
8048
1620
NL-v4
2092
7546
2092
7546
876
2795
7073
1447
ILPC Small
48
10230
78616
6653
20960
2908
6653
20960
2902
ILPC Large
65
46626
202446
29246
77044
10179
29246
77044
10184
HM 1k
11
36237
93364
36311
93364
1771
9899
18638
476
HM
32118
71097
32250
71097
1201
19218
38285
1349
HM 5k
11
28601
57601
28744
57601
900
23792
48425
2124
HM Indigo
229
12721
121601
12797
121601
14121
14775
250195
14904
29

---

Published as a conference paper at ICLR 2026
Table 19: Experiment result on node and relation inductive knowledge hypergraph datasets for JF and WP.
JF-25
JF-50
JF-75
JF-100
Method
MRR H6 I HOB H6 MRR Hid 1 HOB H@10 MRR H 1 H40 H6000 MRR H6#
H80 H 10
G-MPNN
0.006 0.004 0.004 0.007 0.003 0,000 0,000 0.003 0.001 0,000 0,000 0,000
0.002
0.000 0.000
0.000
HCNet
0.011 0.004 0.007 0.011
0.009 0.000 0,900 0.024 0.069 0.038 0.072 0.125
0,028
0.000 0.018
0,054
0.202 0.117 0.226 0.346
0.468 0,358 0,540 0.653
0.207 0.125 0.226 0.357
0.198
0.107 0.161 0.411
HYPER(endZend)
d:003 002 m0005 d:.005
1:.004
+5.077 4:0022
11,033
4:,005 d: 000 1:,006 4:.003
d1.008
41.002 4:004
#.003
ULTRA=((K))0-boo)
0.103 0.039 0.095 0.240
0.437 0,301 0.581 0.699
0.168 0, 0.160 0.288
0.144
0.089 0.143 0.196
ULTRA* shot)
0.011 0.004 0.011 0.035 0.298 0. 0.368 0.468
0.042 0.025 0,050 0.072 0.082
0.071 0.089 0.107
ULTRA (STRRA(50KGXO-bbb
0.001 0.000 0.000 0.000 0.096 0.089 0.1 0.105
0.010 0.006 0.013 0.016 0.001 0.000 0.000 0.000
ULTRA (4HO)O-shot)
0.154 0.067 0,155 0.336
0.442 0.288 0.539 0.696 0.175 0.085 0,185 0.339 0,170 0,107 0.143 0,286
ULTRA ULTRA (3KG-2HGXO-shho)
0.209 0.113 0,216 0,413 0.446 0.293 0.547 0.707 087 0.097 0.197 0,342 0.168
0,107 0,143 0.286
HYpPsa(kK(i(O-ssaat)
0.148 0.071 0.152 0.318
0.297 0.212 0.336 0.460
0.1 0.041 0. 0.254
0.130
0.018 0.107 0.375
HYPEk<4KGi(O-shot)
0.109 0.078 0.122 0.178 0.065 0.009 0.037 0.241 0.
0.078
0.247
0.087 0.000 0.054 0.286
#YPER(50KGX0ssbot)
0,056 0.022 0.044 0.167 0.294 0,204 0.352 0.463
0.084 0.026 0,104 0.208
0.111 0.018 0.089 0.321
HYPER((I(G/O~ssat))
0.187 0,095 0.219 0.360 0.377 0.239 0,476 0.608 0.188 0.110 0.204
0.370
0.181 0.089 0.161 0.464
HYPER(3KG -hh)))
0.216 0.122 0.233
0.413 0.455 0.325 0.556
0.664
0.213 0. 022 0.231
0.367
0.173 0.071 0.179 0.446
ULTRA (LTRA"(KK-2HGXxfncco
0.214 0.109 0.221 0.406
0.301 0.539
0.102
0.174
0.103
0.279
=:005 + 003 -00 +:007
2000
+ 004
+0008 1X0
203
+ 002 2005
+. 200
1:004 +: 003
#:002 1005
0.217 0.131 0.226
0.389
0.456
0.331
0.554
0.672
0.209
1.1
0.238
0.361
0.176
0.089
0.161
0.393
HYYERR(KKG + (inettu))))))
#.001 002 =000 4:00
0000
005 4:002
2:00
5.00
4:005
+ 2:008 2200
Method
WP-25
WP-50
WP-75
WP-100
MRR HθI I H03 H@ 10
MRR H@ H@3 Hθ
MRR
HØ3 10 MRR H@
H@ 10
G-MPNN
0.005 0.003 0.005 0.006
0.001
0.000
0.000
0.000
0.001
HCNer
0.104 0.048 1.1 0.230
0.050 0.025 0.059 0.087
0.019 0.010 0.020
0.032
0.003
0.000
0.000
0.003
HYPEss(nddeed))
0.159 0.071
0.172 0.358 0.143 0.082 0.157 0.260
0.139 0.072 0.129 0.294
0.202
0.106 0.190
0.418
+.003 00000--000000 =.005
+.006 #:002
000 +.004 #0007 #5,00 4 #5005 4:006
#-002 + 4.004
+.007
ULTRA (3KC)-0))))
0.039 0.015 0.034
0.108
0.077 0.035 0.098 0.160
0.073 0.037 0.079 0.158
0.078
0.048 0.084
0.148
ULTRA )
0.009 0.000 0.002 0.041 0.006 0.000 0.002 0.022 0.006 0.001 0.001 0.024
0.004 0.000 0.000
0.023
0.006 0.005 0.007 0.007
0.007 0.012
0.004
0.006
ULTRA (HHG))-shot)
0.052 0.023 0.070 0.103
0.091 0.044 0.121 0.166 0.089 0.048 O. 102
0.168 0.089
0.055 0.103 0.158
(LGGA=OKK-22HGX--h0
0.045 0.016 0.060 0.096 0.086 0,041 0.110 0.161 0.080 0.039 0.096 0.159 0.090 0.055 0.109 0.158
HYPSR(3K(j(O-shat)
0.143 0.057 0.138 0.349
0.147 0.073 0.159 0.327
0.186 0.097 0.186 0.391
0.221 O. 0.106 0.241 0.498
IIYPER(4KGiO0
0.074 0.016 0.094 0.219 0.212 0,141 0.250 0.391 0.175 0.078 0.188 0.438
0.180 0.062 0.188 0.516
HYPeR<50KGG)O-duu
0.067 0.016 0.094
0.156
1.909
0.234
1.1
0.500
0.155 0.031 0.109 0.563
HYpEk(HHGjOO-hhot)
0.075 0.033 0.094
08166 0.068 0.056 0.080
0.081 0.086
0.066 0.107 0.114
0. 0,080 0.190 0.360
HYPER(3KG + 2HG)0-bboo
0.132 0.058 0.151
0.296 0.152 0.086
0.178
0.295
0.192
00107 0.201
0.384
0.222
0.132 0.209
0.453
ULTRA XLTRA-
0.051 0.019 0.066 0. 104 0.092 0.046
118 0.169
0.086
0.044 0. 0.1 0.167 0.097
0.061 0.1 0.166
000
10707
10.
1.006
1:005
1.00
0.169 0.078 0.164
0.399
0.171 0.103
0,201
0.306
0.194
0.112
0.199 0.375 0.210
0.116
0.206
0.424
HYPERGKGG (HG)(inctuned)
-0003 002 0014
+ 005
+ 001
0002
=
0003
=
+. 008
1000 +:
2002
30

---

Published as a conference paper at ICLR 2026
Table 20: Experiment result on node and relation inductive knowledge hypergraph datasets for WD and MFB.
WD-25
WD-50
WD-75
WD-100
Method
MRR H6 I HOB H@'10 MRR Hidl 1 HOB H@10 MRR H6l 1 HO0 H@00 MRR H6#
H@' H
G-MPNN
0.001 0.000 0.000 0.000 0.001 0,000 0,000 0,000
0.001 0,000 0.000 0.001 0.001 0.000 0.000 0.001
HCNet
0,086 0,050 0,096 0.136 0.043 0.027 0.044 0.060
0.015 0.006 0.023 0.030
0.007 0.004 0.005
0.007
0.215 0.132 0.225 0.394 0.205 0.153 0.219 0.317 0.172 0.105 0.194 0.298 0.205 0.139 0.226 0.342
HYPER(endZend)
#:002 + 0006 m.005 ds,004 15,007 +5.03 d:,006 #:,002 4:0003 4: 000 11,003 4:,007
4:.002 41.008 4:004
#:.00
ULTRA=((G))0-boo)
0.117 0.040 0.132 0.315 0.155 0.087 0.175 0.311 0.116 0.060 0.109 0.263 0.161 0.105 0.165 0.311
ULTRA*(4KCII shot)
0.027 0.013 0.033 0.063 0.069 0,060 0.077 0.093 0.063 0.040 0.069 0.128 0.065 0.040 0.070 0.137
ULTRA (STTRA(50KG)0-oho
0.008 0.007 0.010 0.010 0.001 0.000 0.000 0.000
0.001 0.000 0.000 0.000 0.001 0.000 0.004 0.004
ULTRA (4HO))-shot)
0.076 0.096 0.185 0.348 0,175 0.109 0.191 0.311 0.052 0.084 0,162 0.303 0,136 0,128 0.212 0.344
ULTRA ULTRA (3KG-2HGXO-shhol
0.183 10003300 0.209 0.351 0.182 0.115 0.202
0.328
0.127 0.092 0.161 0,302 0.137 0.130 0.211 0.347
HYpPsa(kK(i(O-ssaat)
0.167 0,010 0.172 0.331 D. 1.558 1.4 0.175 0.295
0.123 0.005 0.142 0.255
D. 0.146 0.077 0.168 0.281
HYPER<4KGi(O-shot)
0.148 0.061 0.167 0.394 0. 0.016 0.203 0.297 0.150 0.047 0.188 0.375 0.255 0.209 0.269 0.373
#YPER(50KGX0ssbot)
0,073 0.046 0.091
0.136 0.055 0.031 0.078
0,109
0,130
0,078 0,141 0,281
0.088 0.015 0.164 0.194
HYPER((I(G/O~ssat))
0.087 0.076 0.093 0.103 0.158 0.142 0.164 0.197
0.057 0.051 0.062 0.064 0.165 0.139 0.177 0.233
HYPER(3KG -hh))))
0.223 0.156 0.225
0.404 0.200
148 0.208
0.317
0.154 0.093 0.168 0.275
0.182
0.133 0.177
0.286
ULTRA (LTRA"(KG-2HGG
0.191 0.108 0.218 0.364
0.121
0.145
0.137
0.349
=.004 + 003 =005 +:00
2200 + 004 +:006
IX0
2:00
+ 002 = 005
000
5:003
0:004
2000 1K07
0.225
146
0.245
0.397
0.234
0.186
0.230
0.355
0.166
001
0.189
0.294
0.210
0.140
0.235
0.351
HYYERR(KKG + (inettu)))))))
#.003 005 =004 4:00
20002
+ 007 4:003
1000
2006
4.00
+0002
+ 2.00
1000
Method
MFB-25
MFB-50
MFB-75
MFB-100
MRR HθI I H0S H@ 10 MRR H@ H@3 H&
MRR HỘI
H@3 10
MRR H
H H@ 10
G-MPNN
0.002 0.000 0.000
0.004 0.001 0.003
0.005
HCNer
0.033 0.008 0.008 0.108 0.026 0.013 0.022
0.041
0.016
0.007
0.009 0.021
0.082
0.028
0.085
0.227
HYPEss(nddeed))
0.332 0,221 0.388 0.533
0.200
1.505 0.251 0.374
0.135 0.070 0.143 0.255 0.222
0.169
0.228
0.317
+.005 4:004 =.003 4.002 #:006
+.007
#5,05 #5,00 4 #.002 4:008
#:001
4:005
4:004
+.003
ULTRA (3KC)0Ol
0.255 0,258 0.408 0.525
0.235 0.148 0.269 0.384
0.154 0.084 0.166 0.274
0.277 0.201 0.315
0.412
ULTRA )
0.217 0.158 0.267 0.308 0.170 0.113 0.206 0.269
0.043 0.025 0.048 0.084 0.135 0.032 0.234
0.271
0.225 0.196 0.254 0.263
0.083
0.074 0.094
0.190 0.156
0.247
ULTRA (HHG))-shot)
0.338 0.225 0.400 0.521
0.236
145 0.282 0.404
0.129
0.081 0.171 0.344
0.280 0. 0.194 0.323 0.435
(LTRA=(KK-22HGX0-h0
0.343 0.233 0.413 0.538
0.236 0.137 0.286 0,408
0.128 0.076 0.183 0,352
0.283 0,200 0.325
0,437
HYPeR()K(j(O-ahat)
0.248 0,7 0.283 0.396
0.191 0.123 0.216 0.296 0.039 0.016 0.029 0.073
0.276 0.198 0.311 0.416
IIYPER(4KGiO0
0.116 0.061 0,134 0.268 0.1 0.060 0.155 0.238
0.089 0.011 0.129 0.204 0.148 0.073 0.171 0.293
HYPeR<50KGG)O-duu
0.122 0.061 0.134
1.156
19 0.155
0. 026
0.148
0.073
0.195 0.256
HYpEk(HHGjOO-hhot)
0.349 0.258 0.400 0.546
0.244 0.169 0.286
0.382
0.139 0.082 0. 0,140
0.244
0.278
0.195 0.316 0.441
HYPER(3KG + 2HG)0-sbbo)
0.363 0.263 0,417 0.550
0.250
0.167 0.287
0.393 0.140 0.077 0.140 0.260
0.299 0.214
0.339
0.449
ULTRA XLTRA-
0.351 0,241 0.425
0.552
0.244 145 0. 0.297 0.401 0.136
0.081
0.182 0. 0.364 0.291 0.209 0.336 0.449
100
1:004
1:005 1:00
HYPERGKGG 2HG)(inctuned)
0.347 0,229 0.408
0.533
0.243
0.163
0. 0.286
0.391 0.158
0.088
0.161
0.302 0.275
0.197
0.290 0.452
2.014 006 0013 002
= 0022
+
+. 000
0012 + 008
+. 0044
31

---

Published as a conference paper at ICLR 2026
Table 21: Experiment result on node-inductive knowledge hypergraph datasets.
JF-IND
WP-IND
MFB-IND
Method
MRR
H@1
H@3
MRR
H@1
H@3
MRR
H@] 1
H@3
HGNN
0.102
0.086
0.128
0.072
0.045
0.112
0.121
0.076
0.114
HyperGCN
0.099
0.088
0.133
0.075
0.049
0.111
0.118
0.074
0.117
G-MPNN
0,219
0.155
0.236
0.177
0.108
0.191
0.124
0.071
0.123
RD-MPNN
0,402
0.308
0.453
0.304
0.238
0.328
0.122
0.082
0.125
HCNet
0.435
0.357
0.495
0.414
0.352
0.451
0.368
0.223
0.417
0.422
0.320
0.483
0.435
0.367
0.471
0.427
0.290
0.499
HYPER(endZend)
2:004
2:006
d 007
1:005
= 000
+ 006
1:00
2:005
0:004
(LTRA
0,321
0.221
0.383
0.305
0.242
0.320
0.277
0.161
0.316
ULTRA' ULTRA"(4KG)(0-- (OKh))))shot)
0.065
0.004
0.079
0.123
0.102
0.114
0.096
0.068
0.112
(5OG)
0.008
0.000
0.002
0.029
0.024
0.027
0.026
0.020
0.031
(LIRA((41I))00-5
0.397
0.274
0.466
0.319
0.330
0.467
0.264
0.141
0.299
ULTRA' ULTRA' (BKG+22G000-)))))))
0,410
0.294
0.489
0.341
0.352
0.480
0.294
0.164
0.325
0.263
0.177
0.281
0.259
0.176
0.307
0.184
0.123
0.196
(YPsR(4KG))O-shot)
0,266
0.182
0.313
0.231
0.168
0.267
0.120
0.073
0.115
HYPER(5OKG)O-shht)
0.302
0.212
0.354
0.253
0.188
0.248
0.248
0.157
0.271
(O0ss(4)))()-hho)
0.403
0.277
0.501
0.375
0.297
0.410
0.497
0.351
0,582
HYPER(3KG + (-Ghoo
0.459
0.365
0.515
0.415
0.338
0.454
0.404
0.267
0.480
0.421
0.302
0.501
0.349
0.361
0.492
0.303
0.171
0.337
U.TRAAF(KG--HHG)yfnetteedd
2.006
2:004
0:7
1:00
= 005
+: 006
1:004
2:002
4:00
0.463
0.373
0.517
0.446
0.379
0,482
0.455
0.318
0.530
HyPER(3KG + 2HG)(inetuned)
2:000
2:003
1:008
1.00
1:005
32

---

Published as a conference paper at ICLR 2026
Table 22: HYPER hyper-parameters for pretraining, fine-tuning, and end-to-end training.
Hyperparameter
HYPER
# Layers
Hidden dimension
64
Positional Interaction Encoder
Dropout
Activation
ReLU
# Layers T Hidden dimension
Relation Encoder
Dropout Activation Norm
0
ReLU
LayerNorm
Layers L
Hidden dimension
64
Dec
2-layer MLP
Entity Encoder
Dropout
Activation
ReLU
Norm
LayerNorm
Optimizer
A
Learning rate
0.0005
Training steps
30,000
Pre-training
Adversarial temperature
# Negatives
512
Batch size
32
Optimizer
Adam W
Learning rate
0.0005
Fine-tuning
Adversarial temperature
# Negatives Batch size
256
Optimizer Learning rate
AdamW W
0.0005
End-to-End
Adversarial temperature
# Negatives Batch size
256
33

---

Published as a conference paper at ICLR 2026
Table 23: Hyperparameters for fine-tuning and training end-to-end for HYPER.
Finetune
End-to-End
Datasets
Epoch
Batch per Epoch
Epoch
Batch per Epoch
JF 25-100
3
full
10
full
WP 25-100
full
full
MFB 25-100
3
full
10
full
WD 25-100
full
10
full
JF-IND
full
20
full
WP-IND
full
20
full
MFB-IND
2000
4
10000
FB 25-100
3
full
10
full
WK 25-100
full
full
NL 0-100
3
full
10
full
MT1-MT4
full
full
Metafam, FBNELL
3
full
10
full
FB v1-v4
full
10
full
WN v1-v4
full
10
full
NL v1-v4
3
full
10
full
ILPC Small
3
full
10
full
ILPC Large
1000
10
1000
HM 1k-5k, Indigo
100
10
1000
34


Reviews:
[{"review_id": "lxiJM2fyag", "reviewer": "Reviewer_kwmy", "summary": "The paper proposes and architecture for inductive link prediction with unseen entities as well as unseen relations over knowledge hypergraphs  via knowledge hypergraph foundational models. The authors show the feasibility of the approach over link prediction task with standard evaluation metrics and propose a set of new datasets.", "questions": "See the weaknesses of the approach.", "limitations": "", "rating": 8, "confidence": 4, "soundness": 3, "presentation": 4, "contribution": 3, "strengths": "- The paper introduces a problem which is very much mainstream in the field of knowledge hypergraphs and address an important gap.\n- The paper is very well written and easy to read.\n- The authors performed thorough experimentation with the comparative results along with the analysis.", "weaknesses": "- the authors could cite another relevant paper which is performing inductive link prediction over knowledge graphs considering features related to the relations [1].\n- The role of encoding positional encoding could be explained with the help of an example to show its importance for the proposed approach. \n- It so far seems like a combination of approaches, the authors should highlight the main theoretical contribution in the paper.\n- Table 3 show the MRR results where HCNET outperforms HYPER. Also in many cases the improvements are only marginal. Can authors shed the light over these kind of results since there can be a possibility that the results of the baselines might improve with extensive hyper-parameter optimization. \n\n\n\n[1] https://dl.acm.org/doi/10.1145/3579051.3579066", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "pDSBK8ILZ1", "reviewer": "Reviewer_kmsQ", "summary": "This paper introduces a foundation model (HYPER) for predicting missing hyperedges in knowledge hypergraphs that contain unseen entities and unseen relation types. HYPER could generalize to arbitrary-arity relations through a relation graph encoder that captures positional interactions between relations. The paper also introduces 16 new inductive benchmark datasets derived from existing knowledge hypergraphs.", "questions": "Refer to the Weakness section.", "limitations": "", "rating": 6, "confidence": 3, "soundness": 2, "presentation": 2, "contribution": 3, "strengths": "1.\tHYPER is a general framework that can transfer learned relational patterns across different relation types and arities. This is the first foundation model that supports zero-shot generalization on knowledge hypergraphs of arbitrary arity.\n2.\t16 new inductive benchmark datasets derived from existing knowledge hypergraphs are constructed for evaluation.\n3. Empirical investigation over the positional interaction encoding scheme", "weaknesses": "1.\tThe positional interaction encoding $\\mathrm{EncPI}((a,b)) = \\mathrm{MLP}([p_a \\| p_b])$ may violate symmetry and lacks proof of equivariance or smooth extrapolation to unseen arities; this weakens the theoretical basis for HYPER’s claimed generalization.\n\n2.\tWhile HYPER demonstrates strong zero-shot generalization across diverse hypergraph benchmarks, how practical is it for large-scale real-world knowledge systems—given that the number of positional interactions grows quadratically with relation arity and may impose significant computational and memory costs during training and inference?", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "XOB7vEReYO", "reviewer": "Reviewer_6icB", "summary": "This paper proposes a foundation model named HYPER for inductive link prediction. By constructing a relation graph G_rel and encoding relation representations on it, HYPER utilizes these learned representations to derive entity representations on the original knowledge hypergraph, enabling zero-shot generalization to knowledge hypergraphs of any arity, including new entities and new relations.", "questions": "During the reification process, the positional information between nodes in a hyperedge is transformed into distinctions on edges of the form hasEntityi(edge id, ui). Does this lead to a loss of positional information?\n\nHYPER's pre-training dataset is too small, potentially leading to overfitting to the relational structures of specific graphs. Could HYPER be trained with a larger pre-training dataset to assess its generalization ability?", "limitations": "", "rating": 4, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "The paper proposes a framework that enables zero-shot generalization to knowledge hypergraphs of arbitrary arity, including novel nodes and relations, at test time.\n\nThe idea of encoding hyperedges using positional interaction is innovative.\n\nThe paper is clearly written with precise definitions, illustrative figures for concepts like relation graphs and reification, and provides code.", "weaknesses": "On L39, \"The generality knowledge hypergraphs\" should be corrected to \"The generality of knowledge hypergraphs\". The expression on L320-321 may also be problematic.\n\nThe pre-trained ULTRA model used for comparison, as described in Table 12, has not been pre-trained on any hypergraph, whereas HYPER(4HG) and HYPER(3KG+2HG) have both been trained on hypergraphs, which may lead to unfairness in the comparative experiment.\n\nThe idea of \"constructing a relation graph $G_{rel}$ to learn relation embeddings and then using relation embeddings to learn entity embeddings\" is similar to ULTRA, with only an extension of positional interaction encoding based on the concept of hyperedges, which may lack sufficient novelty.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "ZAlFEw4xaP", "reviewer": "Reviewer_JyfY", "summary": "Proposes a method for inductive link prediction on knowledge hypergraphs (HKG). The approach closely follows ULTRA (for regular KGs), but modifies the representation of arity information in the relation graph (via an MLP position encoder) and replaces NBFNet (KGs) by HCNet (HGKs). Performs an experimental study on fully-inductive and node-inductive HKG link prediction. I like the paper, but I am not convinced that the experimental study is fair (see W2), and I am thus hesitant to recommend acceptance.", "questions": "See W2.", "limitations": "", "rating": 2, "confidence": 4, "soundness": 3, "presentation": 4, "contribution": 3, "strengths": "S1. Simple, convincing approach\n\nS2. Relevant problem\n\nS3. Experimental results are comprehensive and promising", "weaknesses": "W1. Low novelty. The proposed method is ultimately a rather straightforward modification of ULTRA. I do not count this against the paper too much though, because it is the natural approach and exploring and evaluating this approach provides value.\n\nW2. Comparison to ULTRA not convincing. After reading the abstract of this paper, I immediately thought why not use ULTRA + reification. The authors then actually did this but in a way that is not convincing. To me, a key contribution of this paper is a fair and solid evaluation of the proposed method and alternatives, but I am not convinced that this has been done. This is for the following reasons:\n\n1. The reification approach appears problematic. All relations become nodes, and only max-arity relations of form hasEntity-k(hyperedge, entity) + one hasRelationType relation are used. This severely limits the relation modelling capabilities of ULTRA. Instead, the natural reification is to relation-k(hyperedge, entity) and drop the hasRelationType relation. I feel that this approach needs to be explored, as it is what first comes to mind and as it appears much more promising.\n\n2. ULTRA has not been retrained on the reified data (whereas the proposed method is). Since ULTRA has never seen reified relations, I'd not expect it to work well. A fair comparison would do the reification above and then train ULTRA on the same graphs (both KGs and HGs) as the proposed method. Only then I'd consider the study insightful and convincing.\n\nW3. Comparison to HCNet not convincing. The authors seem to use random relation embeddings, as HCNet does not support new relations. I fail to see the value of this experiment; it clearly cannot lead to useful results. The experiment should either be dropped (ok with me) or perhaps (i) transductive results added and (ii) for the inductive setting, fold-in the new relations into HCNet.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)