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Scalable GNN-based Knowledge Graph Representation Learning with Efficient Message Passing
Huu Tan Mai, Cuong Xuan Chu, Heiko Paulheim, Daria Stepanova
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Abstract
Abstract:Graph neural networks (GNNs) excel at representation learning on Knowledge Graphs (KGs), achieving stateof-the-art performance on tasks like link prediction or entity classification. However, their high computational complexity, inherent to their user-defined message passing (MP) algorithm, still prohibits their widespread adoption, especially for large KGs. Current efforts to mitigate the scalability bottlenecks of GNNs on KGs, such as subgraph sampling, are often task- and model-specific, and do not reliably guarantee lossless (if applicable) runtime/space reductions. To address this, we extend Relational Sparse Matrix Multiplication (RSPMM), originally designed to losslessly lower the space complexity of composition-based MP with pointwise composition functions, to support more expressive functions (e.g., 2x2 block-diagonal matrix multiplication, Givens rotation, circular correlation). Our method delivers significant task-independent reductions in runtime and space for current GNNs on KGs and facilitates efficient re-implementations of GNNs that maintain near state-of-the-art performance on challenging KG tasks, for a fraction of computational costs.
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1 *1 *1 Scalable GNN-based Knowledge Graph Representation Learning with Efficient Message Passing Huu Tan Mai Cuong Xuan Chu Heiko Paulheim Daria Stepanova Abstract Graph neural networks (GNNs) excel at representation learning on Knowledge Graphs (KGs), achieving state-of-the-art performance on tasks like link prediction or entity classification. However, their high computational complexity, inherent to their user-defined message passing (MP) algorithm, still prohibits their widespread adoption, especially for large KGs. Current efforts to mitigate the scalability bottlenecks of GNNs on KGs, such as subgraph sampling, are often task- and model-specific, and do not reliably guarantee lossless (if applicable) runtime/space reductions. To address this, we extend Relational Sparse Matrix Multiplication (RSPMM), originally designed to losslessly lower the space complexity of composition-based MP with pointwise composition functions, to support more expressive functions (e.g., 2×22× 2 block-diagonal matrix multiplication, Givens rotation, circular correlation). Our method delivers significant task-independent reductions in runtime and space for current GNNs on KGs and facilitates efficient re-implementations of GNNs that maintain near state-of-the-art performance on challenging KG tasks, for a fraction of computational costs. keywords Knowledge Graph ,Representation Learning ,Graph Neural Network ,Message Passing ,Scalability †copyrightyear: 2026†copyright: Copyright for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (C BY 4.0).†venue: ISWC 2026 Companion Volume, October 25–29, 2026, Bari, Italy†copyrightyear: 2022†copyright: Copyright for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (C BY 4.0).†venue: ISWC’26: Posters and Demos Track, October 25–29, 2026, Bari, Italy†titlenote: This poster is accompanying our conference paper Mai et al. (2026).†email: huutan.mai@de.bosch.com†email: cuongxuan.chu@de.bosch.com†email: heiko.paulheim@uni-mannheim.de†email: daria.stepanova@de.bosch.com†address: Bosch Center for Artificial Intelligence, Robert-Bosch-Campus 1, 71272 Renningen, Germany†address: University of Mannheim, Schloss, 68131 Mannheim, Germany†corresp: Corresponding author. 1 Introduction Knowledge Graphs (KGs) (e.g., YAGO Mahdisoltani et al. (2015), Wikidata Vrandečić and Krötzsch (2014)) represent domain knowledge as multi-relational directed graphs of facts, encoded as labeled edges between entities. Graph representation learning Lerer et al. (2019); Hamilton et al. (2018); Nickel et al. (2016) has emerged as a powerful paradigm that enables machine learning on KGs for tasks such as KG completion (KGC) Bordes et al. (2013); Yang et al. (2015); Trouillon et al. (2016); Zhu et al. (2022), entity classification de Vries and de Rooij (2015); Ristoski and Paulheim (2016); Schlichtkrull et al. (2017) or alignment Ge et al. (2021); Zhu et al. (2017). Two major examples of representation learning approaches are shallow KG embeddings (KGE) Bordes et al. (2013); Yang et al. (2015); Trouillon et al. (2016); Sun et al. (2019); Nickel et al. (2015); Dettmers et al. (2018), and Graph Neural Networks (GNN) Schlichtkrull et al. (2017); Vashishth et al. (2020); Tan et al. (2023); Liu et al. (2021); Zhu et al. (2022). Shallow KGEs directly embed entities and relations into a low-dimensional vector space and are the de facto method for web-scale graphs Wang et al. (2020) thanks to their simple design and dedicated software Zhu et al. (2019); Zheng et al. (2020), but they are limited in terms of accuracy. In contrast, GNNs yield higher predictive accuracy by using message passing (MP) to learn expressive node and relation representations from neighborhoods, but they are computationally expensive. Notations. Given a KG =(ℰ,ℛ,)G=(E,R,T), A=(αjri)∈ℝ|ℰ|×|ℛ|×|ℰ|A= ( _jri ) × × is an adjacency tensor of G when it verifies (j,r,i)∉⟹αjri=0(j,r,i) _jri=0 (non-existent edges have zero weight). Furthermore, we define in(i)=(j,r)∈ℰ×ℛ:(j,r,i)∈. _in(i)= \(j,r) ×R:(j,r,i) \. Problem. For a KG =(ℰ,ℛ,)G=(E,R,T) with entities ℰE, relations ℛR and triples T, and an adjacency tensor A=(αjri)∈ℝ|ℰ|×|ℛ|×|ℰ|A=( _jri) × × , we consider the main building block of the popular composition-based MP method (e.g., Vashishth et al. (2020); Liu et al. (2021); Tan et al. (2023); Zhu et al. (2022); Liang et al. (2023); Chen et al. (2021); Zhang et al. (2023)). The node update equation is typically defined as follows: i′=UPD(i,i),i=⨁(j,r)∈in(i)jri,jri=αjriϕ(j,r), _i=UPD (H_i,M_i ), _i= _(j,r) _in(i)m_jri, _jri= _jriφ (H_j,Z_r ),\ (1) where H is the matrix of input entity representations, Z is the matrix of input relation representations and ′H is the matrix of output entity representations, ⨁ is a permutation invariant aggregation and UPDUPD is an update operation. Traditionally, computing ′H from H and Z requires a gather-scatter methodology (e.g., codebases of Vashishth et al. (2020); Liu et al. (2021); Zhang et al. (2023)): (1) gather H and Z rows, then compute jrim_jri for each edge, and (2) aggregate using a scatter function (e.g., scatter_add in PyG Fey and Lenssen (2019)). If jri∈ℝdm_jri ^d, then the step (2) generates a tensor of size (||d)O( d) in memory (see Figure 1 for illustration). Unless specific simplifications or high-performance CUDA kernels are available, complex MP designs employ this abstraction, and the induced memory footprint is a major hurdle for scalable GNN-based graph learning. Figure 1: Example of traditional implementations of composition-based MP (left), against efficient RSPMMϕRSPMM_φ implementations (right). The latter aim to fuse all operations in lower space complexity, as in practice, |ℰ|≪|| . State-of-the-Art and its Limitations. While vocabulary reduction Galkin et al. (2022); Liang et al. (2024); Zhu et al. (2022); Zhu et al. (2023) and subgraph sampling Zhang et al. (2023); Zhu et al. (2023); Feeney et al. (2021); Li et al. (2023) have been explored to improve the parameter efficiency and scalability of relation-aware GNNs, they do not address the very costly MP methods. RSPMMϕ,ϕ∈+,⊙RSPMM_φ,φ∈\+, \ (Relational Sparse Matrix Multiplication) was introduced Zhu et al. (2022) to compute M in (|ℰ|d)O( d) space complexity, as a fused MP CUDA kernel that modifies GE-SpMM Huang et al. (2020). Since |ℰ|≪|| holds in practice, this improvement is beneficial for the scalability of GNNs using RSPMM+/⊙RSPMM_+/ . However, this option is not trivially available for GNNs with expressive messages (e.g., dense linear transformation, rotation, etc.). Contributions. To address the above scalability and genericity challenges, inspired by NBFNet Zhu et al. (2022), we introduce novel and generic scalability optimizations of relational MP methods by generalizing the aforementioned RSPMM to be applicable to other works. Many existing GNN methods Vashishth et al. (2020); Liu et al. (2021); Tan et al. (2023); Liang et al. (2023); Zhu et al. (2022); Zhu et al. (2023); Zhang et al. (2023); Schlichtkrull et al. (2017); Nathani et al. (2019) for KGs are composition-based Vashishth et al. (2020) (i.e., messages are obtained with a binary operator using the message source embeddings and the relation type), thus directly benefit from this generic optimization. We extend RSPMM to support more complex composition operators, e.g., 2×22× 2 block-diagonal matrix multiplication, Givens rotation and circular correlation. We extend the experiments of Mai et al. (2026) with comparisons against language model methods Wang et al. (2022); Li et al. (2024) for KG representation learning. 2 Approach We assume d∈ℕd to be an even integer. We refer the reader to Mai et al. (2026) for the definitions of ∥ \|, ++,⊙ ,⊙ℂ _C , ⊠ , BlockDiagBlockDiag, RotRot, RefRef and other notations. We focus on the sum aggregation (⊕=+ =+), which is highly popular in the GNN literature, and has desirable properties w.r.t. linearity and distributivity. RSPMM. Let ϕ:ℝd1×ℝd2→ℝd3φ:R^d_1×R^d_2 ^d_3, and let ⟨⋅|⋅|⋅⟩ϕ · |· |· _φ (or RSPMMϕRSPMM_φ) be defined as follows. For any adjacency tensor A∈ℝ|ℰ|×|ℛ|×|ℰ|A × × of G, ∈ℝ|ℰ|×dH × d and ∈ℝ|ℛ|×mZ × m, ∀i∈ℰ,(⟨A||⟩ϕ)i=∑(j,r)∈in(i)Ajriϕ(j,r).∀ i , ( A |H |Z _φ )_i= _(j,r) _in(i)A_jriφ (H_j,Z_r ). (2) Table 1: Extension of RSPMM in (|ℰ|d)O( d) space complexity for operators inspired by shallow KGEs. Definition of ϕ(,)φ(h,z) Remarks +h+z (Addition) Inspired by TransE Bordes et al. (2013), implemented by standard RSPMM Zhu et al. (2022) ⊙h (Multiplication) Inspired by DistMult Yang et al. (2015), implemented by standard RSPMM Zhu et al. (2022) ⊙ℂh _Cz (Complex multiplication) Inspired by ComplEx Trouillon et al. (2016) ⋆h (Circular correlation) Inspired by HolE Nickel et al. (2015) ⋅Rot()h·Rot(z) (Givens rotation) Inspired by RotatE Sun et al. (2019). Givens reflection can also be implemented. ⊠=⋅BlockDiag()h =h·BlockDiag(z) (see Mai et al. (2026)) Inspired by RESCAL Nickel et al. (2011), with 2×22× 2 block-diagonal linear transformations ϕ(,[1∥2])=ϕ0(,1)+2φ (h, bmatrixz_1 \|z_2 bmatrix )= _0 (h,z_1 )+z_2 Assumes d≥|ℛ|d≥ and RSPMMϕ0RSPMM_ _0 can be implemented in (|ℰ|d)O( d) space complexity We propose implementations to compute RSPMMϕ(A,,)RSPMM_φ(A,H,Z) in (|ℰ|d)O( d) space complexity, similarly to Zhu et al. (2022), for a wider variety of operators ϕφ shown in Table 1. See our code (https://github.com/boschresearch/relational-message-passing) and examples below. 2×22× 2 Block-diagonal matrix multiplication. With =[∥]∈ℝ|ℰ|×2dH=[X \|Y] × 2d and =[∥]∈ℝ|ℛ|×4dZ=[P \|S \|Q \|R] × 4d, it can be proven that ⟨A||⟩⊠=⟨A||[∥]⟩⊙+⟨A|[∥]|[∥]⟩⊙ A |H |Z _ = A |H |[P \|S] _ + A |[Y \|X] |[Q \|R] _ . This provides a direct implementation of RSPMM⊠RSPMM_ using two calls of RSPMM⊙RSPMM_ , whose space complexity is (|ℰ|d)O( d). RSPMMϕRSPMM_φ for complex pointwise multiplication and Givens rotation/reflection can be viewed as applications of RSPMM⊠RSPMM_ for a well-designed Z (constructed from the original relation embeddings). RSPMM⋆RSPMM_ can be computed with RSPMM⊙ℂRSPMM_ _C by exploiting the convolution theorem Oppenheim (1999). Additive Bias. Assume that RSPMMϕ0RSPMM_ _0 is computable in (|ℰ|d)O( d) for some operator ϕ0 _0. We split Z into (1)Z^(1) and (2)Z^(2) vertically, s.t. ⟨A||(1)⟩ϕ0 A |H |Z^(1) _ _0 can be computed. We then compute the matrix B, defined as Bir=∑j=1|ℰ|AjriB_ir= _j=1 A_jri of size |ℰ||ℛ|≤|ℰ|d ≤ d when d≥|ℛ|d≥ . Then, it holds: ⟨A||⟩ϕ=⟨A||(1)⟩ϕ0+B(2). A |H |Z _φ= A |H |Z^(1) _ _0+BZ^(2). Generalization. In theory, it is possible to propose memory-efficient implementations for GRSPMMϕ,⊕:(A,,)↦⨁(j,r)∈in(i)αjriϕ(j,r)GRSPMM_φ, :(A,H,Z) _(j,r) _in(i) _jriφ(H_j,Z_r) (3) for ⊕∈+,min,max ∈\+, , \ and ϕφ in Table 1, which is more general. However, in case ⊕∈min,max ∈\ , \, new dedicated CUDA kernels would be needed, and these are out of scope for this work. Theoretical Motivations. Given entity embeddings H and relation embeddings Z, Eq. 2 can be viewed as computing the new representation (⟨A||⟩ϕ)i ( A |H |Z _φ )_i of i∈ℰi as a weighted sum of predictions of the embedding of i, relatively to the embeddings of its neighbors j of relation r, given by ϕ(j,r)φ(H_j,Z_r), so in a trained, vanilla composition-based GNN each layer already encodes the graph’s structural information. These predictions are tied to ϕφ, which can be inspired from KGEs by design Vashishth et al. (2020). However, in terms of relational patterns, different KG embeddings may better express different relational patterns Pavlović and Sallinger (2023). For instance, TransE Bordes et al. (2013) can easily model relational inverses (e.g., (h,r1,t)∈(h,r_1,t) if and only if (t,r2,h)∈(t,r_2,h) , by using r2=−r1z_r_2=-z_r_1) and relational compositions ((h,r1,t1),(t1,r2,t)∈⇔(h,r,t)∈(h,r_1,t_1),(t_1,r_2,t) (h,r,t) , with r=r1+r2z_r=z_r_1+z_r_2), but cannot model symmetric relations ((h,r,t)∈⇔(t,r,h)∈(h,r,t) (t,r,h) ) well, whereas RotatE Sun et al. (2019) can model all of the above. Therefore, the choice of ϕφ is semantically meaningful for composition-based GNNs for KGs, and the ability to represent desirable patterns may lead to performance improvements. Our contribution bridges the gap between theoretical relational expressiveness and practical scalability challenges, by extending the catalogue of affordable ϕφ functions. 3 Experiments Setup. We consider the following popular KG tasks: entity classification and KGC. We conduct multiple experiments to confirm the effectiveness and usefulness of our method: (a) re-implement the MP method of existing GNNs that directly benefit of our RSPMM extension (e.g., Schlichtkrull et al. (2017); Vashishth et al. (2020); Chen et al. (2021)), and compare the computational costs, (b) create lightweight prototypical models inspired by existing, well-established architectures and compare them against SOTA methods, (c) compare GNN methods against other popular language model (LM) embedding-based methods (e.g., Wang et al. (2022); Li et al. (2024)). We refer the reader to Mai et al. (2026) for further details (e.g., training, evaluation, model categories and our code11 1 https://github.com/boschresearch/scalable-gnn-lp) for (a) and (b). Dataset statistics are shown in Table 2. Experiments are run with a NVIDIA A100 GPU, and an AMD Epyc 7543 @ 2.80 GHz CPU. We cut off experiments that take over 24 hours. In case of cutoff (OOT), the best previous checkpoint (over the validation set) is loaded to evaluate the model. Table 2: KG statistics. MCNC, resp. MLNC, stands for multiclass, resp. multilabel, node classification. Dataset Task |ℰ| |ℛ| || Train Valid Test WN18R Dettmers et al. (2018) KGC 40,943 11 86,835 86,835 3,034 3,134 FB15k-237 Toutanova and Chen (2015) KGC 14,541 237 272,115 272,115 17,535 20,466 AM Ristoski et al. (2016) MCNC 1,666,764 265 5,988,321 802 - 198 AM+ Bloem et al. (2021) MCNC 1,153,679 33 2,521,046 13,423 20,000 20,000 dblp Bloem et al. (2021) MCNC 4,470,778 68 21,985,048 26,535 20,000 20,000 Prototypical Models. We propose two prototypical models inspired by earlier works that benefit from an extended RSPMM: (1) MODEL-A, which modifies CompGCN Vashishth et al. (2020) as follows: (1a) the relation updates are carried out by a MLP instead of a linear layer, (1b) Entity and relation transformations are carried out before MP; (2) MODEL-B, which modifies AdaProp Zhang et al. (2023) primarily by (2a) using query-dependent initializations, and (2b) using a shared entity scorer for all layers. As KGs with textual descriptions are common, we extended experiments from Mai et al. (2026) with text, to show that GNNs with frozen LMs scale better than LM-only methods in these scenarios. We create initial entity features by embedding their descriptions with a frozen LM (all-mpnet-base-v2 Reimers and Gurevych (2019); Song et al. (2020)), and feed them to our (R-MPNN) GNNs. Results. Experiments with existing models (Figure 2, where CompGCN and R-GAT use ϕ=⋆φ= ) show that our RSPMM extension results in substantial scalability improvements without sacrificing performance (as the model remains theoretically equivalent), independently of model or task, up to ×10.7× 10.7 reductions in memory footprint and ×32.2× 32.2 reductions in runtime. This also holds for web-scale datasets (dblp Bloem et al. (2021) with 4.5M entities, 22M edges) where R-GCN uses up to 33.8 GiB during a full hyperparameter search (final accuracy: 0.72), while running out of memory without RSPMM. On KGC, Table 3 shows that not only our implementations are substantially resource-friendlier than their counterparts within their respective category, they also perform very competitively. Furthermore, against LM-based methods, R-MPNNs with RSPMM with initial entity features perform comparably or better than methods involving the training of the LM, for substantially less memory and runtime. Figure 2: Runtimes and memory footprints during training for various GNN models. The top figures are results on FB15k-237 Toutanova and Chen (2015), and the bottom figures are results on AM Ristoski et al. (2016). Legends apply to their respective rows. Stress Tests. We also carry out a fully fledged optimization pipeline with 10 trials of hyperparameter search on extremely large testbeds (AM+ and dblp), using R-GCN. We allow up to 72h of runtime. We use up to 4 layers and a hidden dimension up to 64. On AM+, the largest memory footprint occupied with our RSPMM-based implementation is 12.6 GiB over 11 hours (including data preprocessing), versus 21.5 GiB over 14 hours without RSPMM (both having .92 final accuracy, which bests the reported performance in the paper). On DBLP, our implementation achieves a final accuracy of .72 with a maximal footprint of 33.8 GiB over 3 days, while the base R-GCN runs out of memory. Table 3: Runtimes GPU memory footprints and performance metrics of KGC models on WN18R and on FB15k-237. Overall best results are in bold, whereas other notable results (e.g. top results per category) are underlined. Category Method WN18RRDettmers et al. (2018) FB15k-237 Toutanova and Chen (2015) Param. Train T. Train mem. MRR H@10 Param. Train T. Train mem. MRR H@10 KGE ComplEx-N3 Lacroix et al. (2018) 40.975M 19 m 0.80 GiB .469 .541 15.01M 31 m 0.30 GiB .362 .554 RotH Chami et al. (2020) 20.50M 65 m 6.77 GiB .491 .579 7.98M 312 m 6.47 GiB .306 .490 R-MPNN R-GCN (DGL) Schlichtkrull et al. (2017) 10.66M 21 m 2.46 GiB .389 .429 4.88M 21 m 2.32 GiB .263 .457 CompGCN Vashishth et al. (2020) 12.07M 152 m 0.85 GiB .467 .531 9.45M 110 m 1.67 GiB .349 .529 RAGAT Liu et al. (2021) 68.24M 1105 m 3.07 GiB .489 .564 17.77M 425 m 5.45 GiB .364 .548 R-GCN (our impl.) 10.93M 5 m 1.49 GiB .486 .596 4.89M 30 m 0.55 GiB .337 .518 r-GAT (our impl.) 13.02M 16 m 2.50 GiB .526 .644 7.19M 121 m 4.03 GiB .365 .554 MODEL-A (ours) 12.46M 5 m 1.31 GiB .531 .638 5.94M 32 m 1.27 GiB .365 .555 C-MPNN NBFNet Zhu et al. (2022) 90K 521 m 26.12 GiB .548 .657 3.10M 1193 m 18.99 GiB .416 .598 A*Net Zhu et al. (2023) 90K 361 m 3.03 GiB .539 .644 3.10M OOT 13.79 GiB .413 .586 AdaProp Zhang et al. (2023) 78K 434 m 8.95 GiB .555 .655 195K OOT 14.94 GiB .286 .427 MODEL-B (ours) 132K 448 m 1.99 GiB .569 .666 7.07M 446 m 2.79 GiB .417 .596 LM SimKGC Wang et al. (2022) 218M 97 m 61.08 GiB .673 .805 218M 86 m 61.09 GiB .337 .512 KERMIT Li et al. (2024) Out of Memory (¿ 79.27 GiB) Out of Memory (¿ 79.27 GiB) R-GCN (our impl.) + Frozen LM 713K 11 m 1.62 GiB .586 .808 1.87M 78 m 1.38 GiB .353 .541 MODEL-A + Frozen LM 2.24M 17 m 1.52 GiB .660 .818 2.47M 51 m 1.34 GiB .367 .554 4 Conclusion We introduce an extension of RSPMM for diverse composition operators, readily applicable to many existing GNNs for KGs. Extensive experiments show that not only do relational GNNs benefit from significant lossless scalability gains by switching implementations, these improvements also allow one to afford better architectures with the same computational budget, independently of task or model, that can rival SOTA methods for substantially fewer resources. We view RSPMM as a useful tool for KG Machine Learning practitioners to speed up iteration cycles and tackle larger scale problems. Declaration on Generative AI The author(s) have not employed any Generative AI tools. References Bloem et al. (2021) P. Bloem, X. 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