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REVIEW 5 major objections 6 minor 43 references

QuatE-D: A Distance-Based Quaternion Model for Knowledge Graph Embedding

T0 review · 5 major / 6 minor · reviewed 2026-08-16 · deepseek-v4-flash

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Pith's one-line read QuatE-D replaces the inner-product scoring of quaternion knowledge-graph embeddings with Euclidean distance, and reports lower Mean Rank on four link-prediction benchmarks.

desk verdict QuatE-D is a clear, small idea that reduces to RotatE in the complex plane, but its headline MR numbers come from an undefined 'type constraints' variant, and its loss equation is not the margin ranking loss the text describes. read the letter →

arxiv 2504.13983 v1 pith:7LJYVQZC submitted 2025-04-18 cs.LG

Hamideh-Sadat Fazael-Ardakani , Hamid Soltanian-Zadeh This is my paper · ORCID
classification cs.LG
keywords knowledgegraphembeddingquaternionembeddingsdistance-basedscoringHamiltonproductlinkpredictionmeanrankWN18RRFB15k-237
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

QuatE-D is a quaternion knowledge-graph embedding model whose scoring function measures Euclidean distance between the relation-rotated head embedding and the tail embedding, $\phi(h,r,t)=\|Q_h \otimes W_r^\triangleleft - Q_t\|_2$, instead of the inner-product score used by QuatE. The paper argues that this distance-based score is more geometrically interpretable and flexible, and that it captures symmetry, antisymmetry, inversion, and composition through quaternion algebra. On the WN18, FB15k, WN18RR, and FB15k-237 benchmarks, the model reports competitive or best results, with its most consistent gains in Mean Rank. The central message is that the choice of scoring geometry, not just the embedding algebra, is a first-order factor in link prediction.

What carries the argument

The load-bearing object is the normalized relation quaternion $W_r^\triangleleft$ together with the Hamilton product $Q_h \otimes W_r^\triangleleft$ followed by Euclidean distance $\|Q_h \otimes W_r^\triangleleft - Q_t\|_2$. Normalization forces $\|W_r^\triangleleft\|=1$, which makes Hamilton multiplication norm-preserving; associativity yields composition, non-commutativity gives directionality, and zero imaginary parts give symmetry. The same machinery reduces to RotatE when the quaternions are restricted to the complex plane, making RotatE a special case of QuatE-D.

What would settle it

An independent reimplementation that defines the type constraints and applies them identically to all baselines should reproduce MR 160 on WN18 and 71 on FB15k-237; if the constraints are only applied during ranking of candidate tails, the gap between QuatE-D1 and QuatE-D2 would expose them as evaluation-time filtering rather than learned geometry.

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Extended reading notes

Core claim

The central claim is that replacing the Hermitian inner product of the quaternion model QuatE with the Euclidean distance between a Hamilton-rotated head and the tail gives a more general and more accurate scoring rule. The paper defines $Q'_h = Q_h \otimes W_r^\triangleleft$ with $W_r^\triangleleft = W_r / |W_r|$, scores a triple as $\|Q'_h - Q_t\|_2$, and trains with a margin ranking loss plus $\ell^2$ regularization. Under the restriction to complex quaternions the score reduces exactly to RotatE's $\|h \circ r - t\|$, so QuatE-D is presented as the quaternion generalization of rotation-based distance scoring. The reported tables show QuatE-D2, the variant with type constraints, achieving the lowest Mean Rank on all four datasets (160 on WN18, 21 on FB15k, 1050 on WN18RR, 71 on FB15k-237) and the best or tied-best MRR and Hits on WN18RR and FB15k-237. The type-constraint mechanism itself is not defined in the paper.

Load-bearing premise

The best reported results depend on a 'type constraints' variant that is never defined, so the distance-based scoring function may not be what produces the headline Mean Rank gains.

Editorial extensions

If this is right

  • On WN18, QuatE-D2 reports Mean Rank 160, below RotatE's 184 and QuatE's 388, with Hit@3 0.956 and Hit@10 0.960.
  • On FB15k-237, QuatE-D2 reports the best compared MR (71), MRR (0.443), Hit@1 (0.344), Hit@3 (0.487), and Hit@10 (0.638).
  • Because the score reduces to RotatE's when quaternions are confined to the complex plane, QuatE-D is a strict generalization of rotation-based distance scoring rather than a separate family.
  • The theoretical section argues that non-zero imaginary parts in $W_r$ give antisymmetric scores, conjugate relations give inverse scores, and associativity gives composition, so the distance geometry is claimed to support the four classic relational patterns.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The unnamed 'type constraints' behind QuatE-D2's headline numbers may be doing some of the work; a re-run with the constraints removed or fully specified would tell whether the distance scorer alone delivers the gains.
  • The same substitution of inner product with Euclidean distance could be applied inside other quaternion and dual-quaternion models, and the paper's own future-work section suggests this; the transfer is plausible because the score only changes how the rotated head is compared to the tail.
  • Because the model reduces to RotatE, a controlled dimension-for-dimension comparison against RotatE with identical negative sampling would isolate the benefit of the fourth quaternion component; the current tables do not report such a match.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

5 major / 6 minor

Summary. The paper proposes QuatE-D, a knowledge graph embedding model that represents entities and relations as quaternions and scores triples by the Euclidean distance between the Hamilton-rotated head and the tail: phi(h,r,t) = ||Q_h (x) W_r^norm - Q_t||_2 (Eq. 20). Training uses a claimed margin ranking loss with L2 regularization (Eqs. 21-22). The authors argue that quaternion non-commutativity gives antisymmetry and composition, and that inversion is handled by quaternion conjugation, with RotatE as a special case. On WN18, FB15k, WN18RR, and FB15k-237, they report filtered link prediction results for 'QuatE-D1' (without type constraints) and 'QuatE-D2' (with type constraints), claiming state-of-the-art or competitive performance, especially in Mean Rank.

Significance. The proposed scoring function is simple and interpretable, and the paper follows standard evaluation protocols on widely used benchmarks, reporting filtered results and hyperparameter searches. If the method as defined by Eq. (20) genuinely delivered the reported gains, a distance-based quaternion model would be a useful baseline. However, the central claim depends on the undefined 'type constraints' variant (D2), and the theoretical support is weakened by algebraic errors in the norm computations and by a loss function that does not implement the described margin ranking. These issues prevent the paper from supporting its conclusions as written.

major comments (5)
  1. [Tables IV and V; Section VI-E] The headline results for the central claim--'particularly excelling in Mean Rank'--are the QuatE-D2 rows of Tables IV and V, which are labeled only '[with type constraints]' in the table footnotes. The main text never defines these type constraints: they do not appear in the model description (Section IV), the loss (Eq. 22), or the evaluation protocol (Section VI-B). The D1-to-D2 deltas (e.g., WN18RR MR 4206 to 1050; FB15k-237 MR 131 to 71 while MRR changes only from 0.425 to 0.443) are consistent with an evaluation-time filter on candidate entities, rather than a learned model property. Because it is unknown whether the constraints use test-time information, the reported MR gains do not measure the distance-based scoring function of Eq. (20). For the defined model QuatE-D1, the MR results are not competitive (e.g., WN18RR 4206 vs. RotatE 3277; FB15k 45 vs. RotatE 40), so the paper's central empirical claim is not interpretable from the evidence provided.
  2. [Section IV, Eq. (21)-(22)] The loss in Eq. (21) does not implement the margin ranking objective described in the text. With Y=1 for positives, the positive-triple term is max(0, gamma + phi(h,r,t)), which pushes the distance toward zero; with Y=-1, the negative term is max(0, gamma - phi(h',r,t')), which pushes the negative distance above gamma. There is no pairwise term comparing phi_pos and phi_neg, so the claimed property phi_pos + gamma <= phi_neg is not enforced. In addition, the summation indices in Eq. (22) over '(h,r,t) union (h',r,t')' do not specify how positive and negative samples are paired. Since this loss defines the model whose results are reported, the method as stated is not reproducible.
  3. [Section V-B, Eqs. (27)-(28) and (33)-(38)] The proofs of antisymmetry and inversion rely on the identity |A (x) B| = |A| |B| applied to quaternion vectors, writing for instance ||Q'_h||^2 = ||Q_h||^2 ||W^norm_r||^2. For a vector of k quaternions, the squared Euclidean norm of the component-wise Hamilton product is sum_i |q_i w_i|^2, which is not equal to (sum_i |q_i|^2)(sum_i |w_i|^2) in general. The identity holds for a single quaternion, not for the vector norm used in Eq. (20). This invalidates the norm expansions in Eqs. (27), (28), (33), (34), and (38), on which the claimed theoretical properties rest.
  4. [Section V-B2, Inversion] The inversion proof does not actually involve an inverse relation. Equation (32) equates distances computed with the same relation embedding W^norm_r on both sides; it asserts ||Q_h (x) W^norm_r - Q_t||_2 = ||Q_t (x) W^norm_r - Q_h||_2, which is just the symmetry of the Euclidean norm for the two points Q_h (x) W^norm_r and Q_t. To prove inversion one would need to relate the embeddings of r1 and r2 (e.g., W_{r2} as the conjugate of W_{r1}) and show that the distance equality follows from that relation; the manuscript never introduces W_{r1} and W_{r2}. Consequently, the inversion property is unsupported.
  5. [Section V-B1, Antisymmetry] The antisymmetry proof claims that Eq. (26) holds whenever the imaginary parts of W are nonzero, but the argument is incomplete: the expansion (29)-(31) only asserts that the two inner products are different because quaternion multiplication is non-commutative. Even if the inner products differ, it does not follow that the corresponding squared distances differ, since the quadratic terms may compensate. Moreover, the intended conclusion--that the scoring function can distinguish r(x,y) from r(y,x)--requires the inequality to hold for the distance in Eq. (20), not merely for generic quaternion non-commutativity. No counterexample or universal argument is supplied, so the property is not established.
minor comments (6)
  1. [Section III, Eq. (13)] The norm is defined as ||q|| = q q* = q0^2 + q1^2 + q2^2 + q3^2; this is the squared norm, not the norm. The correct expression is ||q|| = sqrt(qq*) = sqrt(q0^2 + q1^2 + q2^2 + q3^2).
  2. [Section VI-D, Table III] The text says 'provided in Table 6' but the table is numbered Table III.
  3. [Figure 1] The figure is titled 'Impact of Embedding Dimension on Triple Classification Performance,' yet no triple classification task or protocol is described in Section VI; the figure appears to be based on link prediction or a different evaluation.
  4. [Section VI-E] The sentence 'DistMult exhibits higher negative sampling rates, which may affect its overall ranking performance' is unclear; negative sampling rates are not reported for baselines.
  5. [Section V-B3, Eq. (39)] The relation indices in Eq. (39) appear inconsistent: the statement r1 = r2 (compose) r3 with the preceding conditions z = r1(y), y = r3(x), x = r2(y) would imply different composition order; please check the notation.
  6. [Throughout] There are recurring typos in model names (e.g., 'DuatE' for DualE) and inconsistent use of 'QuatE-D1/QuatE-D2' and 'Quat-D 2' in Table VI; these should be harmonized.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity found: QuatE-D's scoring function is trained on graph triples and its theoretical properties are algebraic consequences, not restatements of the benchmark targets.

full rationale

The paper's central scoring function, Eq. (20), is a model definition, and the parameters are trained with the loss in Eq. (22) on training triples, with hyperparameters selected by validation. No benchmark metric (MR, MRR, Hits@K) is used as a fitting target, so the reported results are not forced by construction. Section V's symmetry, antisymmetry, inversion, and composition claims follow from quaternion algebra and the unit-norm relation embedding in Eq. (18), and they do not import the target results as premises. The reduction to RotatE in Eqs. (41)-(42) is an explicitly stated special case, not a renamed prediction. The paper contains no load-bearing self-citations: the cited prior work consists of external baselines (RotatE, QuatE, ComplEx, etc.) and a standard quaternion initialization scheme. The only substantive concern is that the QuatE-D2 rows in Tables IV and V are labeled 'with type constraints' without defining those constraints, which undermines interpretability of the headline Mean Rank gains; however, without a specification of what the constraints do, one cannot exhibit a reduction of the results to the constraints, so this is a correctness and reproducibility risk rather than demonstrable circularity.

Assumptions & free parameters 6 free parameters · 6 assumptions · 0 invented entities

The model adds no new physical or mathematical entities. The contribution is a scoring function and a normalization choice. The main unaccounted premises are evaluation details: the type-constrained variant and the benchmark numbers themselves.

free parameters (6)
  • Embedding dimension k = chosen from {50,100,150,200,300,400}; final per dataset not reported
    Grid-selected per dataset, but the paper does not state which value was used for each benchmark.
  • Margin gamma = 1 (fixed)
    Margin for the ranking loss; fixed for all experiments.
  • Regularization coefficients lambda_1, lambda_2 = grid {0, 0.05, 1}; final values not reported
    L2 penalties on entity and relation embeddings; final choices are omitted.
  • Negative sampling rate #neg = grid {1,5,10}; final values not reported
    Number of negative samples per positive triple; the chosen value per dataset is not given.
  • Learning rate alpha = 0.02 (Adagrad)
    Fixed optimizer step size used throughout.
  • Epoch count = Table III reports epochs, e.g., 3000 to 30000
    Early stopping determines the actual number, but the stopping criterion is not specified precisely.
assumptions (6)
  • standard math Quaternion algebra: Hamilton product is associative and norm-multiplicative, |A (x) B| = |A| |B|.
    Used in Eqs. (27) to (40) for the reduction and composition arguments.
  • domain assumption Unit-norm relation normalization in Eq. (18) is a valid modeling choice for stable rotation.
    Chosen for stability and to reduce degrees of freedom; not derived from data or prior constraints.
  • standard math The inverse of a unit quaternion is its conjugate.
    Invoked in the inversion discussion in Section V-B2.
  • domain assumption Composition of relations can be represented by the Hamilton product of normalized relation quaternions.
    Assumed in Eqs. (39) and (40) to model composed relations.
  • ad hoc to paper The type constraints used for QuatE-D2 are well-defined and do not leak test information.
    Appears only in Tables IV and V; no definition or implementation is provided.
  • domain assumption The filtered ranking protocol of Bordes et al. is a valid evaluation method.
    Standard in KGE literature; needed to interpret the reported MR, MRR, and Hits@K values.

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Cite this review

Pith. "Pith review of QuatE-D: A Distance-Based Quaternion Model for Knowledge Graph Embedding." pith.science (2026). https://pith.science/paper/7LJYVQZC

@misc{pith2026250413983,
  author       = {Pith},
  title        = {Pith review of: QuatE-D: A Distance-Based Quaternion Model for Knowledge Graph Embedding},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/7LJYVQZC}},
  note         = {Machine review of arXiv:2504.13983}
}
read the original abstract

Knowledge graph embedding (KGE) methods aim to represent entities and relations in a continuous space while preserving their structural and semantic properties. Quaternion-based KGEs have demonstrated strong potential in capturing complex relational patterns. In this work, we propose QuatE-D, a novel quaternion-based model that employs a distance-based scoring function instead of traditional inner-product approaches. By leveraging Euclidean distance, QuatE-D enhances interpretability and provides a more flexible representation of relational structures. Experimental results demonstrate that QuatE-D achieves competitive performance while maintaining an efficient parameterization, particularly excelling in Mean Rank reduction. These findings highlight the effectiveness of distance-based scoring in quaternion embeddings, offering a promising direction for knowledge graph completion.

Figures

Figures reproduced from arXiv: 2504.13983 by the authors.

Figure 1
Figure 1. Impact of Embedding Dimension on Triple Classification Performance [PITH_FULL_IMAGE:figures/full_fig_p007_1.png] view at source ↗

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Works this paper leans on

43 extracted references · 31 canonical work pages

  1. [1]

    An end-to-end model for question answering over knowledge base with cross-attention combining global knowledge,

    Y . Hao, Y . Zhang, K. Liu, S. He, Z. Liu, H. Wu, and J. Zhao, “An end-to-end model for question answering over knowledge base with cross-attention combining global knowledge,” in Proceedings of the 55th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers), pp. 221–231, 2017

    work page 2017

  2. [2]

    KBQA: Learning Question Answering over QA Corpora and Knowledge Bases

    W. Cui, Y . Xiao, H. Wang, Y . Song, S.-w. Hwang, and W. Wang, “Kbqa: learning question answering over qa corpora and knowledge bases,” arXiv preprint arXiv:1903.02419 , 2019

    work page Pith review arXiv 1903

  3. [3]

    Improving multi-hop question answering over knowledge graphs using knowledge base embeddings,

    A. Saxena, A. Tripathi, and P. Talukdar, “Improving multi-hop question answering over knowledge graphs using knowledge base embeddings,” in Proceedings of the 58th annual meeting of the association for computational linguistics, pp. 4498–4507, 2020

    work page 2020

  4. [4]

    Leveraging Knowledge Bases in LSTMs for Improving Machine Reading

    B. Yang and T. Mitchell, “Leveraging knowledge bases in lstms for improving machine reading,” arXiv preprint arXiv:1902.09091 , 2019

    work page Pith review arXiv 1902

  5. [5]

    Collaborative knowledge base embedding for recommender systems,

    F. Zhang, N. J. Yuan, D. Lian, X. Xie, and W.-Y . Ma, “Collaborative knowledge base embedding for recommender systems,” in Proceedings of the 22nd ACM SIGKDD international conference on knowledge discovery and data mining , pp. 353–362, 2016

    work page 2016

  6. [6]

    Dkn: Deep knowledge-aware network for news recommendation,

    H. Wang, F. Zhang, X. Xie, and M. Guo, “Dkn: Deep knowledge-aware network for news recommendation,” in Proceedings of the 2018 world wide web conference , pp. 1835–1844, 2018

    work page 2018

  7. [7]

    Translating embeddings for modeling multi-relational data,

    A. Bordes, N. Usunier, A. Garcia-Duran, J. Weston, and O. Yakhnenko, “Translating embeddings for modeling multi-relational data,” Advances in neural information processing systems , vol. 26, 2013. 9

    work page 2013

  8. [8]

    Rotate: Knowledge graph embedding by relational rotation in complex space,

    Z. Sun, Z.-H. Deng, J.-Y . Nie, and J. Tang, “Rotate: Knowledge graph embedding by relational rotation in complex space,” arXiv preprint arXiv:1902.10197, 2019

    arXiv 1902

Show all 43 references
  1. [9]

    Quaternion knowledge graph em- beddings,

    S. Zhang, Y . Tay, L. Yao, and Q. Liu, “Quaternion knowledge graph em- beddings,” Advances in neural information processing systems , vol. 32, 2019

    2019

  2. [10]

    Free- base: a collaboratively created graph database for structuring human knowledge,

    K. Bollacker, C. Evans, P. Paritosh, T. Sturge, and J. Taylor, “Free- base: a collaboratively created graph database for structuring human knowledge,” in Proceedings of the 2008 ACM SIGMOD international conference on Management of data , pp. 1247–1250, 2008

    2008

  3. [11]

    Wordnet: a lexical database for english,

    G. A. Miller, “Wordnet: a lexical database for english,” Communications of the ACM , vol. 38, no. 11, pp. 39–41, 1995

    1995

  4. [12]

    Knowledge graph embedding by translating on hyperplanes,

    Z. Wang, J. Zhang, J. Feng, and Z. Chen, “Knowledge graph embedding by translating on hyperplanes,” in Proceedings of the AAAI conference on artificial intelligence , vol. 28, 2014

    2014

  5. [13]

    Learning entity and relation embeddings for knowledge graph completion,

    Y . Lin, Z. Liu, M. Sun, Y . Liu, and X. Zhu, “Learning entity and relation embeddings for knowledge graph completion,” in Proceedings of the AAAI conference on artificial intelligence , vol. 29, 2015

    2015

  6. [14]

    Knowledge graph embedding via dynamic mapping matrix,

    G. Ji, S. He, L. Xu, K. Liu, and J. Zhao, “Knowledge graph embedding via dynamic mapping matrix,” in Proceedings of the 53rd annual meeting of the association for computational linguistics and the 7th international joint conference on natural language processing (volume 1: Lon...

    2015

  7. [15]

    Pairre: Knowledge graph em- beddings via paired relation vectors,

    L. Chao, J. He, T. Wang, and W. Chu, “Pairre: Knowledge graph em- beddings via paired relation vectors,” arXiv preprint arXiv:2011.03798, 2020

    2011 arXiv

  8. [16]

    Multi-relational poincar ´e graph embeddings,

    I. Balazevic, C. Allen, and T. Hospedales, “Multi-relational poincar ´e graph embeddings,” Advances in Neural Information Processing Sys- tems, vol. 32, 2019

    2019

  9. [17]

    Generalized translation-based embedding of knowledge graph,

    T. Ebisu and R. Ichise, “Generalized translation-based embedding of knowledge graph,” IEEE Transactions on Knowledge and Data Engi- neering, vol. 32, no. 5, pp. 941–951, 2019

    2019

  10. [18]

    A three-way model for col- lective learning on multi-relational data.,

    M. Nickel, V . Tresp, H.-P. Kriegel, et al., “A three-way model for col- lective learning on multi-relational data.,” in Icml, vol. 11, pp. 3104482– 3104584, 2011

    2011

  11. [19]

    Embedding entities and relations for learning and inference in knowledge bases,

    B. Yang, W.-t. Yih, X. He, J. Gao, and L. Deng, “Embedding entities and relations for learning and inference in knowledge bases,” arXiv preprint arXiv:1412.6575, 2014

    2014 arXiv

  12. [20]

    Analogical inference for multi- relational embeddings,

    H. Liu, Y . Wu, and Y . Yang, “Analogical inference for multi- relational embeddings,” in International conference on machine learn- ing, pp. 2168–2178, PMLR, 2017

    2017

  13. [21]

    Com- plex embeddings for simple link prediction,

    T. Trouillon, J. Welbl, S. Riedel, ´E. Gaussier, and G. Bouchard, “Com- plex embeddings for simple link prediction,” in International conference on machine learning , pp. 2071–2080, PMLR, 2016

    2016

  14. [22]

    Holographic embeddings of knowledge graphs,

    M. Nickel, L. Rosasco, and T. Poggio, “Holographic embeddings of knowledge graphs,” in Proceedings of the AAAI conference on artificial intelligence, vol. 30, 2016

    2016

  15. [23]

    Dual quaternion knowledge graph embeddings,

    Z. Cao, Q. Xu, Z. Yang, X. Cao, and Q. Huang, “Dual quaternion knowledge graph embeddings,” in Proceedings of the AAAI conference on artificial intelligence , vol. 35, pp. 6894–6902, 2021

    2021

  16. [24]

    Bique: Biquaternionic embeddings of knowledge graphs,

    J. Guo and S. Kok, “Bique: Biquaternionic embeddings of knowledge graphs,” arXiv preprint arXiv:2109.14401 , 2021

    2021 arXiv

  17. [25]

    Effective knowledge graph em- bedding with quaternion convolutional networks,

    Q. Liang, W. Wang, J. Yu, and F. Bao, “Effective knowledge graph em- bedding with quaternion convolutional networks,” in CCF International Conference on Natural Language Processing and Chinese Computing , pp. 183–196, Springer, 2024

    2024

  18. [26]

    Quatde: Dynamic quaternion embedding for knowledge graph comple- tion,

    H. Gao, K. Yang, Y . Yang, R. Y . Zakari, J. W. Owusu, and K. Qin, “Quatde: Dynamic quaternion embedding for knowledge graph comple- tion,” arXiv preprint arXiv:2105.09002 , 2021

    2021 arXiv

  19. [27]

    Hierarchy-aware quaternion embedding for knowledge graph completion,

    Q. Liang, W. Wang, J. Yu, and F. Bao, “Hierarchy-aware quaternion embedding for knowledge graph completion,” in 2024 International Joint Conference on Neural Networks (IJCNN) , pp. 1–8, IEEE, 2024

    2024

  20. [28]

    Quatse: Spherical linear interpolation of quaternion for knowledge graph embeddings,

    J. Li, X. Su, X. Ma, and G. Gao, “Quatse: Spherical linear interpolation of quaternion for knowledge graph embeddings,” in CCF International Conference on Natural Language Processing and Chinese Computing , pp. 209–220, Springer, 2022

    2022

  21. [29]

    A semantic matching energy function for learning with multi-relational data: Application to word-sense disambiguation,

    A. Bordes, X. Glorot, J. Weston, and Y . Bengio, “A semantic matching energy function for learning with multi-relational data: Application to word-sense disambiguation,” Machine learning , vol. 94, pp. 233–259, 2014

    2014

  22. [30]

    Knowledge vault: A web-scale approach to probabilistic knowledge fusion,

    X. Dong, E. Gabrilovich, G. Heitz, W. Horn, N. Lao, K. Murphy, T. Strohmann, S. Sun, and W. Zhang, “Knowledge vault: A web-scale approach to probabilistic knowledge fusion,” in Proceedings of the 20th ACM SIGKDD international conference on Knowledge discovery and data mining, ...

    2014

  23. [31]

    Convolutional 2d knowledge graph embeddings,

    T. Dettmers, P. Minervini, P. Stenetorp, and S. Riedel, “Convolutional 2d knowledge graph embeddings,” in Proceedings of the AAAI conference on artificial intelligence , vol. 32, 2018

    2018

  24. [32]

    A novel embedding model for knowledge base completion based on convolutional neural network,

    D. Q. Nguyen, T. D. Nguyen, D. Q. Nguyen, and D. Phung, “A novel embedding model for knowledge base completion based on convolutional neural network,” arXiv preprint arXiv:1712.02121 , 2017

    2017 arXiv

  25. [33]

    Modeling relational data with graph convolutional networks,

    M. Schlichtkrull, T. N. Kipf, P. Bloem, R. Van Den Berg, I. Titov, and M. Welling, “Modeling relational data with graph convolutional networks,” in The semantic web: 15th international conference, ESWC 2018, Heraklion, Crete, Greece, June 3–7, 2018, proceedings 15 , pp. 593–60...

    2018

  26. [34]

    Composition- based multi-relational graph convolutional networks,

    S. Vashishth, S. Sanyal, V . Nitin, and P. Talukdar, “Composition- based multi-relational graph convolutional networks,” arXiv preprint arXiv:1911.03082, 2019

    1911 arXiv

  27. [35]

    Kg-bert: Bert for knowledge graph completion,

    L. Yao, C. Mao, and Y . Luo, “Kg-bert: Bert for knowledge graph completion,” arXiv preprint arXiv:1909.03193 , 2019

    1909 arXiv

  28. [36]

    Ii. on quaternions; or on a new system of imaginaries in algebra,

    W. R. Hamilton, “Ii. on quaternions; or on a new system of imaginaries in algebra,” The London, Edinburgh, and Dublin Philosophical Maga- zine and Journal of Science , vol. 25, no. 163, pp. 10–13, 1844

  29. [37]

    A survey on dual-quaternions,

    B. Kenwright, “A survey on dual-quaternions,” arXiv preprint arXiv:2303.14765, 2023

    2023 arXiv

  30. [38]

    Quaternion convolutional neural networks for end-to- end automatic speech recognition,

    T. Parcollet, Y . Zhang, M. Morchid, C. Trabelsi, G. Linar`es, R. De Mori, and Y . Bengio, “Quaternion convolutional neural networks for end-to- end automatic speech recognition,” arXiv preprint arXiv:1806.07789 , 2018

    2018 arXiv

  31. [39]

    Understanding the difficulty of training deep feedforward neural networks,

    X. Glorot and Y . Bengio, “Understanding the difficulty of training deep feedforward neural networks,” in Proceedings of the thirteenth international conference on artificial intelligence and statistics, pp. 249– 256, JMLR Workshop and Conference Proceedings, 2010

    2010

  32. [40]

    Delving deep into rectifiers: Surpassing human-level performance on imagenet classification,

    K. He, X. Zhang, S. Ren, and J. Sun, “Delving deep into rectifiers: Surpassing human-level performance on imagenet classification,” in Proceedings of the IEEE international conference on computer vision , pp. 1026–1034, 2015

    2015

  33. [41]

    Observed versus latent features for knowl- edge base and text inference,

    K. Toutanova and D. Chen, “Observed versus latent features for knowl- edge base and text inference,” in Proceedings of the 3rd workshop on continuous vector space models and their compositionality , pp. 57–66, 2015

    2015

  34. [42]

    Knowledge embedding for knowledge graph completion,

    Z. Wang, J. Zhang, J. Feng, and Z. Chen, “Knowledge embedding for knowledge graph completion,” IEEE Transactions on Knowledge and Data Engineering, vol. 30, no. 12, pp. 2281–2293, 2018

    2018

  35. [43]

    Adaptive subgradient methods for online learning and stochastic optimization.,

    J. Duchi, E. Hazan, and Y . Singer, “Adaptive subgradient methods for online learning and stochastic optimization.,” Journal of machine learning research, vol. 12, no. 7, 2011. Hamideh-Sadat Fazael-Ardakani received her B.Sc. degree in electronic engineering from Yazd universi...

    2011

Pith tools

Reviewed August 16, 2026 · model on record in the stance chip above.