Back

RotatE: Knowledge Graph Embedding by Relational Rotation in Complex Space

Zhiqing SunZhihong DengJian-Yun NieJian Tang

article2019ICLR2,900 citations

Proposes a knowledge graph embedding framework that models relations as rotations in complex vector space to capture symmetry, antisymmetry, inversion, and composition patterns, paired with a self-adversarial negative sampling technique for superior link prediction accuracy.

Listen

RotatE introduces a knowledge graph embedding method that represents each relation as a rotation from the head entity to the tail entity in complex vector space. Knowledge graphs such as Freebase and WordNet remain incomplete, so the central task is to predict missing links by recovering unobserved factual triplets. Prior embedding approaches could capture only subsets of the recurring relation patterns—symmetry or antisymmetry, inversion, and composition—leaving performance gaps on realistic data.

The work set out to produce a single, scalable model that can simultaneously represent and infer all three patterns while remaining linear in time and memory. Entities and relations are mapped to complex vectors; each relation is constrained so that its modulus equals one, turning the mapping into an element-wise rotation. A self-adversarial negative-sampling loss then draws hard negatives according to the current model scores. The resulting method was tested on four standard link-prediction benchmarks plus the Countries dataset, which isolates composition, and compared against TransE, DistMult, ComplEx, HolE, and ConvE under identical filtered evaluation protocols.

RotatE records the highest mean reciprocal rank and Hits@10 on every benchmark, including the two subsets that lack inverse relations and therefore emphasize composition. On FB15k-237 and WN18RR the margin over prior leaders widens noticeably. The same model also achieves the best scores on the most demanding Countries task (S3). Histograms of learned phases confirm that symmetric relations concentrate near 0/π, inverse pairs are conjugates, and composed relations satisfy the expected phase-addition property. Self-adversarial sampling alone lifts both RotatE and re-implemented TransE, yet the rotational formulation remains necessary for the full pattern coverage.

These gains matter because accurate link prediction directly improves downstream applications such as question answering, information retrieval, and recommender systems that rely on complete knowledge graphs. Because the model is the first to reach state-of-the-art across all four widely used benchmarks, practitioners can adopt a single embedding technique rather than switching models according to the dominant pattern in a given graph.

The principal limitations are that results rest on standard academic benchmarks whose relation distributions may not match every production graph, and that the method still requires careful tuning of embedding dimension, margin, and temperature. Variance across random seeds is low, but broader testing on larger or noisier graphs would strengthen confidence. Next steps therefore include evaluating RotatE on additional industrial-scale graphs and extending it with probabilistic components that capture embedding uncertainty.

CIFARHEC MontréalMila – Québec Artificial Intelligence InstitutePeking UniversityUniversité de Montréalbipartite graphsknowledge graph embeddinglink predictionRotatEknowledge graph embeddingrelation pattern
arXiv: 1902.10197DeepGraphLearning/KnowledgeGraphEmbedding
Cover for RotatE: Knowledge Graph Embedding by Relational Rotation in Complex Space

Abstract

We study the problem of learning representations of entities and relations in knowledge graphs for predicting missing links. The success of such a task heavily relies on the ability of modeling and inferring the patterns of (or between) the relations. In this paper, we present a new approach for knowledge graph embedding called RotatE, which is able to model and infer various relation patterns including: symmetry/antisymmetry, inversion, and composition. Specifically, the RotatE model defines each relation as a rotation from the source entity to the target entity in the complex vector space. In addition, we propose a novel self-adversarial negative sampling technique for efficiently and effectively training the RotatE model. Experimental results on multiple benchmark knowledge graphs show that the proposed RotatE model is not only scalable, but also able to infer and model various relation patterns and significantly outperform existing state-of-the-art models for link prediction.

Topics

bipartite graphsknowledge graph embeddinglink prediction

Keywords

RotatEknowledge graph embeddingrelation patternsymmetryinversioncompositionself‑adversarial negative samplingcomplex vector spacelink predictionbenchmark dataset

Table of Contents

  • 1 Introduction
  • 2 Related Work
  • 3 RotatE: Relational Rotation in Complex Vector Space
  • 3.1 Modeling and Inferring Relation Patterns
  • 3.2 Modeling Relations as Rotations in Complex Vector Space
  • 3.3 Optimization
  • 4 Experiments
  • 4.1 Experimental Setting
  • 4.2 Main Results
  • 4.3 Inferring Relation Patterns on Countries DataSet
  • 4.4 Implicit Relation Pattern Inference
  • 4.5 Comparing different negative sampling techniques
  • 4.6 Further Experiments on TransE and ComplEx
  • 4.7 Experimental results on FB15k by relation category
  • 5 Conclusion
  • References
  • A Discussion on the Ability of Pattern Modeling and Inference
  • B Proof of Lemma
  • C Proof of Lemma
  • D Proof of Lemma
  • E Properties of RotatE
  • F Proof of Theorem
  • G Link Prediction on YAGO3-10
  • H Hyperparameters
  • I Ablation Study
  • J Variance of the Results
  • K More results of implicit basic pattern inference

Knowls

  1. Knowl 1 — RotatE Knowledge Graph Embedding Model

    model/method

    The RotatE model maps knowledge graph entities and relations into a complex vector space Ck\mathbb{C}^k, defining each relation rr as an element-wise rotation from a head entity h∈Ck\mathbf{h} \in \mathbb{C}^k to a tail entity t∈Ck\mathbf{t} \in \mathbb{C}^k.

    For a candidate factual triplet (h,r,t)(h, r, t), the target relation is parameterized as:

    t=h∘r\mathbf{t} = \mathbf{h} \circ \mathbf{r}

    where ∘\circ denotes the Hadamard (element-wise) product, and each relation embedding dimension ri∈Cr_i \in \mathbb{C} is constrained to have unit modulus:

    ∣ri∣=1for each i∈{1,…,k}|r_i| = 1 \quad \text{for each } i \in \{1, \dots, k\}

    Under this unit-modulus constraint, each relation coordinate has the polar form ri=eiθr,ir_i = e^{i \theta_{r,i}}, representing a counterclockwise rotation by θr,i∈[0,2π)\theta_{r,i} \in [0, 2\pi) radians in the complex plane that modulates the phase of the entity embeddings without altering their moduli.

    The distance function dr(h,t)d_r(\mathbf{h}, \mathbf{t}) for a triplet (h,r,t)(h, r, t) is defined using the complex L1L_1-norm:

    dr(h,t)=∥h∘r−t∥1=∑i=1k∣hiri−ti∣d_r(\mathbf{h}, \mathbf{t}) = \|\mathbf{h} \circ \mathbf{r} - \mathbf{t}\|_1 = \sum_{i=1}^k |h_i r_i - t_i|

    The scoring function measuring triplet salience is fr(h,t)=−dr(h,t)f_r(\mathbf{h}, \mathbf{t}) = -d_r(\mathbf{h}, \mathbf{t}).

  2. Knowl 2 — Self-Adversarial Negative Sampling Loss

    model/method

    To improve training efficiency over uniform negative sampling—where sampled corrupted triplets often become easily separable and uninformative—self-adversarial negative sampling assigns sample weights dynamically based on the current embedding model's predictions.

    Given a positive triplet (h,r,t)(h, r, t) and a set of nn negative candidate triplets {(hi′,r,ti′)}i=1n\{(h'_i, r, t'_i)\}_{i=1}^n generated by corrupting the head or tail entity, the self-adversarial sampling probability for negative candidate (hj′,r,tj′)(h'_j, r, t'_j) is:

    p(hj′,r,tj′∣{(hi,r,ti)})=exp⁡(αfr(hj′,tj′))∑i=1nexp⁡(αfr(hi′,ti′))p(h'_j, r, t'_j \mid \{(h_i, r, t_i)\}) = \frac{\exp(\alpha f_r(h'_j, t'_j))}{\sum_{i=1}^n \exp(\alpha f_r(h'_i, t'_i))}

    where α>0\alpha > 0 is the sampling temperature and fr(h,t)=−dr(h,t)f_r(h, t) = -d_r(\mathbf{h}, \mathbf{t}) is the model's triplet scoring function.

    Treating these probabilities as non-uniform sample weights, the negative sampling loss function is:

    L=−log⁡σ(γ−dr(h,t))−∑i=1np(hi′,r,ti′)log⁡σ(dr(hi′,ti′)−γ)L = -\log \sigma(\gamma - d_r(\mathbf{h}, \mathbf{t})) - \sum_{i=1}^n p(h'_i, r, t'_i) \log \sigma(d_r(h'_i, t'_i) - \gamma)

    where γ>0\gamma > 0 denotes a fixed margin hyperparameter and σ(x)=11+e−x\sigma(x) = \frac{1}{1 + e^{-x}} is the standard sigmoid function.

  3. Knowl 3 — Modeling and Inferring Relational Patterns in RotatE

    theoretical result

    RotatE can model and infer symmetry, antisymmetry, inversion, and composition relational patterns via element-wise complex rotations:

    1. Symmetry and Antisymmetry: A relation rr is symmetric (r(x,y)⇒r(y,x)r(x, y) \Rightarrow r(y, x)) if and only if each coordinate of its embedding vector r∈Ck\mathbf{r} \in \mathbb{C}^k satisfies ri=±1r_i = \pm 1 (ri=e0r_i = e^{0} or ri=eiπr_i = e^{i\pi}), yielding r∘r=1\mathbf{r} \circ \mathbf{r} = \mathbf{1}. A relation is antisymmetric (r(x,y)⇒¬r(y,x)r(x, y) \Rightarrow \neg r(y, x)) if and only if r∘r≠1\mathbf{r} \circ \mathbf{r} \neq \mathbf{1}.

    2. Inversion: Two relations r1r_1 and r2r_2 are inverses (r2(x,y)⇒r1(y,x)r_2(x, y) \Rightarrow r_1(y, x)) if and only if their embedding vectors are complex conjugates: r2=r‾1\mathbf{r}_2 = \overline{\mathbf{r}}_1, which is equivalent to r1=r2−1\mathbf{r}_1 = \mathbf{r}_2^{-1} or θr1,i+θr2,i≡0(mod2π)\theta_{r_1,i} + \theta_{r_2,i} \equiv 0 \pmod{2\pi} for all dimensions ii.

    3. Composition: A relation r1r_1 is composed of relations r2r_2 and r3r_3 (r2(x,y)∧r3(y,z)⇒r1(x,z)r_2(x, y) \land r_3(y, z) \Rightarrow r_1(x, z)) if and only if r1=r2∘r3\mathbf{r}_1 = \mathbf{r}_2 \circ \mathbf{r}_3, which corresponds to element-wise angle addition: θr1,i≡θr2,i+θr3,i(mod2π)\theta_{r_1,i} \equiv \theta_{r_2,i} + \theta_{r_3,i} \pmod{2\pi} for all dimensions ii.

  4. Knowl 4 — Formal Definitions of Relational Patterns in Knowledge Graphs

    definition

    In knowledge graph link prediction, relational patterns describe logical connectivity regularities between entities:

    • Symmetry: A relation rr is symmetric if ∀x,y:r(x,y)⇒r(y,x)\forall x, y: r(x, y) \Rightarrow r(y, x).
    • Antisymmetry: A relation rr is antisymmetric if ∀x,y:r(x,y)⇒¬r(y,x)\forall x, y: r(x, y) \Rightarrow \neg r(y, x).
    • Inversion: A relation r1r_1 is inverse to a relation r2r_2 if ∀x,y:r2(x,y)⇒r1(y,x)\forall x, y: r_2(x, y) \Rightarrow r_1(y, x).
    • Composition: A relation r1r_1 is composed of relations r2r_2 and r3r_3 if ∀x,y,z:r2(x,y)∧r3(y,z)⇒r1(x,z)\forall x, y, z: r_2(x, y) \land r_3(y, z) \Rightarrow r_1(x, z).

  5. Knowl 5 — Polar Coordinate Form and Modulus Lower Bound of RotatE Distance

    equation

    When entity embeddings h,t∈Ck\mathbf{h}, \mathbf{t} \in \mathbb{C}^k and relation embeddings r∈Ck\mathbf{r} \in \mathbb{C}^k are expressed in polar coordinates as hi=mh,ieiθh,ih_i = m_{h,i} e^{i \theta_{h,i}}, ti=mt,ieiθt,it_i = m_{t,i} e^{i \theta_{t,i}}, and ri=eiθr,ir_i = e^{i \theta_{r,i}} (with moduli mh,i,mt,i≥0m_{h,i}, m_{t,i} \ge 0 and phases θh,i,θt,i,θr,i∈[0,2π)\theta_{h,i}, \theta_{t,i}, \theta_{r,i} \in [0, 2\pi)), the RotatE distance metric dr(h,t)=∥h∘r−t∥1d_r(\mathbf{h}, \mathbf{t}) = \|\mathbf{h} \circ \mathbf{r} - \mathbf{t}\|_1 expands to:

    ∥h∘r−t∥1=∑i=1k(mh,i−mt,i)2+4mh,imt,isin⁡2(θh,i+θr,i−θt,i2)\|\mathbf{h} \circ \mathbf{r} - \mathbf{t}\|_1 = \sum_{i=1}^k \sqrt{(m_{h,i} - m_{t,i})^2 + 4 m_{h,i} m_{t,i} \sin^2\left(\frac{\theta_{h,i} + \theta_{r,i} - \theta_{t,i}}{2}\right)}

    This formulation implies two properties:

    1. The difference between entity embedding moduli establishes a strict lower bound on the distance:
    ∥h∘r−t∥1≥∥mh−mt∥1\|\mathbf{h} \circ \mathbf{r} - \mathbf{t}\|_1 \ge \|\mathbf{m}_h - \mathbf{m}_t\|_1

    where mh=(mh,1,…,mh,k)T\mathbf{m}_h = (m_{h,1}, \dots, m_{h,k})^T and mt=(mt,1,…,mt,k)T\mathbf{m}_t = (m_{t,1}, \dots, m_{t,k})^T.

    1. The distance between head and tail entities is invariant under conjugation of the relation:
    ∥h∘r−t∥1=∥t∘r‾−h∥1\|\mathbf{h} \circ \mathbf{r} - \mathbf{t}\|_1 = \|\mathbf{t} \circ \overline{\mathbf{r}} - \mathbf{h}\|_1

    allowing head and tail prediction to be evaluated uniformly.

  6. Knowl 6 — Degeneration of RotatE to TransE

    theoretical result

    The RotatE model can degenerate into and simulate the translation-based TransE model.

    Constraining the moduli of entity embeddings to a constant C>0C > 0 such that ∣hi∣=∣ti∣=C|h_i| = |t_i| = C simplifies the RotatE distance function to:

    ∥h∘r−t∥1=2C∑i=1k∣sin⁡(θh,i+θr,i−θt,i2)∣\|\mathbf{h} \circ \mathbf{r} - \mathbf{t}\|_1 = 2C \sum_{i=1}^k \left| \sin\left( \frac{\theta_{h,i} + \theta_{r,i} - \theta_{t,i}}{2} \right) \right|

    Given real embeddings h′,r′,t′∈Rk\mathbf{h}', \mathbf{r}', \mathbf{t}' \in \mathbb{R}^k from TransE, parameterizing the RotatE phase angles as hetah=ch′\boldsymbol{ heta}_h = c \mathbf{h}', hetar=cr′\boldsymbol{ heta}_r = c \mathbf{r}', hetat=ct′\boldsymbol{ heta}_t = c \mathbf{t}' and setting C=1/cC = 1/c, taking the limit as c→0c \to 0 recovers the TransE distance:

    lim⁡c→0∥h∘r−t∥1=∥h′+r′−t′∥1\lim_{c \to 0} \|\mathbf{h} \circ \mathbf{r} - \mathbf{t}\|_1 = \|\mathbf{h}' + \mathbf{r}' - \mathbf{t}'\|_1

  7. Knowl 7 — pRotatE Baseline Model

    model/method

    pRotatE is a baseline variant of the RotatE model that restricts entity embedding moduli to a constant C>0C > 0, isolating the effect of phase-only relational rotations without modulus variation.

    For entity embeddings h,t∈Ck\mathbf{h}, \mathbf{t} \in \mathbb{C}^k constrained by ∣hi∣=∣ti∣=C|h_i| = |t_i| = C and relation embedding r∈Ck\mathbf{r} \in \mathbb{C}^k with ∣ri∣=1|r_i| = 1, the distance function simplifies to:

    dr(h,t)=2C∥sin⁡(θh+θr−θt2)∥1=2C∑i=1k∣sin⁡(θh,i+θr,i−θt,i2)∣d_r(\mathbf{h}, \mathbf{t}) = 2C \left\| \sin\left( \frac{\boldsymbol{\theta}_h + \boldsymbol{\theta}_r - \boldsymbol{\theta}_t}{2} \right) \right\|_1 = 2C \sum_{i=1}^k \left| \sin\left( \frac{\theta_{h,i} + \theta_{r,i} - \theta_{t,i}}{2} \right) \right|

    where θh,θr,θt∈[0,2π)k\boldsymbol{\theta}_h, \boldsymbol{\theta}_r, \boldsymbol{\theta}_t \in [0, 2\pi)^k are phase angle vectors for the head entity, relation, and tail entity, respectively.

    While pRotatE theoretically retains the capacity to model symmetry, antisymmetry, inversion, and composition, the lack of modulus information reduces empirical performance on datasets where relation composition is prominent.

  8. Knowl 8 — Link Prediction Results on Standard Benchmark Knowledge Graphs

    empirical result

    In filtered link prediction benchmarks, RotatE outperforms baseline methods (TransE, DistMult, HolE, ComplEx, ConvE, and pRotatE) across FB15k, WN18, FB15k-237, and WN18RR:

    FB15k-237 WN18RR
    Model MR MRR H@1 H@10 MR MRR H@1 H@10
    TransE 357 .294 - .465 3384 .226 - .501
    DistMult 254 .241 .155 .419 5110 .43 .39 .49
    ComplEx 339 .247 .158 .428 5261 .44 .41 .51
    ConvE 244 .325 .237 .501 4187 .43 .40 .52
    pRotatE 178 .328 .230 .524 2923 .462 .417 .552
    RotatE 177 .338 .241 .533 3340 .476 .428 .571
    FB15k WN18
    Model MR MRR H@1 H@10 MR MRR H@1 H@10
    TransE - .463 .297 .749 - .495 .113 .943
    DistMult 42 .798 - .893 655 .797 - .946
    HolE - .524 .402 .739 - .938 .930 .949
    ComplEx - .692 .599 .840 - .941 .936 .947
    ConvE 51 .657 .558 .831 374 .943 .935 .956
    pRotatE 43 .799 .750 .884 254 .947 .942 .957
    RotatE 40 .797 .746 .884 309 .949 .944 .959

    On FB15k-237 and WN18RR, where inverse relations have been removed and composition/symmetry patterns dominate, RotatE achieves substantial gains over prior models (e.g., MRR 0.338 vs. ConvE 0.325 on FB15k-237, and MRR 0.476 vs. ConvE 0.43 on WN18RR). On YAGO3-10, RotatE achieves MR = 1767, MRR = .495, Hits@1 = .402, Hits@3 = .550, and Hits@10 = .670, compared to ConvE's MR = 1671, MRR = .44, Hits@1 = .35, Hits@3 = .49, and Hits@10 = .62.

  9. Knowl 9 — Compositional Link Prediction on the Countries Benchmark

    empirical result

    The Countries benchmark tests the capability of models to infer compositional patterns across three tasks of increasing relational path length:

    • S1: baseline pattern modeling.
    • S2: 2-step composition: neighborOf(c1,c2)∧locatedIn(c2,r)⇒locatedIn(c1,r)\text{neighborOf}(c_1, c_2) \land \text{locatedIn}(c_2, r) \Rightarrow \text{locatedIn}(c_1, r).
    • S3: 3-step composition: neighborOf(c1,c2)∧locatedIn(c2,s)∧locatedIn(s,r)⇒locatedIn(c1,r)\text{neighborOf}(c_1, c_2) \land \text{locatedIn}(c_2, s) \land \text{locatedIn}(s, r) \Rightarrow \text{locatedIn}(c_1, r).

    Performance measured by Area Under the Precision-Recall Curve (AUC-PR) shows:

    Task DistMult ComplEx ConvE RotatE
    S1 1.00±0.001.00 \pm 0.00 0.97±0.020.97 \pm 0.02 1.00±0.001.00 \pm 0.00 1.00±0.001.00 \pm 0.00
    S2 0.72±0.120.72 \pm 0.12 0.57±0.100.57 \pm 0.10 0.99±0.010.99 \pm 0.01 1.00±0.001.00 \pm 0.00
    S3 0.52±0.070.52 \pm 0.07 0.43±0.070.43 \pm 0.07 0.86±0.050.86 \pm 0.05 0.95±0.000.95 \pm 0.00

    RotatE achieves 0.95±0.000.95 \pm 0.00 on the hardest task S3, outperforming ComplEx (0.43±0.070.43 \pm 0.07), DistMult (0.52±0.070.52 \pm 0.07), and ConvE (0.86±0.050.86 \pm 0.05).

  10. Knowl 10 — Comparison of Negative Sampling Strategies

    empirical result

    Evaluating a 50-dimensional TransE model across different negative sampling approaches shows that self-adversarial negative sampling consistently outperforms uniform sampling and the generative adversarial sampling model KBGAN:

    FB15k-237 WN18RR WN18
    Sampling Method MRR H@10 MRR H@10 MRR H@10
    Uniform .242 .422 .186 .459 .433 .915
    KBGAN .278 .453 .210 .479 .705 .949
    Self-Adversarial .298 .475 .223 .510 .736 .947

    Self-adversarial sampling achieves these improvements without requiring training a separate discrete generator network.

  11. Knowl 11 — Implicit Representation of Relational Patterns in Learned Phase Angles

    empirical result

    Empirical inspection of the learned relation phase angles {θr,i}i=1k\{\theta_{r,i}\}_{i=1}^k confirms that relational patterns are implicitly acquired during RotatE training:

    1. Symmetric relations: Phase distributions of symmetric relations (such as similar_to on WN18 or /celebrities/celebrity/friendship/friend on FB15k-237) concentrate tightly at 00 (where ri=1r_i = 1) and π\pi (where ri=−1r_i = -1), satisfying ri2=1r_i^2 = 1. General asymmetric relations (such as hypernym) exhibit phase distributions spread across [0,2π)[0, 2\pi).

    2. Inverse relations: For inverse pairs r1r_1 and r2r_2 (e.g., hypernym and hyponym on WN18), the element-wise sum of phase angles θr1,i+θr2,i\theta_{r_1,i} + \theta_{r_2,i} concentrates at 00 and 2π2\pi, showing r1=r‾2=r2−1\mathbf{r}_1 = \overline{\mathbf{r}}_2 = \mathbf{r}_2^{-1}.

    3. Compositional relations: For relations satisfying composition r1=r2∘r3r_1 = r_2 \circ r_3 on FB15k-237, the learned phases satisfy θr2,i+θr3,i≡θr1,i(mod2π)\theta_{r_2,i} + \theta_{r_3,i} \equiv \theta_{r_1,i} \pmod{2\pi}.

  12. Knowl 12 — Link Prediction Performance by Relation Mapping Category

    empirical result

    When relations on FB15k are partitioned into 1-to-1, 1-to-N, N-to-1, and N-to-N based on average tails per head (tphrtph_r) and heads per tail (hptrhpt_r) with threshold 1.5, RotatE trained with self-adversarial negative sampling performs strongly across both injective and complex non-injective relations:

    Prediction Head (Hits@10) Prediction Tail (Hits@10)
    Model 1-to-1 1-to-N N-to-1 N-to-N 1-to-1 1-to-N N-to-1 N-to-N
    TransE .894 .972 .567 .880 .879 .671 .964 .910
    ComplEx .939 .969 .692 .893 .938 .823 .952 .910
    RotatE .922 .967 .602 .893 .923 .713 .961 .922
    Prediction Head (MRR) Prediction Tail (MRR)
    Model 1-to-1 1-to-N N-to-1 N-to-N 1-to-1 1-to-N N-to-1 N-to-N
    TransE .701 .912 .424 .737 .701 .561 .894 .761
    ComplEx .832 .914 .543 .787 .826 .661 .869 .800
    RotatE .878 .934 .465 .803 .872 .611 .909 .832

    RotatE achieves the highest MRR on N-to-N relations for both head prediction (.803) and tail prediction (.832).

Coverage note — All substantial theoretical proofs (Appendix B, C, D, F) are omitted as derivation steps while their corresponding results are captured in dedicated knowls. Minor hyperparameter search ranges and run-to-run variance statistics are omitted.

References

  1. 1.Kurt Bollacker, Colin Evans, Praveen Paritosh, Tim Sturge, and Jamie Taylor. Freebase: 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. AcM, 2008.
  2. 2.Antoine Bordes, Jason Weston, Ronan Collobert, Yoshua Bengio, et al. Learning structured embeddings of knowledge bases. In AAAI, volume 6, pp. 6, 2011.
  3. 3.Antoine Bordes, Nicolas Usunier, Alberto Garcia-Duran, Jason Weston, and Oksana Yakhnenko. Translating embeddings for modeling multi-relational data. In Advances in neural information processing systems, pp. 2787–2795, 2013.
  4. 4.Guillaume Bouchard, Sameer Singh, and Theo Trouillon. On approximate reasoning capabilities of low-rank vector spaces. AAAI Spring Syposium on Knowledge Representation and Reasoning (KRR): Integrating Symbolic and Neural Approaches, 2015.
  5. 5.Liwei Cai and William Yang Wang. Kbgan: Adversarial learning for knowledge graph embeddings. arXiv preprint arXiv:1711.04071, 2017.
  6. 6.Rajarshi Das, Arvind Neelakantan, David Belanger, and Andrew McCallum. Chains of reasoning over entities, relations, and text using recurrent neural networks. arXiv preprint arXiv:1607.01426, 2016.
  7. 7.Tim Dettmers, Pasquale Minervini, Pontus Stenetorp, and Sebastian Riedel. Convolutional 2d knowledge graph embeddings. arXiv preprint arXiv:1707.01476, 2017.
  8. 8.Takuma Ebisu and Ryutaro Ichise. Toruse: Knowledge graph embedding on a lie group. In Proceedings of the Thirty-Second AAAI Conference on Artificial Intelligence, pp. 1819–1826. AAAI Press, 2018.
  9. 9.Kelvin Guu, John Miller, and Percy Liang. Traversing knowledge graphs in vector space. arXiv preprint arXiv:1506.01094, 2015.
  10. 10.Yanchao Hao, Yuanzhe Zhang, Kang Liu, Shizhu He, Zhanyi Liu, Hua Wu, and Jun 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), volume 1, pp. 221–231, 2017.
  11. 11.Katsuhiko Hayashi and Masashi Shimbo. On the equivalence of holographic and complex embeddings for link prediction. arXiv preprint arXiv:1702.05563, 2017.
  12. 12.Shizhu He, Kang Liu, Guoliang Ji, and Jun Zhao. Learning to represent knowledge graphs with gaussian embedding. In Proceedings of the 24th ACM International on Conference on Information and Knowledge Management, pp. 623–632. ACM, 2015.
  13. 13.Rudolf Kadlec, Ondrej Bajgar, and Jan Kleindienst. Knowledge base completion: Baselines strike back. arXiv preprint arXiv:1705.10744, 2017.
  14. 14.Diederik P Kingma and Jimmy Ba. Adam: A method for stochastic optimization. arXiv preprint arXiv:1412.6980, 2014.
  15. 15.Ni Lao, Tom Mitchell, and William W Cohen. Random walk inference and learning in a large scale knowledge base. In Proceedings of the Conference on Empirical Methods in Natural Language Processing, pp. 529–539. Association for Computational Linguistics, 2011.
  16. 16.Yankai Lin, Zhiyuan Liu, Huanbo Luan, Maosong Sun, Siwei Rao, and Song Liu. Modeling relation paths for representation learning of knowledge bases. arXiv preprint arXiv:1506.00379, 2015a.
  17. 17.Yankai Lin, Zhiyuan Liu, Maosong Sun, Yang Liu, and Xuan Zhu. Learning entity and relation embeddings for knowledge graph completion. In AAAI, volume 15, pp. 2181–2187, 2015b.
  18. 18.Farzaneh Mahdisoltani, Joanna Biega, and Fabian M Suchanek. Yago3: A knowledge base from multilingual wikipedias. In CIDR, 2013.
  19. 19.Tomas Mikolov, Ilya Sutskever, Kai Chen, Greg S Corrado, and Jeff Dean. Distributed representations of words and phrases and their compositionality. In Advances in neural information processing systems, pp. 3111–3119, 2013.
  20. 20.George A Miller. Wordnet: a lexical database for english. Communications of the ACM, 38(11): 39–41, 1995.
  21. 21.Arvind Neelakantan, Benjamin Roth, and Andrew McCallum. Compositional vector space models for knowledge base completion. arXiv preprint arXiv:1504.06662, 2015.
  22. 22.Dai Quoc Nguyen, Tu Dinh Nguyen, Dat Quoc Nguyen, and Dinh Phung. A novel embedding model for knowledge base completion based on convolutional neural network. arXiv preprint arXiv:1712.02121, 2017.
  23. 23.Dat Quoc Nguyen, Kairit Sirts, Lizhen Qu, and Mark Johnson. Stranse: a novel embedding model of entities and relationships in knowledge bases. arXiv preprint arXiv:1606.08140, 2016.
  24. 24.Maximilian Nickel, Lorenzo Rosasco, Tomaso A Poggio, et al. Holographic embeddings of knowledge graphs. In AAAI, volume 2, pp. 3–2, 2016.
  25. 25.Tim Rocktäschel and Sebastian Riedel. End-to-end differentiable proving. In Advances in Neural Information Processing Systems, pp. 3788–3800, 2017.
  26. 26.Fabian M Suchanek, Gjergji Kasneci, and Gerhard Weikum. Yago: a core of semantic knowledge. In Proceedings of the 16th international conference on World Wide Web, pp. 697–706. ACM, 2007.
  27. 27.Kristina Toutanova and Danqi Chen. Observed versus latent features for knowledge base and text inference. In Proceedings of the 3rd Workshop on Continuous Vector Space Models and their Compositionality, pp. 57–66, 2015.
  28. 28.Théo Trouillon, Johannes Welbl, Sebastian Riedel, Éric Gaussier, and Guillaume Bouchard. Complex embeddings for simple link prediction. In International Conference on Machine Learning, pp. 2071–2080, 2016.
  29. 29.Zhen Wang, Jianwen Zhang, Jianlin Feng, and Zheng Chen. Knowledge graph embedding by translating on hyperplanes. In AAAI, volume 14, pp. 1112–1119, 2014.
  30. 30.Chenyan Xiong, Russell Power, and Jamie Callan. Explicit semantic ranking for academic search via knowledge graph embedding. In Proceedings of the 26th international conference on world wide web, pp. 1271–1279. International World Wide Web Conferences Steering Committee, 2017.
  31. 31.Bishan Yang and Tom Mitchell. Leveraging knowledge bases in lstms for improving machine reading. In Proceedings of the 55th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers), volume 1, pp. 1436–1446, 2017.
  32. 32.Bishan Yang, Wen-tau Yih, Xiaodong He, Jianfeng Gao, and Li Deng. Embedding entities and relations for learning and inference in knowledge bases. arXiv preprint arXiv:1412.6575, 2014.
  33. 33.Fan Yang, Zhilin Yang, and William W Cohen. Differentiable learning of logical rules for knowledge base completion. CoRR, abs/1702.08367, 2017.
  34. 34.Fuzheng Zhang, Nicholas Jing Yuan, Defu Lian, Xing Xie, and Wei-Ying 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. ACM, 2016.

Citation

MLA
Sun, Z., et al. “RotatE: Knowledge Graph Embedding by Relational Rotation in Complex Space”. arXiv, 2019, https://doi.org/10.48550/arxiv.1902.10197.
APA
Sun, Z., Deng, Z.-H., Nie, J.-Y., & Tang, J. (2019). RotatE: Knowledge Graph Embedding by Relational Rotation in Complex Space. arXiv. https://doi.org/10.48550/arxiv.1902.10197
Chicago
Sun, Z., Z.-H. Deng, J.-Y. Nie, and J. Tang. 2019. “RotatE: Knowledge Graph Embedding by Relational Rotation in Complex Space”. Preprint, ArXiv. https://doi.org/10.48550/arxiv.1902.10197.
Harvard
Sun, Z. et al. (2019) “RotatE: Knowledge Graph Embedding by Relational Rotation in Complex Space”. arXiv. Available at: https://doi.org/10.48550/arxiv.1902.10197.
Vancouver
1. Sun Z, Deng Z-H, Nie J-Y, Tang J (2019) RotatE: Knowledge Graph Embedding by Relational Rotation in Complex Space. https://doi.org/10.48550/arxiv.1902.10197

BibTeX

@misc{https://doi.org/10.48550/arxiv.1902.10197,
  doi = {10.48550/ARXIV.1902.10197},
  url = {https://arxiv.org/abs/1902.10197},
  author = {Sun, Zhiqing and Deng, Zhi-Hong and Nie, Jian-Yun and Tang, Jian},
  keywords = {Machine Learning (cs.LG), Computation and Language (cs.CL), Machine Learning (stat.ML), FOS: Computer and information sciences, FOS: Computer and information sciences},
  title = {RotatE: Knowledge Graph Embedding by Relational Rotation in Complex Space},
  publisher = {arXiv},
  year = {2019},
  copyright = {arXiv.org perpetual, non-exclusive license}
}
Metadata:DOI registry

Source Code

This paper has an official code repository available. Click below to access the source code.

View Repository

Access the Paper

This paper is available from its original source. Click below to access the PDF.

Open PDF

License: Authors