The DOI matches its Crossref record; 23 of the 23 references it cites were found in a registry or an index; 5 of the 14 sources its claims cite were checked for support.
TuckER: Tensor Factorization for Knowledge Graph Completion
Open accessAbstract
Ivana Balazevic, Carl Allen, Timothy Hospedales. Proceedings of the 2019 Conference on Empirical Methods in Natural Language Processing and the 9th International Joint Conference on Natural Language Processing (EMNLP-IJCNLP). 2019.
Overview
AI snapshot
Written from the paper’s full text.
TL;DR
TuckER is a linear link-prediction model based on Tucker decomposition of the binary knowledge-graph tensor, using a shared core tensor and entity/relation embeddings. It achieves state-of-the-art results on standard datasets, is fully expressive, and subsumes several prior linear models as special cases.
Key findings
- TuckER reaches state-of-the-art link prediction results on WN18RR (MRR .470, Hits@10 .526, Hits@3 .482, Hits@1 .443) and FB15k-237 (MRR .358, Hits@10 .544, Hits@3 .394, Hits@1 .266), and on WN18 (MRR .953, Hits@10 .958, Hits@3 .955, Hits@1 .949) and FB15k (MRR .795, Hits@10 .892, Hits@3 .833, Hits@1 .741), apart from Hits@10 on WN18 where R-GCN does better.
- TuckER is fully expressive: Theorem 1 gives a sufficient bound of entity embedding dimensionality \(d_e = n_e\) and relation embedding dimensionality \(d_r = n_r\).
- RESCAL, DistMult, ComplEx, and SimplE can be viewed as special cases of TuckER.
- Parameter sharing through the core tensor helps: on WN18RR TuckER uses ∼9.4M parameters versus ∼16.4M for ComplEx and SimplE at \(d_e=200, d_r=30\); at embedding size 20 (∼300k parameters), TuckER is almost as good as ComplEx and SimplE at embedding size 200 (∼6M parameters), and on FB15k it improves Hits@1 by +14% over ComplEx and +8% over SimplE.
Methods
- TuckER factorizes the third-order binary tensor of triples with Tucker decomposition, scoring \(\phi(e_s, r, e_o) = W \times_1 e_s \times_2 w_r \times_3 e_o\), where \(W\) is a core tensor and subject/object entity embeddings are shared; a logistic sigmoid converts scores to probabilities.
- Training uses reciprocal relations, 1-N scoring, Bernoulli negative log-likelihood, Adam with batch size 128, and random-search hyperparameters; evaluation uses the filtered setting with MRR and Hits@k on FB15k, FB15k-237, WN18, and WN18RR.
- Theoretical analysis proves full expressiveness, derives the dimensionality bound, and shows the relationship between TuckER and prior linear tensor-factorization models.
Limitations
- The paper states future work might include exploring how to incorporate background knowledge on individual relation properties; it does not present a dedicated limitations section.
- Evident from the text: evaluation is limited to four standard link-prediction datasets and MRR/Hits@k metrics, with no broader task or computational-efficiency analysis beyond parameter counts.
- Evident from the text: the full-expressiveness bound \(d_e = n_e, d_r = n_r\) is theoretical and may be much larger than practical embedding sizes; the authors expect smaller dimensionalities to suffice in practice.
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Claims the paper makes
22 Own interpretation · 9 Own result · 6 Sources not found · 3 Partly supported · 3 Own method · 3 No basis given · 2 Supported · 1 No full text of the sources · accuracy not yet measured
Every source the paper cites for this claim was checked and supports it.
In the paper
“The authors show that convolution is a way of introducing sparsity and parameter tying and that HypER can be understood in terms of tensor factorization up to a non-linearity, thus placing HypER closer to the well established family of factorization models.”
§ TuckER: Tensor Factorization for Knowledge Graph Completion > 1 Introduction
What the sources say
- Supportedcites Balažević et al., 2019 source
Section 4.2 (p. 6) describes HypER as tensor multiplication with a constrained core tensor and notes that ReLU is applied before the final dot product. The Related Work section (p. 3) explicitly identifies that ReLU non-linearity as the key difference from existing factorization approaches and describes convolution as multiplication by a sparse tensor with tied weights. (LLM, conf=0.94)
boostedcorrelational- Asserted: passes — The authors put it forward as true.
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- Supported
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In the paper
“They further prove other models are not fully expressive: DistMult, because it cannot model asymmetric relations; and transitive models such as TransE (Bordes et al., 2013) and its variants FTransE (Feng et al., 2016) and STransE (Nguyen et al., 2016), because of certain contradictions that they impose between different relation types.”
§ TuckER: Tensor Factorization for Knowledge Graph Completion > 5.1 Full Expressiveness and Embedding Dimensionality
What the sources say
- Not matchedcites Bordes et al., 2013
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
- Not matchedcites Feng et al., 2016
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
- Supportedcites Nguyen et al., 2016 source
The citation immediately following “STransE” identifies the model, rather than attributing the citing authors’ expressiveness proof to Nguyen et al. The source’s model description (SE section; page unavailable) explicitly introduces STransE. It does not establish the claimed contradictions, but that proof is framed as the citing authors’ own. (LLM, conf=0.91)
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In the paper
“To our knowledge, ComplEx-N3 (Lacroix et al., 2018) is the only other linear link prediction model that benefits from multitask learning.”
§ TuckER: Tensor Factorization for Knowledge Graph Completion > 6.3 Link Prediction Results
What the sources say
- Partly supportedcites Lacroix et al., 2018 sourceExperimental — accuracy not yet measured
The Experimental Setup (p. 7) identifies ComplEx-N3, and the Introduction (pp. 1–2) reports performance gains for ComplEx from modeling inverse predicates and, on harder datasets, from N3 regularization. Our copy does not establish that ComplEx-N3 benefits from multitask learning or that it is the only other linear link-prediction model to do so. (LLM, conf=0.78)
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- Partly supported
The cited sources support only part of this claim — read each source’s verdict below.
In the paper
“There, rank regularization of the embedding matrices is used to encourage a lowrank factorization, thus forcing parameter sharing between relations.”
§ TuckER: Tensor Factorization for Knowledge Graph Completion > 6.3 Link Prediction Results
What the sources say
- Partly supportedcites Lacroix et al., 2018 sourceExperimental — accuracy not yet measured
Section 4 (p. 4) confirms that the paper proposes nuclear 3-norm regularization for tensor-factorization models, including ComplEx. But it does not say that this regularizer forces parameter sharing between relations; Section 2.2 (p. 2) instead describes ComplEx’s parameter sharing as occurring between the subject and object modes. (LLM, conf=0.84)
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- Partly supported
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“TuckER outperforms previous state-of-the-art models across standard link prediction datasets, acting as a strong baseline for more elaborate models.”
- Also stated in: § 1 Introduction · plain
“proposing TuckER, a new linear model for link prediction on knowledge graphs, that is simple, expressive and achieves state-of-theart results across all standard datasets”
§ TuckER: Tensor Factorization for Knowledge Graph Completion > Abstract
plain- Asserted: passes — The authors put it forward as true.
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- The authors state this as an assumption: Subject and object entity embedding matrices are equivalent, i.e. no distinction is made between the embeddings of an entity depending on whether it appears as a subject or as an object.
- Also stated in: § 1 Introduction · plain
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“This is supported by the fact that the margin by which TuckER outperforms other linear models is notably increased on datasets with a large number of relations.”
§ TuckER: Tensor Factorization for Knowledge Graph Completion > 6.3 Link Prediction Results
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In the paper
“Even with fewer parameters than ComplEx and SimplE at d e = 200 and d r = 30 on WN18RR (∼9.4 vs ∼16.4 million), TuckER consistently obtains better results than any of those models.”
§ TuckER: Tensor Factorization for Knowledge Graph Completion > 6.3 Link Prediction Results
plaindirect- Asserted: passes — The authors put it forward as true.
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In the paper
“We can see that the difference between the MRRs of ComplEx, SimplE and TuckER is approximately constant for embedding sizes 100 and 200.”
§ TuckER: Tensor Factorization for Knowledge Graph Completion > 6.4 Influence of Parameter Sharing
plain- Asserted: passes — The authors put it forward as true.
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In the paper
“However, running their model with equivalent parameter number to TuckER shows comparable performance, supporting our belief that the two models both attain the benefits of multi-task learning, although by different means.”
§ TuckER: Tensor Factorization for Knowledge Graph Completion > 6.3 Link Prediction Results
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In the paper
“It is important to note that at embedding dimensionalities 20, 50 and 100, TuckER has fewer parameters than Com-plEx and SimplE (e.g.ComplEx and SimplE have ∼3 million and TuckER has ∼2.5 million parameters for embedding dimensionality 100).”
§ TuckER: Tensor Factorization for Knowledge Graph Completion > 6.4 Influence of Parameter Sharing
plain- Asserted: passes — The authors put it forward as true.
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In the paper
“At embedding size 20 (∼300k parameters), the performance of TuckER is almost as good as the performance of ComplEx and SimplE at embedding size 200 (∼6 million parameters), which supports our initial assumption.”
§ TuckER: Tensor Factorization for Knowledge Graph Completion > 6.4 Influence of Parameter Sharing
plain- Asserted: passes — The authors put it forward as true.
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A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“We show that TuckER is a fully expressive model, derive sufficient bounds on its embedding dimensionalities and demonstrate that several previously introduced linear models can be viewed as special cases of TuckER.”
- Also stated in: § 1 Introduction · boosted
“We thus show that TuckER is fully expressive, i.e. given any ground truth over the triples, there exists an assignment of values to the entity and relation embeddings that accurately separates the true triples from false ones.”
- Also stated in: § 1 Introduction · plain
“proving that TuckER is fully expressive and deriving a bound on the embedding dimensionality for full expressiveness”
- Also stated in: § 7 Conclusion · plain
“Whilst being fully expressive, TuckER's number of parameters grows linearly with respect to the number of entities or relations in the knowledge graph.”
§ TuckER: Tensor Factorization for Knowledge Graph Completion > Abstract
boosted- Asserted: passes — The authors put it forward as true.
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- Load-bearing: passes — The paper’s conclusions depend on it.
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- The authors state this as an assumption: Subject and object entity embedding matrices are equivalent, i.e. no distinction is made between the embeddings of an entity depending on whether it appears as a subject or as an object.
- Also stated in: § 1 Introduction · boosted
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The SimplE scoring function (see Table 1) is therefore equivalent to that of TuckER (see Equation 1), with core tensor Z ∈ R P ×Q×R , P = Q = R = 2d e , where 2d e elements on two tensor diagonals are set to 1 2 and all other elements are set to 0 (see Figure 2c).”
§ TuckER: Tensor Factorization for Knowledge Graph Completion > 5.2 Relation to Previous Linear Models
plain- Asserted: passes — The authors put it forward as true.
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A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Similarly to DistMult, we can regard the scoring function of ComplEx (see Table 1) as equivalent to the scoring function of TuckER (see Equation 1), with core tensor Z ∈ R P ×Q×R , P = Q = R = 2d e , where 3d e elements on different tensor diagonals are set to 1, d e elements on one tensor diagonal are set to -1 and all other elements are set to 0 (see Figure 2b).”
§ TuckER: Tensor Factorization for Knowledge Graph Completion > 5.2 Relation to Previous Linear Models
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In the paper
“Although a very expressive and powerful model, RESCAL is prone to overfitting due to its large number of parameters, which increases quadratically in the embedding dimension with the number of relations in a knowledge graph.”
§ TuckER: Tensor Factorization for Knowledge Graph Completion > 1 Introduction
What the sources say
- Not matchedcites Nickel et al., 2011
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
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In the paper
“Rather than learning distinct relation-specific matrices, the core tensor of TuckER can be viewed as containing a shared pool of”
§ TuckER: Tensor Factorization for Knowledge Graph Completion > 4 Tucker Decomposition for Link Prediction
plaindirect- Asserted: passes — The authors put it forward as true.
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- The authors state this as an assumption: Subject and object entity embedding matrices are equivalent, i.e. no distinction is made between the embeddings of an entity depending on whether it appears as a subject or as an object.
In the paper
“The authors show that SimplE belongs to the family of bilinear models by concatenating embeddings for head and tail entities for both subject and object into vectors [h es ; t es ] ∈ R 2de and [h eo ; t eo ] ∈ R 2de and constraining the relation matrix W r ∈ R 2de×2de so that it contains the relation embedding vector 1 2 w r on its d e -diagonal and the inverse relation embedding vectorfoot_0 2 w”
§ TuckER: Tensor Factorization for Knowledge Graph Completion > 5.2 Relation to Previous Linear Models
What the sources say
- Not matchedcites Kazemi and Poole (2018)
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
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In the paper
“The purpose of Theorem 1 is to prove that TuckER is capable of potentially capturing all information (and noise) in the data.”
§ TuckER: Tensor Factorization for Knowledge Graph Completion > 5.1 Full Expressiveness and Embedding Dimensionality
plainconditional- Asserted: passes — The authors put it forward as true.
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- The authors state this as an assumption: Subject and object entity embedding matrices are equivalent, i.e. no distinction is made between the embeddings of an entity depending on whether it appears as a subject or as an object.
In the paper
“They further prove other models are not fully expressive: DistMult, because it cannot model asymmetric relations; and transitive models such as TransE (Bordes et al., 2013) and its variants FTransE (Feng et al., 2016) and STransE (Nguyen et al., 2016), because of certain contradictions that they impose between different relation types.”
§ TuckER: Tensor Factorization for Knowledge Graph Completion > 5.1 Full Expressiveness and Embedding Dimensionality
What the sources say
- Not matchedcites Kazemi and Poole (2018)
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
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In the paper
“Theorem 1.Given any ground truth over a set of entities E and relations R, there exists a TuckER model with entity embeddings of dimensionality d e = n e and relation embeddings of dimensionality d r = n r , where n e = |E| is the number of entities and n r = |R| the number of relations, that accurately represents that ground truth.”
§ TuckER: Tensor Factorization for Knowledge Graph Completion > 5.1 Full Expressiveness and Embedding Dimensionality
plain- Asserted: passes — The authors put it forward as true.
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- The authors state this as an assumption: Subject and object entity embedding matrices are equivalent, i.e. no distinction is made between the embeddings of an entity depending on whether it appears as a subject or as an object.
In the paper
“The binary tensor learned by DistMult is symmetric in the subject and object entity mode and thus Dist-Mult cannot model asymmetric relations.”
§ TuckER: Tensor Factorization for Knowledge Graph Completion > 1 Introduction
What the sources say
- Not matchedcites Yang et al., 2015
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
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In the paper
“Further, its number of parameters increases linearly with respect to entity and relation embedding dimensionality d e and d r , as the number of entities and relations increases, since the number of parameters of W depends only on the entity and relation embedding dimensionality and not on the number of entities or relations.”
§ TuckER: Tensor Factorization for Knowledge Graph Completion > 4 Tucker Decomposition for Link Prediction
plaindirect- Asserted: passes — The authors put it forward as true.
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- The authors state this as an assumption: Subject and object entity embedding matrices are equivalent, i.e. no distinction is made between the embeddings of an entity depending on whether it appears as a subject or as an object.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“By having the core tensor W, unlike simpler models such as DistMult, Com-plEx and SimplE, TuckER does not encode all the learned knowledge into the embeddings; some is stored in the core tensor and shared between all entities and relations through multi-task learning.”
§ TuckER: Tensor Factorization for Knowledge Graph Completion > 4 Tucker Decomposition for Link Prediction
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- The authors state this as an assumption: Subject and object entity embedding matrices are equivalent, i.e. no distinction is made between the embeddings of an entity depending on whether it appears as a subject or as an object.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Due to the low rank of the core tensor, TuckER benefits from multi-task learning by parameter sharing across relations.”
§ TuckER: Tensor Factorization for Knowledge Graph Completion > 1 Introduction
plaindirect- Asserted: passes — The authors put it forward as true.
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- The authors state this as an assumption: Subject and object entity embedding matrices are equivalent, i.e. no distinction is made between the embeddings of an entity depending on whether it appears as a subject or as an object.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“This shows that the scoring function of ComplEx, which computes a bilinear product with complex entity and relation embeddings and disregards the imaginary part of the obtained result, is equivalent to a hard regularization of the core tensor of TuckER in the real domain.”
§ TuckER: Tensor Factorization for Knowledge Graph Completion > 5.2 Relation to Previous Linear Models
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In the paper
“demonstrating the expressive power of linear models”
§ TuckER: Tensor Factorization for Knowledge Graph Completion > 6.3 Link Prediction Results
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In the paper
“We believe this is because TuckER exploits knowledge sharing between relations through the core tensor, i.e. multi-task learning.”
§ TuckER: Tensor Factorization for Knowledge Graph Completion > 6.3 Link Prediction Results
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In the paper
“while still keeping the desirable property of allowing relations to be asymmetric”
§ TuckER: Tensor Factorization for Knowledge Graph Completion > 5.3 Representing Asymmetric Relations
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In the paper
“However, the drawback of the latter approach is quadratic growth of parameter number with the number of relations”
§ TuckER: Tensor Factorization for Knowledge Graph Completion > 5.3 Representing Asymmetric Relations
plaindirect- Asserted: passes — The authors put it forward as true.
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In the paper
“We do not include their published results in Tables 3 and 4, since they use the highly non-standard d e = d r = 2000 and thus a far larger parameter number (18x more parameters than TuckER on WN18RR; 5.5x on FB15k-237), making their results incomparable to those typically reported, including our own.”
§ TuckER: Tensor Factorization for Knowledge Graph Completion > 6.3 Link Prediction Results
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A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Whilst being fully expressive, TuckER's number of parameters grows linearly with respect to the number of entities or relations in the knowledge graph.”
§ TuckER: Tensor Factorization for Knowledge Graph Completion > 7 Conclusion
plaindirect- Asserted: passes — The authors put it forward as true.
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In the paper
“supporting our belief that the two models both attain the benefits of multi-task learning, although by different means.”
§ TuckER: Tensor Factorization for Knowledge Graph Completion > 6.3 Link Prediction Results
hedgedcorrelational- Asserted: passes — The authors put it forward as true.
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A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“We further show that previous linear state-of-the-art models, RESCAL, DistMult, ComplEx and Sim-plE, can be interpreted as special cases of our model.”
§ TuckER: Tensor Factorization for Knowledge Graph Completion > 7 Conclusion
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- Probably not a substantial claim. 9
- It may state two separate claims as one. 9
Every source the paper cites for this claim was checked and supports it.
In the paper
“As shown in (Trouillon et al., 2017), ComplEx is fully expressive with the embedding dimensionality bound d e = d r = n e • n r .”
§ TuckER: Tensor Factorization for Knowledge Graph Completion > 5.1 Full Expressiveness and Embedding Dimensionality
What the sources say
- Supportedcites Trouillon et al., 2017 source
Theorem 4 in §3.2 (p. 14) shows that ComplEx can represent arbitrary families of relation matrices using a shared entity embedding matrix and diagonal relation matrices of dimension nm, where n is the number of entities and m the number of relations. It states that the decomposition rank is at most nm, matching the claimed dimensionality bound for entity and relation embeddings. (LLM, conf=0.92)
boosted- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
- Supported
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“However, for lower embedding sizes, the dif-ference between MRRs increases by 0.7% for embedding size 50 and by 4.2% for embedding size 20 for ComplEx and by 3% for embedding size 50 and by 9.9% for embedding size 20 for Sim-plE.”
§ TuckER: Tensor Factorization for Knowledge Graph Completion > 6.4 Influence of Parameter Sharing
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Results achieved by TuckER are not only better than those of other linear models, such as DistMult, ComplEx and SimplE, but also better than the results of many more complex deep neural network and reinforcement learning architectures, e.g.R-GCN, MINERVA, ConvE and HypER, demonstrating the expressive power of linear models and supporting our claim that simple linear models should serve as a”
§ TuckER: Tensor Factorization for Knowledge Graph Completion > 6.3 Link Prediction Results
boosted- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Overall, TuckER outperforms previous state-of-the-art models on all metrics across all datasets (apart from hits@10 on WN18 where a non-linear model, R-GCN, does better).”
§ TuckER: Tensor Factorization for Knowledge Graph Completion > 6.3 Link Prediction Results
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“For example, improvement on FB15k is +14% over ComplEx and +8% over SimplE on the toughest hits@1 metric.”
§ TuckER: Tensor Factorization for Knowledge Graph Completion > 6.3 Link Prediction Results
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“It is trivial to show that both RESCAL and DistMult belong to the family of bilinear models.”
§ TuckER: Tensor Factorization for Knowledge Graph Completion > 5.2 Relation to Previous Linear Models
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
In the paper
“It is interesting to note that the TuckER interpretation of the DistMult scoring function, given that matrices A and C are identical, can alternatively be interpreted as a special case of CP decomposition (Hitchcock, 1927), since Tucker decomposition with a superdiagonal core tensor is equivalent to CP decomposition.”
§ TuckER: Tensor Factorization for Knowledge Graph Completion > 5.2 Relation to Previous Linear Models
What the sources say
- Not checked — no full text of the sourcecites Hitchcock, 1927 source
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“We show that TuckER is a fully expressive model, derive sufficient bounds on its embedding dimensionalities and demonstrate that several previously introduced linear models can be viewed as special cases of TuckER.”
- Also stated in: § 1 Introduction · plain
“Finally, we show that several previous stateof-the-art linear models, RESCAL (Nickel et al., 2011), DistMult (Yang et al., 2015), ComplEx (Trouillon et al., 2016) and SimplE (Kazemi and Poole, 2018), are special cases of TuckER.”
- Also stated in: § 1 Introduction · plain
“showing how TuckER subsumes several previously proposed tensor factorization approaches to link prediction.”
§ TuckER: Tensor Factorization for Knowledge Graph Completion > Abstract
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
- The authors state this as an assumption: Subject and object entity embedding matrices are equivalent, i.e. no distinction is made between the embeddings of an entity depending on whether it appears as a subject or as an object.
- Also stated in: § 1 Introduction · plain
In the paper
“Similarly to Com-plEx, Kazemi and Poole (2018) show that SimplE is fully expressive with entity and relation embeddings of size d e = d r = min(n e • n r , γ + 1), where γ represents the number of true facts.”
§ TuckER: Tensor Factorization for Knowledge Graph Completion > 5.1 Full Expressiveness and Embedding Dimensionality
What the sources say
- Not matchedcites Kazemi and Poole (2018)
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
- Not matched
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“So far, there have been two possible ways in which linear link prediction models introduce asymmetry into factorization of the binary tensor of triples: • distinct (although possibly related) embeddings for subject and object entities and a diagonal matrix (or equivalently a vector) for each relation, as is the case with models such as ComplEx and SimplE; or • equivalent subject and object entity”
§ TuckER: Tensor Factorization for Knowledge Graph Completion > 5.3 Representing Asymmetric Relations
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. It may state two separate claims as one.
What the paper did — it cites no source for this, so there is none to check. The quote shows it is in the paper.
In the paper
“We use evaluation metrics standard across the link prediction literature: mean reciprocal rank (MRR) and hits@k, k ∈ {1, 3, 10}.”
§ TuckER: Tensor Factorization for Knowledge Graph Completion > 6.2 Implementation and Experiments
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“TuckER overcomes this by representing relations as vectors w r , which makes the parameter number grow linearly with the number of relations, while still keeping the desirable property of allowing relations to be asymmetric”
§ TuckER: Tensor Factorization for Knowledge Graph Completion > 5.3 Representing Asymmetric Relations
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
- Rests on an assumption: The full rank matrix approach for relations often leads to overfitting, especially for relations with a small number of training triples.
What the paper did — it cites no source for this, so there is none to check. The quote shows it is in the paper.
In the paper
“To test this, we re-implement ComplEx and SimplE with reciprocal relations, 1-N scoring, batch normalization and dropout for fair comparison, perform random search to choose best hyper-parameters”
§ TuckER: Tensor Factorization for Knowledge Graph Completion > 6.4 Influence of Parameter Sharing
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. It may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“TuckER achieves state-of-the-art results on standard link prediction datasets, in part due to its ability to perform multi-task learning across relations.”
§ TuckER: Tensor Factorization for Knowledge Graph Completion > 7 Conclusion
plainconditional- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
In the paper
“We use the filtered setting (Bordes et al., 2013), i.e. all known true triples are removed from the candidate set except for the current test triple.”
§ TuckER: Tensor Factorization for Knowledge Graph Completion > 6.2 Implementation and Experiments
What the sources say
- Not matchedcites Bordes et al., 2013
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim.
- Not matched
What the paper did — it cites no source for this, so there is none to check. The quote shows it is in the paper.
In the paper
“We choose all hyper-parameters by random search based on validation set performance.”
§ TuckER: Tensor Factorization for Knowledge Graph Completion > 6.2 Implementation and Experiments
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
The paper relies on this without support.
Knowledge graphs typically contain only a small subset of all possible facts.
“However, they typically contain only a small subset of all possible facts.”
“However, far from all available information is currently stored in existing knowledge graphs”
The paper relies on this without support.
Manually adding new information to knowledge graphs is costly.
“and manually adding new information is costly”
The authors state this as an assumption.
Subject and object entity embedding matrices are equivalent, i.e. no distinction is made between the embeddings of an entity depending on whether it appears as a subject or as an object.
“Subject and object entity embedding matrices are assumed equivalent, i.e. we make no distinction between the embeddings of an entity depending on whether it appears as a subject or as an object in a particular triple.”
The paper relies on this without support.
The full rank matrix approach for relations often leads to overfitting, especially for relations with a small number of training triples.
“which often leads to overfitting, especially for relations with a small number of training triples.”
The authors state this as an assumption.
TuckER should need a lower number of parameters for obtaining good results than ComplEx or SimplE.
“The ability of knowledge sharing through the core tensor suggests that TuckER should need a lower number of parameters for obtaining good results than ComplEx or SimplE.”
“which supports our initial assumption.”
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
Each contradiction between two passages listed here was confirmed by an independent check.
Rated minor: it would not touch a result — a value no result rests on, a p-value that stays on the same side of the significance level, or a conflict that is clerical, resolved elsewhere in the paper, or outside its own findings.
In the paper
§ TuckER: Tensor Factorization for Knowledge Graph Completion > Model
“RESCAL (Nickel et al., 2011) e s W r e o W r ∈ R de 2 O(n e d e + n r d 2 r )”
§ TuckER: Tensor Factorization for Knowledge Graph Completion > 5.2 Relation to Previous Linear Models
“the relation matrices W r ∈ R de×de are the d e × d e slices of the core tensor Z.”
Rated minor: it would not touch a result — a value no result rests on, a p-value that stays on the same side of the significance level, or a conflict that is clerical, resolved elsewhere in the paper, or outside its own findings.
In the paper
§ TuckER: Tensor Factorization for Knowledge Graph Completion > Model
“W ∈ R de×de×dr is the core tensor of a Tucker decomposition.”
§ TuckER: Tensor Factorization for Knowledge Graph Completion > 4 Tucker Decomposition for Link Prediction
“w r ∈ R dr the rows of R representing the relation embedding vector and W ∈ R de×dr×de is the core tensor.”
Rated minor: it would not touch a result — a value no result rests on, a p-value that stays on the same side of the significance level, or a conflict that is clerical, resolved elsewhere in the paper, or outside its own findings.
In the paper
§ TuckER: Tensor Factorization for Knowledge Graph Completion > 6.3 Link Prediction Results
“Overall, TuckER outperforms previous state-of-the-art models on all metrics across all datasets (apart from hits@10 on WN18 where a non-linear model, R-GCN, does better).”
§ TuckER: Tensor Factorization for Knowledge Graph Completion > Additional information
“| HypER (Balažević et al., 2019) | no | .951 | 958 | .955 | .947 | .790 | .885 | .829 | .734 | | SimplE (Kazemi and Poole, 2018) | yes | .942 | .947 | .944 | .939 | .727 | .838 | .773 | .660 | | TuckER (ours) | yes | .953 | .958 | .955 | .949 | .795 | .892 | .833 | .741 |”
Citations
Cites
The publisher hasn’t deposited this paper’s reference list.
Research works printed but not linked: 6
- Antoine Bordes, Nicolas Usunier, Alberto Garcia- Duran, Jason Weston, and Oksana Yakhnenko. 2013. Translating Embeddings for Modeling Multi- relational Data. In Advances in Neural Information Processing Systems.
- Rajarshi Das, Shehzaad Dhuliawala, Manzil Zaheer, Luke Vilnis, Ishan Durugkar, Akshay Krishna- murthy, Alex Smola, and Andrew McCallum. 2018. Go for a Walk and Arrive at the Answer: Reason- ing over Paths in Knowledge Bases Using Rein- forcement Learning. In International Conference on Learning Representations.
- Seyed Mehran Kazemi and David Poole. 2018. Sim- plE Embedding for Link Prediction in Knowledge Graphs. In Advances in Neural Information Pro- cessing Systems.
- Maximilian Nickel, Volker Tresp, and Hans-Peter Kriegel. 2011. A Three-Way Model for Collective Learning on Multi-Relational Data. In International Conference on Machine Learning.
- Adam Paszke, Sam Gross, Soumith Chintala, Gre- gory Chanan, Edward Yang, Zachary DeVito, Zem- ing Lin, Alban Desmaison, Luca Antiga, and Adam Lerer. 2017. Automatic Differentiation in PyTorch. In NIPS-W.
- Bishan Yang, Wen-tau Yih, Xiaodong He, Jianfeng Gao, and Li Deng. 2015. Embedding Entities and Relations for Learning and Inference in Knowledge Bases. In International Conference on Learning Representations.
Cited by
Sorted by citations
A Survey on Knowledge Graphs: Representation, Acquisition, and Applications
Ji, S., Pan, S., Cambria, E., Marttinen, P., & Yu, P. S. (2022) · IEEE Transactions on Neural Networks and Learning Systems · doi:10.1109/tnnls.2021.3070843 · Cited by 2,947
“nt. & Rel. embed. Scoring Function f r(h;t) RotatE [23] h;t 2Cd, r 2Cd khr tk TorusE [30] [h];[t] 2Tn, [r] 2Tn min (x;y)2([h]+[r]) [t] kx yk i SimplE [47] h;t 2Rd, r;r02Rd 1 2 hrt+ tr0t TuckER [51] h;t 2Rd e , r 2R d r W 1 h 2 r 3 t ITransF [36] h;t 2Rd, r 2Rd H r Dh+ r T r Dt ‘ HolEx [40] h;t 2Rd, r 2Rd P l j=0 p…”
BackgroundMethodInfluentialKnowledge Graphs: Opportunities and Challenges
Peng, C., Xia, F., Naseriparsa, M., & Osborne, F. (2023) · Artificial Intelligence Review · doi:10.1007/s10462-023-10465-9 · Cited by 717
“The core idea of tensor factorization-based methods is transforming the triplets in the knowledge graph into a 3D tensor (Balažević et al. 2019).”
MethodKEPLER: A Unified Model for Knowledge Embedding and Pre-trained Language Representation
Wang, X., Gao, T., Zhu, Z., Zhang, Z., Liu, Z., Li, J., & Tang, J. (2021) · Transactions of the Association for Computational Linguistics · doi:10.1162/tacl_a_00360 · Cited by 676
“This may be because it uses the TuckER (Balazevic et al., 2019) KE model while ERNIE and KEPLER follow TransE (Bordes et al.”
MethodGenerative artificial intelligence: a systematic review and applications
Sengar, S. S., Hasan, A. B., Kumar, S., & Carroll, F. (2024) · Multimedia Tools and Applications · doi:10.1007/s11042-024-20016-1 · Cited by 763
“In this context, Balazevic et al. [10] introduce TuckER, a linear model that employs Tucker decomposition of the binary tensor representation of knowledge graph triples.”
A Comprehensive Survey on Automatic Knowledge Graph Construction
Zhong, L., Wu, J. X., Li, Q., Peng, H., & Wu, X. (2023) · ACM Computing Surveys · doi:10.1145/3618295 · Cited by 494
“Some models, such as RESCAL [246], TuckerER [247], DistMult [248] and NTN [249], consider matching entity pair representations to a latent relational semantic space for predictions with large graphs.”
Method
Metadata
- Authors
- Balazevic, I., Allen, C., & Hospedales, T.
- Affiliations
- University of Edinburgh (GB)
- Venue
- Proceedings of the 2019 Conference on Empirical Methods in Natural Language Processing and the 9th International Joint Conference on Natural Language Processing (EMNLP-IJCNLP)
- Published
- 2019
- Pages
- 5184-5193
- OpenAlex
- W2914592219
- Cited by
- 696
- References
- 0
- Citations by year
- 2026: 81 · 2025: 125 · 2024: 165 · 2023: 137 · 2022: 109 · 2021: 55 · 2020: 21 · 2019: 3
- FWCI
- 17.97
- Type
- conference paper
- Language
- en
- Open access
- gold
- doi.org
- Licence
- cc-by
- Locations
- arXiv (Cornell University) (submittedVersion)
- Edinburgh Research Explorer (University of Edinburgh) (submittedVersion, cc-by)
- arXiv (Cornell University)
- Funders
- University of Edinburgh
- Engineering and Physical Sciences Research Council (EP/L016427/1)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Advanced Graph Neural Networks
- Physical Sciences › Computer Science › Artificial Intelligence › Topic Modeling
- Physical Sciences › Mathematics › Computational Mathematics › Tensor decomposition and applications
- Keywords
- knowledge graph completion, tensor decomposition, Tucker, knowledge graphs
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