Probabilistic Box Embeddings for Uncertain Knowledge Graph Reasoning

Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

ConceptNet is a multilingual KG of commonsense concepts, where triples are assigned confidence measures reflecting crowdsourcing agreement.

“ConceptNet (Speer et al., 2017) is a multilingual KG of commonsense concepts, where triples are assigned with confidence measures reflecting crowdsourcing agreement.”

• cites Speer et al., 2017 sourcePartly supported

  The Introduction (p. 1) describes ConceptNet as a multilingual knowledge graph with weighted assertions, and the paper represents assertions as triples (p. 1). It does not say that the weights measure crowdsourcing agreement; Knowledge Sources (p. 2) describes inputs from crowdsourcing alongside dictionaries and other resources. (LLM, conf=0.87)

  Experimental — accuracy not yet measured

Probably not a substantial claim: may not pass S3 (load-bearing).

UKGE trains the embedding model as a regressor to predict the confidence score.

“the representative work UKGE (Chen et al., 2019) models the triple plausibility in the form of embedding product (Yang et al., 2015), and trains the embedding model as a regressor to predict the confidence score.”

• cites Chen et al., 2019 sourceSupported
• cites Yang et al., 2015Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

Probably not a substantial claim: may not pass S3 (load-bearing).

UKGE models triple plausibility in the form of embedding product.

“the representative work UKGE (Chen et al., 2019) models the triple plausibility in the form of embedding product (Yang et al., 2015), and trains the embedding model as a regressor to predict the confidence score.”

• cites Chen et al., 2019 sourceSupported
• cites Yang et al., 2015Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

Poincaré embeddings represent entities in hyperbolic space, leveraging the inductive bias of negative curvature to fit hierarchies.

“Poincaré embeddings (Nickel and Kiela, 2017) represent entities in hyperbolic space, leveraging the inductive bias of negative curvature to fit hierarchies.”

• cites Nickel and Kiela, 2017 sourceSupported

Probably not a substantial claim: may not pass S3 (load-bearing).

Hyperbolic entailment cones combine order embeddings with hyperbolic geometry.

“Hyperbolic entailment cones (Ganea et al., 2018) combine order embeddings with hyperbolic geometry.”

• cites Ganea et al., 2018 sourceSupported

Probably not a substantial claim: may not pass S3 (load-bearing).

UKGE is the first work of UKG embedding methods.

“UKGE (Chen et al., 2019) is the first work of this kind, which models triple plausibility as product of embedding vectors (Yang et al., 2015), and maps the plausibility to the confidence score range of [0, 1].”

• cites Chen et al., 2019 sourceSupported

May combine two claims.

The rigid structure imposed by the cone representation limits representational capacity, and the resulting model cannot model negative correlation or disjointness.

“Lai and Hockenmaier (2017) extend order embeddings with a probabilistic interpretation by integrating the volume of the infinite cones under the negative exponential measure, however the rigid structure imposed by the cone representation limits the representational capacity, and the resulting model cannot model negative correlation or disjointness.”

• cites Lai and Hockenmaier, 2017 sourceSupported

Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

Adam was used as the optimizer and hyper-parameters were fine-tuned by grid search based on validation set performance.

“We use Adam (Kingma and Ba, 2014) as the optimizer and fine-tune the following hyper-parameters by grid search based on the performance on the validation set, i.e.MSE for confidence prediction and normalized Discounted Cumulative Gain (nDCG) for fact ranking.”

• cites Kingma and Ba, 2014 sourceSupported

Probably not a substantial claim: may not pass S3 (load-bearing).

Following Chen et al. (2019), only facts with confidence above the threshold τ = 0.85 were used to train deterministic models.

“Following Chen et al. (2019), we only use facts with confidence above the threshold τ = 0.85 to train deterministic models.”

• cites Chen et al. (2019) sourcePartly supported

  Section 5.4 (pp. 5–6) says the deterministic baseline models were trained using only high-confidence relation facts, selected with a KG-specific threshold τ. Section 5.7 (p. 7) defines a strong fact as one whose confidence exceeds that threshold. Our copy does not establish τ = 0.85 as the threshold, so the numerical part of the attribution is unsupported. (LLM, conf=0.88)

  Experimental — accuracy not yet measured

May combine two claims.

Box embeddings capture probabilistic semantics based on box volumes, and are capable of compactly representing conditional probability distributions.

“Box embeddings not only demonstrate improved performance on modeling hierarchies, such embeddings also capture probabilistic semantics based on box volumes, and are capable of compactly representing conditional probability distributions.”

• cites Vilnis et al., 2018 sourceSupported

Classified as probably not a substantial claim.

Probabilistic box embeddings represent elements using axis-aligned hyperrectangles (boxes).

“Introduced by Vilnis et al. (2018), probabilistic box embeddings represent elements using axis-aligned hyperrectangles (or boxes).”

• cites Vilnis et al., 2018 sourceSupported

Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

Patel et al. demonstrate the capability of box embeddings to jointly model two hierarchical relations, which is improved upon using a learned transform by Dasgupta et al.

“In (Patel et al., 2020), the authors demonstrate the capability of box embeddings to jointly model two hierarchical relations, which is improved upon using a learned transform in (Dasgupta et al., 2021).”

• cites Patel et al., 2020Not checked — no full text of the source
• cites Dasgupta et al., 2021 sourceSupported

May combine two claims.

Query2Box and BoxE make use of boxes in the loss function of their models, but entities themselves are represented as vectors.

“Query2Box (Ren et al., 2020) and BoxE (Abboud et al., 2020) make use of boxes in the loss function of their models, however entities themselves are represented as vectors, and thus these models do not benefit from the probabilistic semantics of box embeddings, which we rely on heavily for modeling UKGs.”

• cites Ren et al., 2020 sourceSupported
• cites Abboud et al., 2020 sourceSupported

Classified as probably not a substantial claim.

Box volumes can be interpreted as unnormalized probabilities.

“Vilnis et al. (2018) note that this allows one to interpret box volumes as unnormalized probabilities.”

• cites Vilnis et al., 2018 sourceSupported

Probably not a substantial claim: may not pass S3 (load-bearing).

GumbelBox is a training improvement method for box embeddings.

“A few training improvement methods for box embeddings have been proposed (Li et al., 2019;Dasgupta et al., 2020), and we make use of the latter, which is termed GumbelBox after the distribution used to model endpoints of boxes.”

• cites Dasgupta et al., 2020 sourceSupported

Probably not a substantial claim: may not pass S3 (load-bearing).

Deterministic KG embedding models TransE, DistMult, ComplEx, RotatE, and TuckER have demonstrated high performance on reasoning tasks for deterministic KGs.

“Deterministic KG embedding models TransE (Bordes et al., 2013), DistMult (Yang et al., 2015), ComplEx (Trouillon et al., 2016), RotatE (Sun et al., 2019), and TuckER (Balazevic et al., 2019) have demonstrated high performance on reasoning tasks for deterministic KGs, and we also include them as baselines.”

• cites Bordes et al., 2013Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

• cites Yang et al., 2015Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

• cites Trouillon et al., 2016 sourceSupported

May combine two claims.

BEUrRE makes use of a learned transform for each relation, differs from Ren et al. in that entities themselves are boxes, and differs from both Ren et al. and Dasgupta et al. in the structure of the learned transform.

“Similarly to Ren et al. (2020) and Dasgupta et al. (2021), we also make use of a learned transform for each relation, however we differ from Ren et al. (2020) in that entities themselves are boxes, and differ from both in the structure of the learned transform.”

• cites Ren et al., 2020 sourceSupported
• cites Dasgupta et al., 2021 sourceSupported

May combine two claims.

Extensive experiments on two benchmark datasets show that BEUrRE consistently outperforms baseline models on ranking and predicting confidence of unseen facts.

“Extensive experiments on two benchmark datasets show that BEUrRE effectively captures the uncertainty, and consistently outperforms the baseline models on ranking and predicting confidence of unseen facts.”

May combine two claims.

Under both the unconstrained and logically constrained settings, BEUrRE outperforms the baselines in terms of MSE on both CN15k and NL27k.

“Under both settings, BEUrRE outperforms the baselines in terms of MSE on both datasets.”

May combine two claims.

On NL27k, BEUrRE offers 0.009 higher linear nDCG and 0.013 higher exponential nDCG.

“On NL27k, it offers 0.009 higher linear nDCG and 0.013 higher exponential nDCG.”

May combine two claims.

Under the unconstrained setting, BEUrRE improves MSE of the best baseline UKGE by 0.012 (ca.14% relative improvement) on CN15k and 0.003 (ca.11% relative improvement) on NL27k.

“Under the unconstrained setting, BEUrRE improves MSE of the best baseline UKGE by 0.012 (ca.14% relative improvement) on CN15k and 0.003 (ca.11% relative improvement) on NL27k.”

May combine two claims.

With logical constraints, BEUrRE (rule+) further enhances the performance of BEUrRE and reduces its MSE by 0.0031 (ca.4% relative improvement) on CN15k and 0.0036 (ca.15% relative improvement) on NL27k.

“With logical constraints, BEUrRE (rule+) further enhances the performance of BEUrRE and reduces its MSE by 0.0031 (ca.4% relative improvement) on CN15k and 0.0036 (ca.15% relative improvement) on NL27k.”

May combine two claims.

UKGE explicitly models uncertainty of facts and is the best performing baseline.

“UKGE explicitly models uncertainty of facts and is the best performing baseline.”

May combine two claims.

The proposed BEUrRE leads to more improvements under both the unconstrained and logically constrained settings.

“The proposed BEUrRE leads to more improvements under both the unconstrained and logically constrained settings.”

May combine two claims.

URGE ignores relation information and yields worse predictions than other models.

“URGE ignores relation information and yields worse predictions than other models.”

• AssumptionRests on an assumption: URGE cannot handle multirelational graphs.

May combine two claims.

Under the unconstrained setting, using soft boxes increases MSE by 0.0033 on CN15k (ca.4% relative degradation), with even worse performance observed when adding logical constraints.

“Under the unconstrained setting, using soft boxes increases MSE by 0.0033 on CN15k (ca.4% relative degradation), with even worse performance observed when adding logical constraints.”

May combine two claims.

Even without constraints in learning, BEUrRE can still achieve comparable MSE and MAE to the logically constrained UKGE (rule+) on both datasets and even outperforms UKGE (rule+) on CN15k.

“It is worth noting that even without constraints in learning, BEUrRE can still achieve comparable MSE and MAE to the logically constrained UKGE (rule+) on both datasets and even outperforms UKGE (rule+) on CN15k.”

Probably not a substantial claim: may not pass S4 (based).

The geometry of boxes allows efficient calculation of intersections and volumes.

“The geometry of the boxes allows for efficient calculation of intersections and volumes, endowing the model with calibrated probabilistic semantics and facilitating the incorporation of relational constraints.”

Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

Order embeddings represent nodes of a graph using infinite cones, and use containment between cones to represent edges.

“Order embeddings (Vendrov et al., 2016) take a regionbased approach, representing nodes of a graph using infinite cones, and using containment between cones to represent edges.”

• cites Vendrov et al., 2016Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

Probably not a substantial claim: may not pass S4 (based).

It is difficult to model marginal and joint probabilities for entities using simple geometric objects like vectors.

“It is difficult to model marginal and joint probabilities for entities using simple geometric objects like vectors.”

Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

NELL collects facts from web pages with an active-learnable information extraction model, and measures their confidence scores by semi-supervised learning with the Expectation-Maximum (EM) algorithm.

“NELL (Mitchell et al., 2018) collects facts from web pages with an active-learnable information extraction model, and measures their confidence scores by semi-supervised learning with the Expectation-Maximum (EM) algorithm.”

• cites Mitchell et al., 2018Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

The quote only partly states this claim.

BEUrRE's technique is more robust to noise than UKGE's PSL-based method.

“This technique is more robust to noise and has wide coverage that is not restricted by the scarcity of the existing triples.”

Probably not a substantial claim: may not pass S3 (load-bearing).

UOKGE jointly encodes the graph structure and the ontology structure to improve confidence prediction performance.

“UOKGE (Boutouhami et al., 2020) jointly encodes the graph structure and the ontology structure to improve the confidence prediction performance, which however requires an additional ontology of entity types that is not always available to all KGs.”

• cites Boutouhami et al., 2020 sourceNot checked — no full text of the source

Probably not a substantial claim: may not pass S3 (load-bearing).

Probase is a general probabilistic taxonomy obtained from syntactic extraction.

“Probase (Wu et al., 2012) is a general probabilistic taxonomy obtained from syntactic extraction.”

• cites Wu et al., 2012Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

Probably not a substantial claim: may not pass S4 (based).

Reasoning results of existing embedding methods lack global consistency.

“however existing embedding methods only model triple-level uncertainty and reasoning results lack global consistency.”

Probably not a substantial claim: may not pass S3 (load-bearing).

URGE only considers node proximity in networks.

“However, URGE only considers the node proximity in the networks.URGE cannot handle multi-relational data and only generates node embeddings.”

• cites Hu et al., 2017Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

Probably not a substantial claim: may not pass S2 (checkable), S4 (based).

Without an explicit dependency structure it is difficult to enforce logical reasoning rules to maintain global consistency.

“Without an explicit dependency structure it is difficult to enforce logical reasoning rules to maintain global consistency.”

May combine two claims.

BEUrRE's outperformance is due to its probabilistic calibration and ability to capture high-order dependencies among facts.

“Extensive experiments on two benchmark datasets show that BEUrRE consistently outperforms baselines on confidence prediction and fact ranking due to it's probabilistic calibration and ability to capture high-order dependencies among facts.”

Probably not a substantial claim: may not pass S4 (based).

Existing embedding methods only model triple-level uncertainty.

“however existing embedding methods only model triple-level uncertainty and reasoning results lack global consistency.”

Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

Each experiment was repeated five times and the average results were reported.

“We repeat each experiment five times and report the average results.”

Probably not a substantial claim: may not pass S4 (based).

The constraints of relations in CN15k mainly describe transitivity.

“Considering that constraints of relations in CN15k mainly describe transitivity, the aforementioned observation is consistent with the fact that box embeddings are naturally good at capturing transitive relations, as shown in the recent study (Vilnis et al., 2018).”

May combine two claims.

Although deterministic models do not explicitly capture the confidence of facts, they are trained with high-confidence facts and have a certain ability to differentiate high confidence facts from lesser ones.

“Although the deterministic models do not explicitly capture the confidence of facts, those models are trained with highconfidence facts and have a certain ability to differentiate high confidence facts from lesser ones.”

May combine two claims.

Box embeddings improve accuracy and consistency of reasoning and BEUrRE delivers better fact ranking performance than baselines.

“In summary, box embeddings improve accuracy and consistency of reasoning and BEUrRE delivers better fact ranking performance than baselines.”

May combine two claims.

Box volume effectively represents probabilistic semantics and captures specificity/granularity of concepts.

“This observation confirms that the box volume effectively represents probabilistic semantics and captures specificity/granularity of concepts, which we believe to be a reason for the performance improvement.”

Classified as probably not a substantial claim. May combine two claims.

The model proposed in the paper aims to model uncertainty in knowledge graphs more accurately, and the effectiveness of the proposed model is supported by the empirical experiment results.

“The model pro-posed in the paper aims to model uncertainty in knowledge graphs more accurately, and the effectiveness of the proposed model is supported by the empirical experiment results.”

Classified as probably not a substantial claim.

Deterministic KG embedding models cannot predict confidence scores for uncertain facts.

“These models cannot predict confidence scores for uncertain facts, so we compare our method with them only on the ranking task.”

Probably not a substantial claim: may not pass S3 (load-bearing).

Training terminates with early stopping based on the same metric with a patience of 30 epochs.

“Training terminates with early stopping based on the same metric with a patience of 30 epochs.”

Classified as probably not a substantial claim.

Those entities are very specific locations.

“Those entities are very specific locations.”