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Title: MDE: Multiple Distance Embeddings for Link Prediction in Knowledge Graphs

Paper content:
Over the past decade, knowledge graphs became popular for capturing structured domain knowledge.
Relational learning models enable the prediction of missing links inside knowledge graphs.
More specifically, latent distance approaches model the relationships among entities via a distance between latent representations.
Translating embedding models (e.g., TransE) are among the most popular latent distance approaches which use one distance function to learn multiple relation patterns.
However, they are mostly inefficient in capturing symmetric relations since the representation vector norm for all the symmetric relations becomes equal to zero.
They also lose information when learning relations with reflexive patterns since they become symmetric and transitive.
We propose the Multiple Distance Embedding model (MDE) that addresses these limitations and a framework which enables collaborative combinations of latent distance-based terms (MDE).
Our solution is based on two principles:
1) using limit-based loss instead of margin ranking loss and
2) by learning independent embedding vectors for each of terms we can collectively train and predict using contradicting distance terms.
We further demonstrate that MDE allows modeling relations with (anti)symmetry, inversion, and composition patterns.
We propose MDE as a neural network model which allows us to map non-linear relations between the embedding vectors and the expected output of the score function.
Our empirical results show that MDE outperforms the state-of-the-art embedding models on several benchmark datasets.
While machine learning methods conventionally model functions given sample inputs and outputs, a subset of Statistical Relational Learning (SRL) (De Raedt, 2008; Nickel et al., 2015) approaches specifically aim to model "things" (entities) and relations between them.
These methods usually model human knowledge which is structured in the form of multi-relational Knowledge Graphs (KG).
KGs allow semantically rich queries and are used in search engines, natural language processing (NLP) and dialog systems.
However, they usually miss many of the true relations (West et al., 2014) , therefore, the prediction of missing links/relations in KGs is a crucial challenge for SRL approaches.
A KG usually consists of a set of facts.
A fact is a triple (head, relation, tail) where heads and tails are called entities.
Among the SRL models, distance-based KG embeddings are popular because of their simplicity, their low number of parameters, and their efficiency on large scale datasets.
Specifically, their simplicity allows integrating them into many models.
Previous studies have integrated them with logical rule embeddings (Guo et al., 2016) , have adopted them to encode temporal information (Jiang et al., 2016) and have applied them to find equivalent entities between multi-language datasets (Muhao et al., 2017) .
Soon after the introduction of the first multi-relational distance-based method TransE (Bordes et al., 2013) it was acknowledged that it is inefficient in learning of symmetric relations, since the norm of the representation vector for all the symmetric relations in the KG becomes close to zero.
This means the model cannot distinguish well between different symmetric relations in a KG.
To extend this model many variations are studied afterwards, e.g., TransH (Wang et al., 2014b) , TransR (Lin et al., 2015b) , TransD (Ji et al., 2015) , and STransE (Dat et al., 2016) .
Even though they solved the issue of symmetric relations, they introduced a new problem: these models were no longer efficient in learning the inversion and composition relation patterns that originally TransE could handle.
Besides, as noted in (Kazemi & Poole, 2018; Sun et al., 2019) , within the family of distancebased embeddings, usually reflexive relations are forced to become symmetric and transitive.
In this study, we take advantage of independent vector representations of vectors that enable us to view the same relations from different aspects and put forward a translation-based model that addresses these limitations and allows the learning of all three relation patterns.
In addition, we address the issue of the limit-based loss function in finding an optimal limit and suggest an updating limit loss function to be used complementary to the current limit-based loss function which has fixed limits.
Moreover, we frame our model into a neural network structure that allows it to learn non-linear patterns between embedding vectors and the expected output which substantially improves the generalization power of the model in link prediction tasks.
The model performs well in the empirical evaluations, improving upon the state-of-the-art results in link prediction benchmarks.
Since our approach involves several elements that model the relations between entities as the geometric distance of vectors from different views, we dubbed it multipledistance embeddings (MDE).
In this study, we showed how MDE relieves the expressiveness restrictions of the distance-based embedding models and proposed a general method to override these limitations for the older models.
Beside MDE and RotatE, most of the existing KG embedding approaches are unable to allow modeling of all the three relation patterns.
We framed MDE into a Neural Network structure and validated our contributions via both theoretical proofs and empirical results.
We demonstrated that with multiple views to translation embeddings and using independent vectors (that previously were suggested to cause poor performance (Trouillon et al., 2017; Kazemi & Poole, 2018) ) a model can outperform the existing state-of-the-art models for link prediction.
Our experimental results confirm the competitive performance of MDE and particularly MDE N N that achieves state-of-the-art MR and Hit@10 performance on all the benchmark datasets.

assistant: text: A novel method of modelling Knowledge Graphs based on Distance Embeddings and Neural Networks