# Knowledge Graph & Relational Embeddings

> One thread of 9 from the "embedding" map, covering the 17 papers in it. The other threads are not represented here.
>
> Every quotation was copied word for word from the paper's own text, and
> checked against that text. Quotes marked *inferred* failed that check and
> must be re-checked before use. Quotes marked *not re-checked* have not been
> matched against the paper's text as it now stands, so they carry no current
> verification either. Lines labelled *the tool's reading* are
> model judgment, not quotation, and carry no verification.
>
> **This is a scaffold, not prose.** The citations, quotes and structure are
> real; the argument is yours to write.

> Connects to: Graph Neural Network Embeddings, Domain-Specific Metric Embeddings.

Started with embedding knowledge graph entities and relations as vectors for link prediction (2014-2015), developed sophisticated parameterizations (complex numbers, rotations, tensor decomposition) to model relational structure (2016-2019), then integrated with recommendation systems and heterogeneous information networks (2017-2020).


**Embedding Entities and Relations for Learning and Inference in Knowledge Bases** (2014) \cite{yang2014embedding}

What it did: Unified embedding frameworks under linear/bilinear operators  *(the tool's reading)*

This paper presents a general framework unifying existing multi-relational embedding models like TransE and NTN. It shows that bilinear formulations achieve state-of-the-art results and introduces embedding-based rule extraction via relation composition.  *(the tool's reading)*

> “We consider learning representations of entities and relations in KBs using the neural-embedding approach.”
>
> ✓ verified: found word for word in the paper's own text


**Traversing Knowledge Graphs in Vector Space** (2015) \cite{guu2015traversing}

What it did: Extended embeddings to multi-hop path query answering  *(the tool's reading)*

This work shows embedding models can be recursively applied to answer multi-hop queries by treating them as soft edge traversal operators. It introduces compositional training that improves both path query answering and knowledge base completion.  *(the tool's reading)*

> “An elegant solution to incompleteness is using vector space representations: Controlling the dimensionality of the vector space forces generalization to new facts […].”
>
> ✓ verified: found word for word in the paper's own text


**Holographic Embeddings of Knowledge Graphs** (2015) \cite{nickel2015holographic}

What it did: Holographic embeddings via circular correlation operator  *(the tool's reading)*

This paper proposes holographic embeddings using circular correlation as the compositional operator, achieving efficiency via FFT while capturing rich tensor-product-like interactions. It establishes connections to associative memory models.  *(the tool's reading)*

> “Learning embeddings of entities and relations is an efficient and versatile method to perform machine learning on relational data such as knowledge graphs.”
>
> ✓ verified: found word for word in the paper's own text


**A Review of Relational Machine Learning for Knowledge Graphs** (2015) \cite{nickel2015review}

> “This could be class labels, a regression score, or an unsupervised cluster id or latent vector (embedding).”
>
> ✓ verified: found word for word in the paper's own text


**LINE** (2015) \cite{tang2015line}

> “Given a large network G=(V,E), the problem of Large-scale Information Network Embedding aims to represent each vertex v∈ V into a low-dimensional space R^d, i.e., learning a function f_G:V→ R^d, where d ≪ |V|. In the space R^d, both the first-order proximity and the second-order proximity between the vertices are preserved.”
>
> ✓ verified: found word for word in the paper's own text


**Complex Embeddings for Simple Link Prediction** (2016) \cite{trouillon2016complex}

What it did: Complex-valued embeddings for symmetric/antisymmetric relations  *(the tool's reading)*

This paper introduces complex-valued embeddings with Hermitian dot product composition, enabling natural modeling of both symmetric and antisymmetric relations while maintaining linear complexity. It outperforms prior tensor-based models like NTN and HolE.  *(the tool's reading)*

> “A partially observed matrix or tensor is decomposed into a product of embedding matrices with much smaller rank, resulting in fixed-dimensional vector representations for each entity and relation in the database.”
>
> ✓ verified: found word for word in the paper's own text


**Graph embedding techniques, applications, and performance: A survey** (2017) \cite{goyal2017graph}

> “(Graph embedding) Given a graph G=(V,E), a graph embedding is a mapping f:v_i →y_i∈ℝ^d ∀ i ∈ [n] such that d ≪ |V| and the function f preserves some proximity measure defined on graph G.”
>
> ✓ verified: found word for word in the paper's own text


**Translation-based Recommendation** (2017) \cite{he2017translation}

> “Methodologically, we embed items into a `transition space' where users are modeled as translation vectors operating on item sequences.”
>
> ✓ verified: found word for word in the paper's own text


**A Novel Embedding Model for Knowledge Base Completion Based on Convolutional Neural Network** (2017) \cite{nguyen2017novel}

> “Many embedding models have proposed to learn vector or matrix representations for entities and relations, obtaining state-of-the-art (SOTA) link prediction results […]. In these embedding models, valid triples obtain lower implausibility scores than invalid triples.”
>
> ✓ verified: found word for word in the paper's own text


**Modeling Relational Data with Graph Convolutional Networks** (2017) \cite{schlichtkrull2017modeling}

> “The encoder maps each entity v_i ∈𝒱 to a real-valued vector e_i ∈ℝ^d.”
>
> ✓ verified: found word for word in the paper's own text


**RippleNet** (2018) \cite{wang2018ripplenet}

> “KGE intends to embed entities and relations in a KG into continuous vector spaces while preserving its inherent structure.”
>
> ✓ verified: found word for word in the paper's own text


**Learning Heterogeneous Knowledge Base Embeddings for Explainable Recommendation** (2018) \cite{zhang2018learning}

> “Inspired by […], we project each entity and relation into a unified low-dimensional embedding space. Intuitively, the embedding of a tail entity should be close to its translated head entity embedding.”
>
> ✓ verified: found word for word in the paper's own text


**TuckER: Tensor Factorization for Knowledge Graph Completion** (2019) \cite{balazevic2019tucker}

> “In our case, rows of the matrices contain entity and relation embeddings, while entries of the core tensor determine the level of interaction between them.”
>
> ✓ verified: found word for word in the paper's own text


**Unifying Knowledge Graph Learning and Recommendation: Towards a Better Understanding of User Preferences** (2019) \cite{cao2019unifying}

> “Its basic idea is to learn embeddings for entities and relations, satisfying 𝐞_h+𝐫≈𝐞_t if there is a triplet (e_h, e_t, r) in KG.”
>
> ✓ verified: found word for word in the paper's own text


**RotatE: Knowledge Graph Embedding by Relational Rotation in Complex Space** (2019) \cite{sun2019rotate}

What it did: Rotations in complex space model all relation patterns  *(the tool's reading)*

RotatE redefines relations as rotations in complex vector space, simultaneously modeling symmetry, antisymmetry, inversion, and composition patterns. It generalizes TransE and achieves state-of-the-art across all benchmarks.  *(the tool's reading)*

> “Specifically, the RotatE model maps the entities and relations to the complex vector space and defines each relation as a rotation from the source entity to the target entity.”
>
> ✓ verified: found word for word in the paper's own text


**KGAT** (2019) \cite{wang2019kgat}

> “It recursively propagates the embeddings from a node's neighbors (which can be users, items, or attributes) to refine the node's embedding, and employs an attention mechanism to discriminate the importance of the neighbors.”
>
> ✓ verified: found word for word in the paper's own text


**A Survey on Knowledge Graphs: Representation, Acquisition, and Applications** (2020) \cite{ji2020survey}

> “Recent advances in knowledge-graph-based research focus on knowledge representation learning (KRL) or knowledge graph embedding (KGE) by mapping entities and relations into low-dimensional vectors while capturing their semantic meanings […].”
>
> ✓ verified: found word for word in the paper's own text


_[Your synthesis: what it enabled, what it left unsolved.]_


## Where this thread connects

Each crossing is where one line of work fed another. These are the tool's reading of
the corpus, not quotations.

- **Knowledge Graph & Relational Embeddings** → **Graph Neural Network Embeddings** (2016): Structure-aware node vectors
- **Knowledge Graph & Relational Embeddings** → **Domain-Specific Metric Embeddings** (2018): Knowledge-aware recommendations