## SME Linear

Tags: #machine learning #KG### Equation

$$\epsilon(lhs,rel,rhs)=E_{lhs(rel)}^{T}E_{rhs(rel)} \\=(W_{l1}E_{lhs}^{T} + W_{l2}E_{rel}^{T} + b_{l})^{T}(W_{r1}E_{rhs}^{T} + W_{r2}E_{rel}^{T} + b_{r})$$### Latex Code

\epsilon(lhs,rel,rhs)=E_{lhs(rel)}^{T}E_{rhs(rel)} \\=(W_{l1}E_{lhs}^{T} + W_{l2}E_{rel}^{T} + b_{l})^{T}(W_{r1}E_{rhs}^{T} + W_{r2}E_{rel}^{T} + b_{r})

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### Introduction

#### Equation

#### Latex Code

#### Explanation

The energy function E (denoted SME) is encoded using a neural network, whose architecture first processes each entity in parallel, like in siamese networks. The intuition is that the relation type should first be used to extract relevant components from each argument’s embedding, and put them in a space where they can then be compared. See paper A Semantic Matching Energy Function for Learning with Multi-relational Data for more details.

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