# BoxLitE: A Faithful Knowledge Base Embedding Based on Convex Optimization

arXiv: https://arxiv.org/abs/2605.23937 · HTML: https://mlsanity.com/paper/2605.23937/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 21 of its 57 references that are in the map.
- First posted on arXiv 27 Apr 2026.

## Builds on (most cited first, 21 of 21)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Embedding Entities and Relations for Learning and Inference in Knowledge Bases](https://mlsanity.com/paper/1412.6575/) (2014)
- [Complex Embeddings for Simple Link Prediction](https://mlsanity.com/paper/1606.06357/) (2016)
- [RotatE: Knowledge Graph Embedding by Relational Rotation in Complex Space](https://mlsanity.com/paper/1902.10197/) (2019)
- [CVXPY: A Python-Embedded Modeling Language for Convex Optimization](https://mlsanity.com/paper/1603.00943/) (2016)
- [TuckER: Tensor Factorization for Knowledge Graph Completion](https://mlsanity.com/paper/1901.09590/) (2019)
- [SimplE Embedding for Link Prediction in Knowledge Graphs](https://mlsanity.com/paper/1802.04868/) (2018)
- [A Rewriting System for Convex Optimization Problems](https://mlsanity.com/paper/1709.04494/) (2017)
- [Stochastic subgradient method converges on tame functions](https://mlsanity.com/paper/1804.07795/) (2018)
- [BoxE: A Box Embedding Model for Knowledge Base Completion](https://mlsanity.com/paper/2007.06267/) (2020)
- [PyKEEN 1.0: A Python Library for Training and Evaluating Knowledge Graph Embeddings](https://mlsanity.com/paper/2007.14175/) (2020)
- [Conservative set valued fields, automatic differentiation, stochastic gradient method and deep learning](https://mlsanity.com/paper/1909.10300/) (2019)
- [EL Embeddings: Geometric construction of models for the Description Logic EL ++](https://mlsanity.com/paper/1902.10499/) (2019)
- [Dual Box Embeddings for the Description Logic EL++](https://mlsanity.com/paper/2301.11118/) (2023)
- [The DL-Lite Family and Relations](https://mlsanity.com/paper/1401.3487/) (2014)
- [From Knowledge Graph Embedding to Ontology Embedding? An Analysis of the Compatibility between Vector Space Representations and Rules](https://mlsanity.com/paper/1805.10461/) (2018)
- [Description Logic EL++ Embeddings with Intersectional Closure](https://mlsanity.com/paper/2202.14018/) (2022)
- [Geometric Models for (Temporally) Attributed Description Logics](https://mlsanity.com/paper/2108.12239/) (2021)
- [Knowledge Base Embeddings: Semantics and Theoretical Properties](https://mlsanity.com/paper/2408.04913/) (2024)
- [Faithful Differentiable Reasoning with Reshuffled Region-based Embeddings](https://mlsanity.com/paper/2406.09529/) (2024)

## Abstract (arXiv)

Knowledge base (KB) embeddings aim at combining the capability of classical knowledge graph embeddings to generalize the information present in facts, the ABox, with conceptual knowledge represented in an ontology language, the TBox. Several authors have recently explored the idea of mapping concepts to convex regions in a vector space. This is useful to represent hierarchies, typically present in TBoxes, since more general concepts can be mapped to larger regions, containing those regions associated with more specific concepts. However, the power of convexity is rarely leveraged during the actual learning tasks. Here, we introduce BoxLitE, a KB embedding model for DL-LiteH that allows for convex optimization. We show that for any satisfiable DL-LiteH KB, there is a BoxLitE embedding that is a weakly faithful model. As a proof of concept, we show how to formulate the KB embedding task as a convex optimization problem and how to obtain embeddings with such desirable faithfulness properties.