KG Embedding

Knowledge graph embedding (KGE) models typically represent each relation as an operator on entity embeddings. In this work, we identify three structural axioms that any principled relation operator must satisfy, linearity, trace preservation, and complete positivity, and show that they characterize a Kraus channel structure via the Kraus representation theorem. The completeness constraint defining this family is equivalent to these axioms, providing a principled foundation rather than an externally imposed condition. Under this formulation, most existing operator-based KGE models are recoverable as special cases with Kraus rank $κ= 1$ under specific embedding choices. We further generalize this characterization to arbitrary metric geometries by introducing \mbox{w-Kraus} channels, which satisfy completeness by construction within their respective spaces. Building on this theory, we propose \textsc{KrausKGE}, a principled KGE model that naturally handles $1$-to-$N$ and $N$-to-$N$ relations, supports $k$-hop reasoning without requiring explicit path encoders, and eliminates the need for norm constraints on entity embeddings. Additionally, our framework yields the first theoretically grounded per-relation complexity measure in the KGE literature, with a provable lower bound in terms of the empirical relation matrix rank. Empirical evaluation demonstrates that \textsc{KrausKGE} consistently outperforms strong baselines on $N$-to-$N$ relations, with performance gains that increase monotonically with relation fan-out, in alignment with theoretical predictions.

We present a method for finding hierarchy-aware embeddings of knowledge graphs (KGs) using graph neural networks (GNNs) enriched with a semantic loss derived from underlying ontologies. This method yields embeddings that better reflect domain knowledge. To demonstrate their utility, we predict and interpret the effects of gene deletions in the yeast Saccharomyces cerevisiae and learn box embeddings for KGs in the absence of a prediction task. We further show how box embeddings can serve as the basis for evaluating KG revisions. Our yeast KG is constructed from community databases and ontology terms. Low-dimensional box embeddings combined with GNNs are used to predict cell growth for double gene knockouts. Over 10-fold cross validation, these predictions have a mean $R^2$scoreof~0.360, significantly higher than baseline comparisons, demonstrating that high-level qualitative knowledge is informative about experimental outcomes. Incorporating semantic loss terms in the training of the models improves their predictive performance ($R^2$=0.377) by aligning embeddings with ontology structure. This shows that class hierarchies from ontologies can be exploited for quantitative prediction. We also test the trained models on triple gene knockouts, showing they generalise to data beyond those seen in training. Additionally, by identifying co-occurring relations in the yeast KG important for the cell-growth predictions, we construct hypotheses about interacting traits in yeast. A biological experiment validates one such finding, revealing an association between inositol utilisation and osmotic stress resistance, highlighting the model's potential to guide biological discovery.

Most multi-modal knowledge graph completion (MMKGC) models use one embedding scorer to do both retrieval over the full entity set and final decision making. We argue that this coupling is a core bottleneck: global high-recall search and local fine-grained disambiguation require different inductive biases. Therefore, we propose a Retrieval-Augmented Discrete Diffusion (RADD) framework to decouple retrieve and reranking for MMKGC. A relation-aware multimodal KGE retriever serves as both global retriever and distillation teacher, while a conditional discrete denoiser performs shortlist-level entity-identity generation for reranking. Training combines KGE supervision, denoising cross-entropy, and temperature-scaled distillation from the retriever to the denoiser. At inference, the designed Diff-Rerank first forms a top-$K$ shortlist with the retriever and then reranks it with the denoiser, ensuring that recall is a strict prerequisite for precision. Experiments on three MMKGC benchmarks show that RADD achieves the best performance and consistent gains over strong unimodal, multimodal, and LLM-based baselines, while ablations further verify the contribution of each component.

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-Lite$^{\mathcal{H}}$ that allows for convex optimization. We show that for any satisfiable DL-Lite$^{\mathcal{H}}$ 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.

Accurate mapping between Common Vulnerabilities and Exposures (CVE) and Common Weakness Enumeration (CWE) entries is critical for effective vulnerability management and risk assessment. However, public databases, such as the National Vulnerability Database (NVD), suffer from inconsistent and incomplete CVE to CWE mappings, complicating automated analysis and remediation. We introduce FixV2W, a lightweight approach that leverages knowledge graph embeddings and longitudinal trends to improve mapping accuracy of the NVD. FixV2W systematically analyzes historical remapping patterns and leverages hierarchical relationships within NVD and CWE data to predict more precise CWE mappings for vulnerabilities linked to Prohibited or Discouraged categories. We run extensive experimental evaluation of FixV2W, based on test data set collected between August 2021 and December 2024. Considering the Top 10 ranked predictions, the results show that FixV2W predicts the correct CWE mappings for 69% of exploited vulnerabilities that had invalid CWEs before they were exploited. We also show that FixV2W significantly improves the performance of ML models relying on NVD data. For instance, for a model geared at uncovering unknown CVE-CWE mappings, FixV2W improves the Mean Reciprocal Rank (MRR) from 0.174 to 0.608. These results show that FixV2W is a promising approach to identify and thwart emerging threats.

Knowledge Graph Embeddings (KGEs) support a wide range of downstream tasks over Knowledge Graphs (KGs). In practice, KGs evolve as new entities and facts are added, motivating Continual Knowledge Graph Embedding (CKGE) methods that update embeddings over time. Current CKGE approaches address catastrophic forgetting (i.e., the performance degradation on previously learned tasks) primarily by limiting changes to existing embeddings. However, we show that this view is incomplete. When new entities are introduced, their embeddings can interfere with previously learned ones, causing the model to predict them in place of previously correct answers. This phenomenon, which we call entity interference, has been largely overlooked and is not accounted for in current CKGE evaluation protocols. As a result, the assessment of catastrophic forgetting becomes misleading, and CKGE methods performance is systematically overestimated. To address this issue, we introduce a corrected CKGE evaluation protocol that accounts for entity interference. Through experiments on multiple benchmarks, we show that ignoring this effect can lead to performance overestimation of up to 25%, particularly in scenarios with significant entity growth. We further analyze how different CKGE methods and KGE models are affected by the different sources of forgetting, and introduce a catastrophic forgetting metric tailored to CKGE.

Temporal knowledge graph (TKG) extrapolation is an important task that aims to predict future facts through historical interaction information within KG snapshots. A key challenge for most existing TKG extrapolation models is handling entities with sparse historical interaction. The ontological knowledge is beneficial for alleviating this sparsity issue by enabling these entities to inherit behavioral patterns from other entities with the same concept, which is ignored by previous studies. In this paper, we propose a novel encoder-decoder framework OntoTKGE that leverages the ontological knowledge from the ontology-view KG (i.e., a KG modeling hierarchical relations among abstract concepts as well as the connections between concepts and entities) to guide the TKG extrapolation model's learning process through the effective integration of the ontological and temporal knowledge, thereby enhancing entity embeddings. OntoTKGE is flexible enough to adapt to many TKG extrapolation models. Extensive experiments on five data sets demonstrate that OntoTKGE not only significantly improves the performance of many TKG extrapolation models but also surpasses many state-of-the-art(SOTA) baseline methods.