Leveraging 3 D G aussian for Temporal Knowledge Graph Embedding (2025)

Abstract: Representation learning in knowledge graphs (KGs) has predominantly focused on static data, yet many real-world knowledge graphs are inherently dynamic. For instance, the fact (The CEO of Apple, holds position, Steve Jobs) was valid until 2011, after which it changed, emphasizing the need to incorporate temporal information into knowledge representation. In this paper, we propose 3DG-TE, a novel temporal KG embedding method inspired by 3D Gaussian Splatting, where entities, relations, and timestamps are modeled as 3D Gaussian distributions with learnable structured covariance. This approach optimizes the Gaussian distributions of entities, relations, and timestamps to improve the overall KG representation. To effectively capture temporal-relational interactions, we design structured covariances that form composite transformation operators: relations induce rotational transformations, while timestamps regulate adaptive scaling. We also design a compound scoring function that integrates mean positions and structured covariance, preserving geometric interpretability. Experimental results on three benchmark TKG datasets demonstrate that 3DG-TE outperforms state-of-the-art baselines in temporal link prediction tasks. Theoretical analysis further confirms our model’s ability to capture key relation patterns.

## introduction knowledge graphs (kgs) are extensively employed as structured frameworks for modeling and organizing complex relationships among entities, and they have become foundational tools in domains such as semantic search @xcite , recommendation systems @xcite , and question answering @xcite . while traditional kgs are effective in many contexts, they fall short in capturing the temporal dimension of knowledge, which is essential for representing real-world * corresponding author data where facts are time-dependent. for instance, the statement "barack obama is the president of the united states" is only valid between 2009 and 2017. to address this limitation, temporal knowledge graph embedding (tkge) models have been developed. these models extend traditional kgs by incorporating temporal information to indicate when a fact is valid. early tkge methods built upon translationbased kge method transe @xcite by encoding time as translations same as relations @xcite . recent works have pointed out that tkgs inherently exhibit uncertainties and randomness. atise @xcite ) employs an additive time series decomposition approach that models temporal uncertainty using gaussian noise. tkgc-agp @xcite uses multivariate gaussian processes to model temporal dependencies and uncertainties. in addition, tensor decomposition-based tkge models @xcite @xcite have been developed. the latest research introduces mod-els that encode tkgs using composite structures. hge @xcite employs a hybrid space to enhance the representation of temporal dynamics, while tcompounde @xcite ) leverages relation-specific and time-specific compound geometric operations to model both temporal evolution and relational structures more effectively. tkge has become a key research area for modeling the temporal kgs. in this paper, we propose 3dg-te, a novel tkge approach inspired by the principles of 3d gaussian splatting @xcite . in computer graphics, 3d gaussian splatting is widely used for scene representation and rendering, where each gaussian models a local point distribution to efficiently reconstruct complex surfaces. inspired by 3d gaussian splatting, 3dg-te encodes each quadruple (s, r, o, t) as a structured representation of a fact, where entities, relations, and timestamps are modeled as 3d gaussian ellipsoid, as shown in figure 1 . 3dg-te optimizes 3d gaussian ellipsoid of entities, relations, and timestamps to more accurately represent quadruple facts, thereby enhancing link prediction performance. to more accurately model relation and timestamp interactions, we further design structured covariance representations in which relations induce rotational transformations, while timestamps regulate adaptive scaling, forming composite transformation operators. 3dg-te focuses on 3d gaussian space modeling over conventional probabilistic kge modeling, such as atise @xcite and tkgc-agp @xcite . this enables our model to capture rich temporal interactions among entities, relations, and timestamps in tkgs, thereby facilitating more effective tkg modeling. specifically, atise captures temporal evolution through additive time series decomposition. however, it primarily assumes independent gaussian noise to model temporal uncertainty, which may limit its ability to capture complex interactions among time, entities, and relations. in contrast, our model is designed with a full 3d gaussian structured covariance, but rather gaussian noise, thus enabling accurate learning of the dynamics of relation and timestamp interactions in the tkg. tkgc-agp models temporal evolution using multivariate gaussian processes, leveraging kernel functions to ensure smooth temporal transitions. howerer, its reliance on gaussian process regression may limit scalability when applied to large-scale knowledge graphs. instead, our approach replaces gaussian process regression with a learnable 3d gaussian that designs relation-and time-structured covariances to capture tkg interactions. this design enables our model to achieve superior performance on large-scale datasets gdelt. in addition, experimental results on other benchmark tkg datasets confirm that our approach surpasses state-of-the-art tkge models foot_0 . due to space constraints, the content of the related work section can be found in appendix a. ## conclusion we presented 3dg-te, a novel temporal knowledge graph embedding framework that leverages 3d gaussian representations to model temporalrelational interactions. by decomposing covariance matrices into relation-driven rotations and time-specific scaling operations, our approach effectively encodes tkgs and achieves the excellent performance. furthermore, our experiments confirm the critical roles of relations and time in modeling temporal knowledge graphs, providing quantitative evidence to support this claim. finally, theoretical proofs demonstrate 3dg-te can encode important relational patterns.