Is Architectural Complexity Overrated? Competitive and Interpretable Knowledge Graph Completion with RelatE

TL;DR

The paper challenges the notion that architectural complexity is necessary for strong knowledge graph completion by proposing RelatE, a fully real-valued, interpretable model that decomposes entity and relation representations into phase and modulus components. RelatE uses sinusoidal phase alignment and a slope-weighted modulus scoring to capture symmetry, inversion, and composition, while incorporating lightweight type bias and self-adversarial training for robustness. Theoretical results establish full expressivity with dimension $d = |E||R|$, and empirical results on FB15k-237, WN18RR, and YAGO3-10 show competitive or state-of-the-art performance, with notable efficiency and robustness advantages over complex baselines like RotatE and ComplEx. These findings demonstrate that simple, well-designed real-valued models can match or exceed the performance of more complex architectures while offering practical benefits in training speed, inference latency, memory usage, and interpretability for real-world KG applications.

Abstract

We revisit the efficacy of simple, real-valued embedding models for knowledge graph completion and introduce RelatE, an interpretable and modular method that efficiently integrates dual representations for entities and relations. RelatE employs a real-valued phase-modulus decomposition, leveraging sinusoidal phase alignments to encode relational patterns such as symmetry, inversion, and composition. In contrast to recent approaches based on complex-valued embeddings or deep neural architectures, RelatE preserves architectural simplicity while achieving competitive or superior performance on standard benchmarks. Empirically, RelatE outperforms prior methods across several datasets: on YAGO3-10, it achieves an MRR of 0.521 and Hit@10 of 0.680, surpassing all baselines. Additionally, RelatE offers significant efficiency gains, reducing training time by 24%, inference latency by 31%, and peak GPU memory usage by 22% compared to RotatE. Perturbation studies demonstrate improved robustness, with MRR degradation reduced by up to 61% relative to TransE and by up to 19% compared to RotatE under structural edits such as edge removals and relation swaps. Formal analysis further establishes the model's full expressiveness and its capacity to represent essential first-order logical inference patterns. These results position RelatE as a scalable and interpretable alternative to more complex architectures for knowledge graph completion.

Figures (7)

• Figure 1: RelatE’s phase-modulus decomposition and its modeling of symmetry, inversion, and composition.
• Figure 2: 2D illustrations of RelatE's entity and relation decomposition into modulus and phase components. Left: abstract formulation. Right: example grounded in real-world semantics.
• Figure 3: Retention evaluation (Hit@10) for three models under five perturbation types. RelatE consistently retains the highest performance across conditions, demonstrating robustness to counterfactual injection, relation swaps, and edge manipulations as shown in the UMAP.
• Figure 4: Heatmap showing the relative drop in Mean Reciprocal Rank (%$\Delta$MRR) for RelatE, RotatE, and TransE across five perturbation scenarios. Each cell quantifies the performance degradation from the unperturbed base to the perturbed graph.
• Figure 5: RelatE’s phase and modulus decomposition on YAGO3-10. The modulus space absorbs topological deformation, while phase embeddings retain directional semantic structure under perturbation.

Theorems & Definitions (6)

• Theorem 1
• Lemma 1
• Lemma 2
• proof
• Theorem 2
• proof