FITTER: Vocabulary-Agnostic Cross-Domain Inference on Temporal Knowledge Graphs

Temporal knowledge graphs are central to many uses of the Semantic Web, but existing completion methods assume the entities, relation names, and timestamps to be reasoned about are already known at training time, restricting each model to a single graph and vocabulary. We propose FITTER, the first fully-inductive structural model for temporal knowledge graph link prediction that supports cross-domain transfer: the inference graph may contain entirely unseen entities, relation names, and timestamps drawn from a different domain. FITTER represents each predicate by its interaction patterns with others and time through encodings of relative rather than absolute ordering; message-passing fuses local and global temporal context to produce vocabulary-agnostic embeddings. We prove the temporal encoding is time-shift invariant and evaluate FITTER on cross-domain, cross-graph transfer over six temporal knowledge graph benchmarks of diverse domains, granularities, and time spans. FITTER consistently outperforms inductive baselines without retraining, indicating that vocabulary-agnostic structural learning is a viable foundation for inference over the heterogeneous knowledge graphs of the Semantic Web.

STEREODISCO: Discovering Stereotypicality in LLMs

LLMs encode, convey, and perpetuate stereotypes. Prior computational research focuses on a small set of semantic axes investigated in social psychology, and operates on word embeddings produced by language models, leaving open which other semantic axes carry stereotypical associations in LLMs and how LLMs internally represent such axes. We introduce STEREODISCO, a framework that adapts the semantic differential method (Osgood et al., 1957) to the systematic study of stereotypes in LLM internal representations. STEREODISCO constructs approx. 2,000 candidate semantic axes from WordNet antonym synsets, recovers each as a geometric axis in the LLM's activation space via probing, and identifies stereotypical axes via a statistical test over concept projections. As a case study, we apply STEREODISCO to social group stereotypes with LLAMA-3-8B-INSTRUCT and MISTRAL-7B-INSTRUCT. We find that the two LLMs agree with each other on social group ratings more than with humans, suggesting that LLM-encoded stereotype content diverges from that documented in social psychology. We also discover stereotypical axes not investigated in prior work -- including humble vs. proud, narrow-minded vs. broad-minded, and cowardly vs. brave, which human annotators independently confirm.

Leveraging Graph Structure in Seq2Seq Models for Knowledge Graph Link Prediction

We introduce Graph-Augmented Sequence-to-Sequence (GA-S2S), a novel framework that integrates a T5-small encoder-decoder with a Relational Graph Attention Network (RGAT) to improve link prediction in knowledge graphs. While existing Seq2Seq models rely solely on surface-level textual descriptions of entities and relations and at best, flatten the neighborhoods of a query entity into a single linear sequence, thereby discarding the inherent graph structure, GA-S2S jointly encodes both textual features and the full $k$-hop subgraph topology surrounding the query entity. By integrating raw encoder outputs with RGAT's relation-aware embeddings, our model captures and leverages richer multi-hop relational patterns and textual information. Our preliminary experiments on the CoDEx dataset demonstrate that GA-S2S outperforms competitive Seq2Seq-based baseline models, achieving up to a 19\% relative gain in link prediction accuracy.

Geometric Structural Knowledge Graph Foundation Model

Structural knowledge graph foundation models aim to generalize reasoning to completely new graphs with unseen entities and relations. A key limitation of existing approaches like Ultra is their reliance on a single relational transformation (e.g., element-wise multiplication) in message passing, which can constrain expressiveness and fail to capture diverse relational and structural patterns exhibited on diverse graphs. In this paper, we propose Gamma, a novel foundation model that introduces multi-head geometric attention to knowledge graph reasoning. Gamma replaces the single relational transformation with multiple parallel ones, including real, complex, split-complex, and dual number based transformations, each designed to model different relational structures. A relational conditioned attention fusion mechanism then adaptively fuses them at link level via a lightweight gating with entropy regularization, allowing the model to robustly emphasize the most appropriate relational bias for each triple pattern. We present a full formalization of these algebraic message functions and discuss how their combination increases expressiveness beyond any single space. Comprehensive experiments on 56 diverse knowledge graphs demonstrate that Gamma consistently outperforms Ultra in zero-shot inductive link prediction, with a 5.5% improvement in mean reciprocal rank on the inductive benchmarks and a 4.4% improvement across all benchmarks, highlighting benefits from complementary geometric representations.

Mathematical Reasoning for Unmanned Aerial Vehicles: A RAG-Based Approach for Complex Arithmetic Reasoning

Autonomous UAV operation necessitates reliable mathematical reasoning for tasks such as trajectory planning and power management. While traditional flight control relies on hardcoded equations, recent Large Language Models (LLMs) offer potential for more flexible problem-solving but struggle with reliably selecting and applying correct mathematical formulations and executing precise multi-step arithmetic. We propose RAG-UAV, a retrieval-augmented generation framework designed to improve the mathematical reasoning of several LLMs (including GPT o1/Turbo, Llama-3.2/3.3, Mistral, and DeepSeek R1) in UAV-specific contexts by providing access to relevant domain literature. To conduct an initial assessment, we introduce the UAV-Math-Bench, a small problem set comprising 20 UAV-centric mathematical problems across four difficulty levels. Our experiments demonstrate that incorporating retrieval substantially increases exact answer accuracy (achieving up to 75% with o1), reduces instances of incorrect formulation selection (from 25% without RAG to 5% with RAG), decreases numerical errors, reducing Mean Squared Error (MSE) by orders of magnitude for the best-performing models. This pilot study indicates that RAG can enable general-purpose LLMs to function as more reliable tools for engineering analysis, although direct real-time flight control requires further investigation and validation on a larger scale. All benchmark data, question and answer are publicly available.

Towards Foundation Model on Temporal Knowledge Graph Reasoning

Temporal Knowledge Graphs (TKGs) store temporal facts with quadruple formats (s, p, o, t). Existing Temporal Knowledge Graph Embedding (TKGE) models perform link prediction tasks in transductive or semi-inductive settings, which means the entities, relations, and temporal information in the test graph are fully or partially observed during training. Such reliance on seen elements during inference limits the models' ability to transfer to new domains and generalize to real-world scenarios. A central limitation is the difficulty in learning representations for entities, relations, and timestamps that are transferable and not tied to dataset-specific vocabularies. To overcome these limitations, we introduce the first fully-inductive approach to temporal knowledge graph link prediction. Our model employs sinusoidal positional encodings to capture fine-grained temporal patterns and generates adaptive entity and relation representations using message passing conditioned on both local and global temporal contexts. Our model design is agnostic to temporal granularity and time span, effectively addressing temporal discrepancies across TKGs and facilitating time-aware structural information transfer. As a pretrained, scalable, and transferable model, POSTRA demonstrates strong zero-shot performance on unseen temporal knowledge graphs, effectively generalizing to novel entities, relations, and timestamps. Extensive theoretical analysis and empirical results show that a single pretrained model can improve zero-shot performance on various inductive temporal reasoning scenarios, marking a significant step toward a foundation model for temporal KGs.

SEMMA: A Semantic Aware Knowledge Graph Foundation Model

Knowledge Graph Foundation Models (KGFMs) have shown promise in enabling zero-shot reasoning over unseen graphs by learning transferable patterns. However, most existing KGFMs rely solely on graph structure, overlooking the rich semantic signals encoded in textual attributes. We introduce SEMMA, a dual-module KGFM that systematically integrates transferable textual semantics alongside structure. SEMMA leverages Large Language Models (LLMs) to enrich relation identifiers, generating semantic embeddings that subsequently form a textual relation graph, which is fused with the structural component. Across 54 diverse KGs, SEMMA outperforms purely structural baselines like ULTRA in fully inductive link prediction. Crucially, we show that in more challenging generalization settings, where the test-time relation vocabulary is entirely unseen, structural methods collapse while SEMMA is 2x more effective. Our findings demonstrate that textual semantics are critical for generalization in settings where structure alone fails, highlighting the need for foundation models that unify structural and linguistic signals in knowledge reasoning.

Predictive Multiplicity of Knowledge Graph Embeddings in Link Prediction

Knowledge graph embedding (KGE) models are often used to predict missing links for knowledge graphs (KGs). However, multiple KG embeddings can perform almost equally well for link prediction yet suggest conflicting predictions for certain queries, termed \textit{predictive multiplicity} in literature. This behavior poses substantial risks for KGE-based applications in high-stake domains but has been overlooked in KGE research. In this paper, we define predictive multiplicity in link prediction. We introduce evaluation metrics and measure predictive multiplicity for representative KGE methods on commonly used benchmark datasets. Our empirical study reveals significant predictive multiplicity in link prediction, with $8\%$ to $39\%$ testing queries exhibiting conflicting predictions. To address this issue, we propose leveraging voting methods from social choice theory, significantly mitigating conflicts by $66\%$ to $78\%$ according to our experiments.

Approximating Probabilistic Inference in Statistical EL with Knowledge Graph Embeddings

Statistical information is ubiquitous but drawing valid conclusions from it is prohibitively hard. We explain how knowledge graph embeddings can be used to approximate probabilistic inference efficiently using the example of Statistical EL (SEL), a statistical extension of the lightweight Description Logic EL. We provide proofs for runtime and soundness guarantees, and empirically evaluate the runtime and approximation quality of our approach.

Generating SROI^{-} Ontologies via Knowledge Graph Query Embedding Learning

Query embedding approaches answer complex logical queries over incomplete knowledge graphs (KGs) by computing and operating on low-dimensional vector representations of entities, relations, and queries. However, current query embedding models heavily rely on excessively parameterized neural networks and cannot explain the knowledge learned from the graph. We propose a novel query embedding method, AConE, which explains the knowledge learned from the graph in the form of SROI^{-} description logic axioms while being more parameter-efficient than most existing approaches. AConE associates queries to a SROI^{-} description logic concept. Every SROI^{-} concept is embedded as a cone in complex vector space, and each SROI^{-} relation is embedded as a transformation that rotates and scales cones. We show theoretically that AConE can learn SROI^{-} axioms, and defines an algebra whose operations correspond one to one to SROI^{-} description logic concept constructs. Our empirical study on multiple query datasets shows that AConE achieves superior results over previous baselines with fewer parameters. Notably on the WN18RR dataset, AConE achieves significant improvement over baseline models. We provide comprehensive analyses showing that the capability to represent axioms positively impacts the results of query answering.