Each question and answer group has a unique list of corresponding visuals used for image creation. The list of visible objects, which combines the correct-answer objects with an arbitrary'noise' object

Hierarchical relations are prevalent and indispensable for organizing human knowledge captured by a knowledge graph (KG). The key property of hierarchical relations is that they induce a partial ordering over the entities, which needs to be modeled in order to allow for hierarchical reasoning.

Abstract--Neuro-symbolic reasoning systems face fundamental challenges in maintaining semantic coherence while satisfying physical and logical constraints. Building upon our previous work on Ontology Neural Networks, we present an enhanced framework that integrates topological conditioning with gradient stabilization mechanisms. The approach employs Forman-Ricci curvature to capture graph topology, Deep Delta Learning for stable rank-one perturbations during constraint projection, and Covariance Matrix Adaptation Evolution Strategy for parameter optimization. Experimental evaluation across multiple problem sizes demonstrates that the method achieves mean energy reduction to 1.15 compared to baseline values of 11.68, with 95 percent success rate in constraint satisfaction tasks. The framework exhibits seed-independent convergence and graceful scaling behavior up to twenty-node problems, suggesting that topological structure can inform gradient-based optimization without sacrificing interpretability or computational efficiency. Integrating symbolic reasoning with neural learning remains a central challenge in artificial intelligence. While neural networks excel at pattern recognition and gradient-based optimization, they often struggle to maintain explicit constraints or provide interpretable intermediate representations. The opacity of deep neural representations makes it difficult to verify whether learned policies respect domain knowledge or physical laws. Conversely, symbolic systems offer logical transparency and formal guarantees but lack the flexibility to learn from noisy, incomplete data or adapt to distributional shifts.

Small language models (SLMs) have shown promises for relation extraction (RE) when extracting RDF triples guided by SHACL shapes focused on common datatype properties. This paper investigates how SLMs handle both datatype and object properties for a complete RDF graph extraction. We show that the key bottleneck is related to long-tail distribution of rare properties. To solve this issue, we evaluate several strategies: stratified sampling, weighted loss, dataset scaling, and template-based synthetic data augmentation. We show that the best strategy to perform equally well over unbalanced target properties is to build a training set where the number of occurrences of each property exceeds a given threshold. To enable reproducibility, we publicly released our datasets, experimental results and code. Our findings offer practical guidance for training shape-aware SLMs and highlight promising directions for future work in semantic RE.

The availability of Large Language Models (LLMs) presents a unique opportunity to reinvigorate research on Knowledge Engineering (KE) automation. This trend is already evident in recent efforts developing LLM-based methods and tools for the automatic generation of Competency Questions (CQs), natural language questions used by ontology engineers to define the functional requirements of an ontology. However, the evaluation of these tools lacks standardization. This undermines the methodological rigor and hinders the replication and comparison of results. To address this gap, we introduce Bench4KE, an extensible API-based benchmarking system for KE automation. The presented release focuses on evaluating tools that generate CQs automatically. Bench4KE provides a curated gold standard consisting of CQ datasets from 17 real-world ontology engineering projects and uses a suite of similarity metrics to assess the quality of the CQs generated. We present a comparative analysis of 6 recent CQ generation systems, which are based on LLMs, establishing a baseline for future research. Bench4KE is also designed to accommodate additional KE automation tasks, such as SPARQL query generation, ontology testing and drafting. Code and datasets are publicly available under the Apache 2.0 license.