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This research explores using formal mathematical ontologies to ground language models, aiming to reduce hallucinations in high-stakes reasoning tasks through retrieval-augmented generation. The study demonstrates that while injecting relevant domain definitions can boost performance on benchmarks like MATH, poor retrieval quality actively degrades model reliability. This work highlights the critical trade-offs and technical challenges inherent in integrating neuro-symbolic approaches with standard neural architectures.
Ontology-Guided Neuro-Symbolic Inference: Grounding Language Models with Mathematical Domain Knowledge
arXiv:2602.17826v2 Announce Type: replace-cross Abstract: Language models exhibit fundamental limitations -- hallucination, brittleness, and lack of formal grounding -- that are particularly problematic in high-stakes specialist fields requiring verifiable reasoning. I investigate whether formal domain ontologies can enhance language model reliability through retrieval-augmented generation. Using mathematics as proof of concept, I implement a neuro-symbolic pipeline leveraging the OpenMath ontology with hybrid retrieval and cross-encoder reranking to inject relevant definitions into model prompts. Evaluation on the MATH benchmark with three open-source models reveals that ontology-guided context improves performance when retrieval quality is high, but irrelevant context actively degrades it -- highlighting both the promise and challenges of neuro-symbolic approaches.
Abstract:Language models exhibit fundamental limitations -- hallucination, brittleness, and lack of formal grounding -- that are particularly problematic in high-stakes specialist fields requiring verifiable reasoning. I investigate whether formal domain ontologies can enhance language model reliability through retrieval-augmented generation. Using mathematics as proof of concept, I implement a neuro-symbolic pipeline leveraging the OpenMath ontology with hybrid retrieval and cross-encoder reranking to inject relevant definitions into model prompts. Evaluation on the MATH benchmark with three open-source models reveals that ontology-guided context improves performance when retrieval quality is high, but irrelevant context actively degrades it -- highlighting both the promise and challenges of neuro-symbolic approaches.
Artificial Intelligence (cs.AI); Machine Learning (cs.LG); Symbolic Computation (cs.SC)
arXiv:2602.17826 [cs.AI]
(or arXiv:2602.17826v2 [cs.AI] for this version)
https://doi.org/10.48550/arXiv.2602.17826 Focus to learn more arXiv-issued DOI via DataCite
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