{"id":5,"identifier":"LOR-00005","url":"https://lifeofresearch.com/articles/5","title":"Sheaf-Theoretic Semantics and Quantum Contextuality in Large Language Models: A Unified Categorical Framework for Understanding Semantic Coherence and Hallucination Phenomena","abstract":"Abstract\nThis paper introduces a novel theoretical framework for understanding semantic processing in Large Language\nModels through the lens of sheaf theory and quantum contextuality. We propose that the semantic structure of\nLLM-generated text can be rigorously modeled as a sheaf over the topological space of prompt contexts, where\nlocal semantic sections may fail to glue into globally consistent interpretations. This mathematical formalization\nreveals a deep structural parallel between LLM behavior and quantum mechanical systems exhibiting\ncontextuality, as characterized by the Kochen-Specker theorem. Our central thesis posits that hallucination\nphenomena in LLMs arise fundamentally from cohomological obstructions to the existence of global semantic\nsections, analogous to how quantum systems exhibit measurement outcomes that cannot be explained by preexisting hidden variables. We develop a complete categorical framework using topos-theoretic methods, introduce\nformal definitions of semantic presheaves and their associated Grothendieck topologies, and demonstrate how\nCech cohomology groups can quantify the degree of semantic inconsistency in model outputs. This work bridges\nabstract mathematics with practical AI interpretability, offering new diagnostic tools for understanding when and\nwhy language models produce incoherent or factually inconsistent outputs.","authors":[{"name":"Pranay Mahendrakar","affiliation":"SONYTECH","orcid":"0009-0003-7224-029X"}],"type":"article","license":"CC-BY-4.0","keywords":[],"publication_date":"2025-12-28","version":1,"views":6,"downloads":6,"created_at":"2026-09-22 17:33:35","doi":"10.5281/zenodo.18074071","source":"Zenodo","source_url":"https://zenodo.org/records/18074071","files":[{"id":5,"name":"Sheaf-Theoretic Semantics and Quantum Contextuality in Large Language.pdf","size":263384,"mime":"application/pdf","downloads":6,"download_url":"https://lifeofresearch.com/articles/5/files/5/Sheaf-Theoretic%20Semantics%20and%20Quantum%20Contextuality%20in%20Large%20Language.pdf"}]}