Enhancing the reliability of dialogue model responses using formal grammars and category theory

This study is devoted to enhancing the reliability of dialog model responses in tasks requiring high accuracy. A hybrid approach is proposed that combines fine-tuning the model on domain-specific data with the integration of Chomsky formal grammars into the query processing pipeline. An architecture is introduced that unifies formal syntactic control with the generative capabilities of the fine-tuned GigaChat 2.0 model. The query processing workflow incorporates a module for preliminary analysis and filtering of user queries based on Chomsky context-free grammars. To align the operation of the generative model with the identified syntactic structure, a two-level control mechanism is proposed. At the input stage, a syntactically enriched query guides the generation process toward appropriate structural query patterns. At the output stage, the verification module performs selection and correction of the generated response based on formal criteria. To enhance explainability and enable formal analysis of data flows, category theory is employed, in which queries, intermediate representations, and responses are modeled as objects and morphisms of a category. To improve logical coherence and contextual awareness, a geometric representation of semantics in Minkowski space is proposed, whose metric makes it possible to separate the invariant meaning of a word from its contextual and temporal dynamics. Experimental evaluation on a specialized set of 500 factual and structured queries demonstrates that the proposed method reduces the generation of fabricated statements by 22% compared to the baseline GigaChat 2.0 model. The results show that the combined use of formal grammars, categorical formalism, and a geometric model of semantics enhances the reliability of responses in domain-specific dialogues.