Verifiable Hybrid Reasoning (VHR): A Self-Contained Framework for Solving Intractable Problems in Modern LLMs

Manuscript received May 19, 2025; accepted June 12, 2025; published August 11, 2025

Abstract—While Large Language Models (LLMs) like DeepSeek-R1 and Manus AI have achieved remarkable success in reasoning and tool-augmented tasks, critical limitations persist in domains requiring guaranteed correctness, dynamic verification, and autonomous workflow optimization. Existing models like DeepSeek-R1 and Manus AI excel in reasoning and tool-augmented tasks but struggle with guaranteed correctness, dynamic verification, and workflow optimization. This paper introduces Verifiable Hybrid Reasoning (VHR), a novel framework that integrates neural-symbolic architectures with runtime validation to address unsolved challenges in mathematical proof generation, safety-critical decision-making, and high-stakes professional applications. VHR eliminates dependency on external tools through its adaptive complexity routing, hybrid representation space, and self-verification mechanisms. Benchmarking on 1,200 previously unsolvable problems demonstrates 83% success in geometric reasoning (vs. 12% in DeepSeekMath) and 79% reduction in safety violations compared to state-of-the-art models. VHR bridges the neural-symbolic divide through its integrated verification framework, solving previously intractable problems in mathematical reasoning and safety-critical domains. Future work will explore quantum-enhanced SMT solvers for real-time validation.

keywords—Verifiable hybrid reasoning, neural-symbolic architectures, runtime validation, mathematical proof generation, safety-critical decision-making, and autonomous workflow optimization

Cite: Prashant D. Sawant,"Verifiable Hybrid Reasoning (VHR): A Self-Contained Framework for Solving Intractable Problems in Modern LLMs," Journal of Advances in Artificial Intelligence, vol. 3, no. 3, pp. 206-214, 2025. doi: 10.18178/JAAI.2025.3.3.206-214

Copyright © 2025 by the authors. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).