[2603.02504] NeuroProlog: Multi-Task Fine-Tuning for Neurosymbolic Mathematical Reasoning via the Cocktail Effect

Computer Science > Artificial Intelligence arXiv:2603.02504 (cs) [Submitted on 3 Mar 2026] Title:NeuroProlog: Multi-Task Fine-Tuning for Neurosymbolic Mathematical Reasoning via the Cocktail Effect Authors:Pratibha Zunjare, Michael Hsiao View a PDF of the paper titled NeuroProlog: Multi-Task Fine-Tuning for Neurosymbolic Mathematical Reasoning via the Cocktail Effect, by Pratibha Zunjare and Michael Hsiao View PDF HTML (experimental) Abstract:Large Language Models (LLMs) achieve strong performance on natural language tasks but remain unreliable in mathematical reasoning, frequently generating fluent yet logically inconsistent solutions. We present \textbf{NeuroProlog}, a neurosymbolic framework that ensures verifiable reasoning by compiling math word problems into executable Prolog programs with formal verification guarantees. We propose a multi-task Cocktail training strategy that jointly optimizes three synergistic objectives in a unified symbolic representation space: (i) mathematical formula-to-rule translation (KB), (ii) natural language-to-program synthesis (SOLVE), and (iii) program-answer alignment. This joint supervision enables positive transfer, where symbolic grounding in formula translation directly improves compositional reasoning capabilities. At inference, we introduce an execution-guided decoding pipeline with fine-grained error taxonomy that enables iterative program repair and quantifies model self-debugging capacity. Comprehensive evaluation on GSM8K ac...