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

• URL: http://arxiv.org/abs/2603.02504v2
• Date: Wed, 04 Mar 2026 13:59:59 GMT
• Title: NeuroProlog: Multi-Task Fine-Tuning for Neurosymbolic Mathematical Reasoning via the Cocktail Effect
• Authors: Pratibha Zunjare, Michael Hsiao,
• Abstract summary: Large Language Models (LLMs) achieve strong performance on natural language tasks but remain unreliable in mathematical reasoning.<n>We present textbfNeuroProlog, a neurosymbolic framework that ensures verifiable reasoning by compiling math word problems into executable Prolog programs.
• Score: 0.12277343096128711
• License: http://creativecommons.org/licenses/by/4.0/
• 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 across four model scales (3B--32B parameters) demonstrates consistent improvements: cocktail training achieves significant accuracy gains of +5.23\% (Qwen-32B, $p < 0.01$), +3.43\% (GPT-OSS-20B, $p < 0.01$), and +5.54\% (Llama-3B, $p < 0.05$) over single-task baselines. Systematic error analysis reveals scale-dependent learning dynamics: at 32B scale, cocktail training transforms unfixable type errors (12\% repair rate) into correctable domain errors (96\% repair rate), achieving 92.7\% overall correction; at 8B scale, the same training eliminates syntactic errors but introduces semantic failures, revealing a critical capacity threshold for type-safe symbolic reasoning.

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