Title: MetaRuleReasoner: Beyond Chain-of-Thought—Neural Rule-Based Reasoning for Reliable Mathematical Computation
Primary area: neurosymbolic & hybrid AI systems (physics-informed, logic & formal reasoning, etc.)
Keywords: Reasoning, Neural Rule, Mathematics, Large Language Models

Abstract: Chain-of-thought reasoning has emerged as the dominant paradigm for mathematical reasoning in large language models, yet it suffers from fundamental limitations: hallucination in reasoning steps, inconsistent performance, and lack of systematic reliability. We introduce neural rule-based reasoning as a distinct alternative that achieves systematic reliability through explicit rule application and complete domain coverage. Our MetaRuleReasoner demonstrates this approach, achieving 100% accuracy on multi-digit arithmetic tasks, while chain-of-thought models show systematic degradation with increasing complexity—GPT-4 drops to 90.9% accuracy on 10-digit operations. Our neural rule-based approach provides systematic reliability guarantees within learned domains by mastering finite rule sets that compose deterministically, contrasting sharply with the probabilistic reliability of chain-of-thought reasoning that must learn patterns for exponentially many problem combinations.