A new way to make LLMs reason better: divide problems, score thoughts, and learn from mistakes
RDoLT (Recursive Decomposition of Logical Thoughts) introduces a three-tier decomposition system for LLMs that breaks down complex reasoning into manageable steps while tracking both successful and rejected thoughts for better decision-making.
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https://arxiv.org/abs/2501.02026
🤔 Original Problem:
LLMs struggle with complex reasoning tasks, often making mistakes in mathematical problem-solving and logical thinking. Current methods like Chain-of-Thought and Least-to-Most lack effective mechanisms to evaluate intermediate thoughts and handle errors.
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🔧 Solution in this Paper:
→ RDoLT decomposes reasoning tasks into easy, intermediate, and final tiers, allowing systematic progression through complexity levels
→ Each tier generates multiple thoughts that are evaluated using four criteria: Logical Validity, Coherence, Simplicity, and Adaptiveness
→ A Knowledge Propagation Module (KPM) tracks both selected and rejected thoughts, enabling dynamic re-evaluation throughout the reasoning process
→ The system uses a scoring mechanism to select the most promising thoughts at each stage while maintaining awareness of previously rejected ideas
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💡 Key Insights:
→ Breaking down complex reasoning into progressive difficulty levels reduces cognitive load
→ Tracking rejected thoughts prevents premature discarding of potentially valuable solutions
→ Systematic scoring of thoughts using multiple criteria leads to more reliable reasoning
→ Dynamic feedback loops between decomposition levels enable error correction
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📊 Results:
→ Achieved 90.98% accuracy on GSM8K benchmark with ChatGPT-4, surpassing previous methods by 6.28%
→ Demonstrated consistent improvements across multiple benchmarks with accuracy gains of 5.5-6.75%
→ Performed effectively across different model sizes and architectures
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