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Recursive Decomposition of Logical Thoughts: Framework for Superior Reasoning and Knowledge Propagation in Large Language Models

Kaleem Ullah Qasim, Jiashu Zhang, Tariq Alsahfi, Ateeq Ur Rehman Butt

TL;DR

RDoLT tackles core weaknesses in large language model reasoning by integrating three components: recursive task decomposition into Easy/Intermediate/Final levels, a four-feature thought scoring system, and a Knowledge Propagation Module that preserves both strong and weak thoughts across reasoning stages. The framework combines elements from CoT, CoT-SC, and graph-based reasoning while maximizing flexibility and error recovery through cross-stage knowledge propagation. Empirical results across GSM8K, SVAMP, MultiArith, LastLetterConcatenation, and Gaokao 2023 Math show consistent improvements over state-of-the-art prompting methods, with notable gains on open models and ChatGPT-4o, and robust performance across varied thresholds and thought-quantity configurations. These findings suggest RDoLT offers a scalable, generalizable approach to complex reasoning tasks, with open-source releases to foster broader adoption and further research.

Abstract

Enhancing the reasoning capabilities of Large Language Models remains a critical challenge in artificial intelligence. We introduce RDoLT, Recursive Decomposition of Logical Thought prompting, a novel framework that significantly boosts LLM reasoning performance. RDoLT is built on three key innovations: (1) recursively breaking down complex reasoning tasks into sub-tasks of progressive complexity; (2) employing an advanced selection and scoring mechanism to identify the most promising reasoning thoughts; and (3) integrating a knowledge propagation module that mimics human learning by keeping track of strong and weak thoughts for information propagation. Our approach was evaluated across multiple benchmarks, including GSM8K, SVAMP, MultiArith, LastLetterConcatenation, and Gaokao2023 Math. The results demonstrate that RDoLT consistently outperforms existing state-of-the-art techniques, achieving a 90.98 percent accuracy on GSM8K with ChatGPT-4, surpassing state-of-the-art techniques by 6.28 percent. Similar improvements were observed on other benchmarks, with accuracy gains ranging from 5.5 percent to 6.75 percent. These findings highlight RDoLT's potential to advance prompt engineering, offering a more effective and generalizable approach to complex reasoning tasks.

Recursive Decomposition of Logical Thoughts: Framework for Superior Reasoning and Knowledge Propagation in Large Language Models

TL;DR

RDoLT tackles core weaknesses in large language model reasoning by integrating three components: recursive task decomposition into Easy/Intermediate/Final levels, a four-feature thought scoring system, and a Knowledge Propagation Module that preserves both strong and weak thoughts across reasoning stages. The framework combines elements from CoT, CoT-SC, and graph-based reasoning while maximizing flexibility and error recovery through cross-stage knowledge propagation. Empirical results across GSM8K, SVAMP, MultiArith, LastLetterConcatenation, and Gaokao 2023 Math show consistent improvements over state-of-the-art prompting methods, with notable gains on open models and ChatGPT-4o, and robust performance across varied thresholds and thought-quantity configurations. These findings suggest RDoLT offers a scalable, generalizable approach to complex reasoning tasks, with open-source releases to foster broader adoption and further research.

Abstract

Enhancing the reasoning capabilities of Large Language Models remains a critical challenge in artificial intelligence. We introduce RDoLT, Recursive Decomposition of Logical Thought prompting, a novel framework that significantly boosts LLM reasoning performance. RDoLT is built on three key innovations: (1) recursively breaking down complex reasoning tasks into sub-tasks of progressive complexity; (2) employing an advanced selection and scoring mechanism to identify the most promising reasoning thoughts; and (3) integrating a knowledge propagation module that mimics human learning by keeping track of strong and weak thoughts for information propagation. Our approach was evaluated across multiple benchmarks, including GSM8K, SVAMP, MultiArith, LastLetterConcatenation, and Gaokao2023 Math. The results demonstrate that RDoLT consistently outperforms existing state-of-the-art techniques, achieving a 90.98 percent accuracy on GSM8K with ChatGPT-4, surpassing state-of-the-art techniques by 6.28 percent. Similar improvements were observed on other benchmarks, with accuracy gains ranging from 5.5 percent to 6.75 percent. These findings highlight RDoLT's potential to advance prompt engineering, offering a more effective and generalizable approach to complex reasoning tasks.
Paper Structure (20 sections, 10 equations, 4 figures, 3 tables)

This paper contains 20 sections, 10 equations, 4 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Methods
  4. Task Decomposition
  5. Thought Generation
  6. Scoring and Evaluation
  7. Knowledge Propagation Module and Edge Case Management
  8. Experiments
  9. Benchmarks & Models Selection
  10. Method Selected for Comparison
  11. Main Results
  12. Robustness of RDoLT Variants
  13. Impact of Thought Quantity on Success Rates
  14. Limitations and Future Directions
  15. Conclusion
  16. ...and 5 more sections

Figures (4)

  • Figure 1: Illustration of Recursive Decomposition of Logical Thoughts (RDoLT) Framework. Each Yellow box represents decomposed task into Easy, Intermediate, and Final tiers. Each tier generates multiple thoughts (T1, T2, T3) evaluated on four features (logical validity, coherence, simplicity, and adaptiveness). Thoughts meeting the threshold criteria (green) are propagated to the next tier via the Knowledge Propagation Module (KPM), which tracks selected (strong) and rejected (weak) thoughts to inform future evaluations.
  • Figure 2: Edge cases handled by the Knowledge Propagation Module (KPM) during thought selection in decomposition steps. The complete Selection scenario (left) shows all thoughts (T1, T2, T3) selected. The Complete Rejection scenario (center) depicts all thoughts rejected, leading to regeneration. Mixed Selection scenario (right) highlights partial selection, with some thoughts accepted and others rejected. These scenarios demonstrate how the KPM ensures optimal thought progression
  • Figure 3: Detailed example illustrating how RDoLT addresses problems by decomposing them into three reasoning steps, generating thoughts for each step, and scoring and propagating knowledge through a Knowledge Propagation Module (KPM) across subsequent steps. The system performs scoring and selection at each step, ensuring that both accepted and rejected thoughts are transmitted to enhance learning and understand why certain thoughts were discarded
  • Figure 4: Impact of different thought selection strategies on accuracy using KPM. Strategies include using only selected thoughts, both selected and non-selected thoughts, highest-scoring selected thoughts, and lowest-threshold non-selected thoughts. Incorporating both selected and non-selected thoughts yields a wider range of accuracy, while selecting only final thoughts ensures more consistent accuracy results