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Towards Data Science

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Empowering LLMs to Think Deeper by Erasing Thoughts

  • Recent large language models (LLMs) such as OpenAI’s o1/o3, DeepSeek’s R1, and Anthropic’s Claude 3.7 exhibit enhanced reasoning capabilities through deep thinking using chain-of-thought (CoT) approach.
  • The CoT-based test-time scaling may hit ceilings due to exceeding model context windows, burying critical information, and high self-attention complexities.
  • The article proposes a new reasoning paradigm named PENCIL that allows LLMs to both generate and erase thoughts for optimal reasoning efficiency.
  • PENCIL uses erasure mechanism inspired by logic rewriting rules and functional programming to discard intermediate thoughts when not needed.
  • PENCIL supports various reasoning patterns like task decomposition, branch and backtrack, and summarization/tail recursion for efficient problem-solving.
  • PENCIL demonstrates significant space efficiency in tasks like Boolean Satisfiability (SAT) compared to traditional CoT, improving computational resource usage.
  • Experimental results reveal that PENCIL outperforms CoT in inherently hard reasoning tasks such as 3-SAT, QBF, and Einstein’s Puzzle, achieving higher accuracy and faster convergence.
  • Theoretical analysis shows that PENCIL achieves Turing completeness with optimal time and space complexity, making it efficient for solving arbitrary computable tasks.
  • The proposed reasoning paradigm opens up possibilities for fine-tuning LLMs with memory-efficient capabilities, inspiring reexamination of existing reasoning models.

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