通过符号压缩增强大型语言模型效率：一种面向可解释性的形式化方法
Enhancing Large Language Model Efficiencyvia Symbolic Compression: A Formal Approach Towards Interpretability
AI总结：
本文提出基于符号压缩的形式化框架，融合组合逻辑与信息论编码，在代码生成中实现78.3%的token压缩率并将逻辑可追溯性提升62%，为LLM高效推理与可解释性研究提供新理论工具。
摘要：
大型语言模型（LLMs）在代码生成和逻辑推理任务中面临显著的 token 效率瓶颈，这一挑战直接影响推理成本和模型可解释性。本文提出了一个基于符号压缩的形式化框架，融合组合逻辑、信息论最优编码和上下文感知推理技术，在保持语义完整性的同时实现 token 效率的阶跃式提升。我们在函数式编程范式中建立数学框架，推导符号密度与模型可解释性之间的定量关系，并提出可微压缩因子指标来评估编码效率。此外，我们利用参数高效微调（PEFT）技术实现 GAEL 语言的低成本应用。实验结果表明，该方法在代码生成任务中实现了 78.3% 的 token 压缩率，同时通过结构显式性将逻辑可追溯性提升了 62%。本研究为 LLMs 的高效推理提供了新的理论工具，并为模型可解释性研究开辟了符号化路径。
英文摘要：
Large language models (LLMs) face significant token efficiency bottlenecks in code generation and logical reasoning tasks, a challenge that directly impacts inference cost and model interpretability. This paper proposes a formal framework based on symbolic compression,integrating combinatory logic, information-theoretic optimal encoding, and context-aware inference techniques to achieve a step-change improvement in token efficiency while preserving semantic integrity. We establish a mathematical framework within a functional programming paradigm, derive the quantitative relationship between symbolic density and model interpretability, and propose a differentiable compression factor metric to evaluate encoding efficiency. Furthermore, we leverage parameter-efficient fine-tuning (PEFT) techniques to achieve a low-cost application of the GAEL language. Experimental results show that this method achieves a 78.3% token compression rate in code generation tasks while improving logical traceability by 62% through structural explicitness. This research provides new theoretical tools for efficient inference in LLMs and opens a symbolic path for modelinterpretability research.
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