Enhancing Large Language Model Efficiencyvia Symbolic Compression: A Formal Approach Towards Interpretability

TL;DR

This paper introduces a formal symbolic compression framework that significantly improves token efficiency and interpretability in large language models, especially for code generation and reasoning tasks.

Contribution

It presents a novel mathematical framework combining symbolic compression, combinatory logic, and information theory to enhance LLM efficiency and interpretability.

Findings

78.3% token compression in code generation

62% improvement in logical traceability

Establishment of a quantitative relationship between symbolic density and interpretability

Abstract

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.