用信息科学构建统一理论框架,解决模型可解释性与伦理安全的根基问题。
Information Science Principles of Machine Learning: A Causal Chain Meta-Framework Based on Formalized Information Mapping
- 基于形式化信息映射,建立机器学习元框架
- 证明可解释性等价于信息存在,给出伦理安全上界
- 为模型透明与安全提供可验证的理论支撑
本文针对机器学习理论缺乏统一形式化框架、可解释性与伦理安全缺乏坚实理论基础的问题,构建形式化信息模型,通过良构公式(WFFs)明确定义机器学习核心组件的本体状态与载体映射。引入可学习与可处理的谓词及函数,分析模型中因果链背后的逻辑推理与约束规则,建立机器学习理论元框架(MLT-MF)。在此基础上,提出模型可解释性与伦理安全的通用定义,并严格证明与验证四项关键定理:可解释性与信息存在的等价性、伦理安全保证的构造性表达,以及两类总变差距离(TVD)的上界。该工作克服了以往零散方法的局限,从信息科学视角为机器学习面临的重大挑战提供系统性理论基础。
原文摘要 · Abstract (English)
This paper addresses the current lack of a unified formal framework in machine learning theory, as well as the absence of robust theoretical foundations for interpretability and ethical safety assurance. We first construct a formal information model, employing sets of well-formed formulas (WFFs) to explicitly define the ontological states and carrier mappings for the core components of machine learning. By introducing learnable and processable predicates, as well as learning and processing functions, we analyze the logical inference and constraint rules underlying causal chains in models, thereby establishing the Machine Learning Theory Meta-Framework (MLT-MF). Building upon this framework, we propose universal definitions for model interpretability and ethical safety, and rigorously prove and validate four key theorems: the equivalence between model interpretability and information existence, the constructive formulation of ethical safety assurance and two types of total variation distance (TVD) upper bounds. This work overcomes the limitations of previous fragmented approaches, providing a unified theoretical foundation from an information science perspective to systematically address the critical challenges currently facing machine learning.
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