📝 SummarXiv

Abstract

[Objective] This study addresses key challenges in machine learning, namely the absence of a unified formal theoretical framework and the lack of foundational theories for model interpretability and ethical safety. [Methods] We first construct a formal information model, explicitly defining the ontological states and carrier mappings of typical machine learning stages using sets of well-formed formulas. By introducing learnable and processable predicates, as well as learning and processing functions, we analyze the causal chain logic and constraint laws governing machine learning processes. [Results] We establish the Machine Learning Theory Meta-Framework (MLT-MF), on which we further propose universal definitions for model interpretability and ethical safety. We prove and validate three key theorems: the relationship between model interpretability and information existence, ethical safety assurance, and the upper bound estimation of total variation distance (TVD). [Limitations] The current framework assumes ideal, noise-free information enabling mappings and focuses primarily on model learning and processing logic in static scenarios. It does not yet address information fusion and conflict resolution across ontological spaces in multimodal or multi-agent systems. [Conclusions] This work overcomes the limitations of fragmented research and provides a unified theoretical foundation for systematically addressing critical issues in contemporary machine learning.