Information Science Principles of Machine Learning: A Causal Chain Meta-Framework Based on Formalized Information Mapping

TL;DR

This work introduces an information-theoretic, logic-grounded framework (MLT-MF) to unify the ML lifecycle via Objective Information Theory (OIT), modeling state, enabling mappings, and causal information chains. It defines formal notions of model interpretability and ethical safety, and proves theorems that connect interpretability to information existence, enable SafeMax-based ethical safety, and provide computable TVD upper bounds for generalization under both noiseless and noisy conditions. A practical instantiation on a simple feedforward network demonstrates multi-modal interpretability, SafeMax guarantees, and TVD-based performance estimation across training, input processing, and online learning stages. The experimental results underscore the framework’s potential for deployable ML assurance, while acknowledging limitations such as NP-hardness of optimal safety and conservative TVD bounds, pointing to future work in scaling, cross-modal information chains, and empirical observability of the theory. The approach offers a principled pathway to quantify and guarantee interpretability, safety, and reliability in ML systems along the full lifecycle, with practical implications for safer, auditable AI deployment.

Abstract

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.

Figures (7)

• Figure 1: Schematic Diagram of Enabling Mapping, Noisy Information, and Information Chain.
• Figure 1: Schematic diagram of feedforward neural network model M
• Figure 2: Causal Chains of Multiple Information Mappings in Machine Learning.
• Figure 3: Experimental Evaluation and Results of the TVD Upper Bound under Noiseless Input and Conservative Prediction Strategy.
• Figure 4: Experimental Evaluation and Results of the TVD Upper Bound under Noisy Input and Arbitrary Prediction Strategy.