Admissibility-Based Training Systems: A Structural Interpretation within the Paton System

This paper presents a structural interpretation of training processes in artificial intelligence systems within the Paton System framework. Rather than treating training as purely optimisation of a loss function, training is interpreted as navigation through an admissible region defined by constraint compatibility. Model updates occur only within admissible configurations that preserve system stability and coherence. The admissible region defines the set of valid parameter configurations, while the loss function provides directional guidance within that region. Training is therefore understood as constrained navigation rather than unconstrained optimisation. This interpretation introduces no new computational mechanisms and does not modify existing machine learning methods. It provides a pre-theoretical structural lens in which training is governed by admissibility before optimisation dynamics. The framework complements prior work on optimisation as admissibility navigation while extending the interpretation specifically to learning dynamics in artificial intelligence systems.