Platonic Projection Structures-Based Information Dynamics (PPS-ID): Recursive Transformation of Observable Information

In recursive learning, model outputs can be reused in subsequent training, linking successive models through the reuse and transformation of observable information. Assessing these processes requires distinguishing changes in observable states from the preservation of task-relevant properties. We introduce PPS-Based Information Dynamics (PPS-ID), a framework connecting the observability perspective of Platonic Projection Structures with trajectory-based evaluation of repeated learning. PPS-ID separates latent-to-observable mappings from training-state transitions and evaluates observable discrepancies, task-dependent directional variation, and example-level correctness histories. Standard factorization conditions specify when the chosen observations admit a closed transition, while decision-margin conditions relate changes in prediction probabilities to preservation of classification decisions. Experiments with CIFAR-10 and sentiment classification using Bidirectional Encoder Representations from Transformers (BERT) illustrate three distinctions: local similarity can coexist with departure from an initial state; accuracy decline can coexist with lower expected calibration error and higher prediction entropy; and endpoint improvement can coexist with intermediate losses. In five-generation CIFAR-10 distillation across five seeds, fixed-teacher final accuracy exceeds recursive final accuracy by a mean of 1.542 percentage points under soft-only supervision. Mixing ground-truth and soft-target supervision reverses this ranking and raises mean recursive final accuracy from 70.672% to 73.910%. On the binary Stanford Sentiment Treebank task (SST-2) and IMDb, BERT experiments yield dataset- and seed-dependent endpoint rankings; first-generation branch differences limit causal attribution to teacher replacement. PPS-ID provides a common evaluation structure for examining how observable information changes and which task-relevant properties are preserved along a learning trajectory. The results show how supervision regime, reference choice, and intermediate variation affect the interpretation of repeated learning.