Unified dynamics of training, learning, inference, and reinforcement in neural networks

arXiv:2611.01345v2 Announce Type: replace Abstract: Through nine nanoGPT experiments, we established training-learning-inference relations: realized updates elicit state-dependent finite-amplitude responses; learning persistently reorganizes distributed functional support, with target-specific readout-boundary crossings determining capability transitions; inference recruits learned support without changing the learned state. Factors identified in the fifth experiment yielded a direct predictor of post-update capability transitions, achieving 91.43% accuracy and 91.49% four-way macro recall across 5,088 targets. We tested these relations and prediction across five additional neural architectures. In a seventh system, concentrated correct feedback eroded previously mastered skills; rebalanced feedback restored their accuracy from 70.31% to 99.48%. Linking inference consequences to subsequent training closes these relations into unified training-learning-inference-reinforcement dynamics. We subsequently established a unified system of dynamical equations, used it to reconcile positive and negative findings across existing research, and derived mathematical relationships in other neural-network theories using only the assumptions of the original studies.