Training, learning and inference: unified dynamics of neural systems

Abstract:We define an atomic generation fact f=(u,tau,omega,z;rho), recording the origin, realized transformation, concrete occurrence, generated result and relation role. Compiled into a Generation-Fact Graph (GFG), these facts provide an AI-native, compilable scientific fact substrate preserving generation histories. We establish a GFG-based recursive scientific process in which analysis, intervention, replay and validation form facts for later cycles. Using nanoGPT, we establish unified training-learning dynamics. Training is the evolution of a parameter-optimizer system with state and memory: each actual training action enters the receiving state and produces a finite-amplitude nonlinear functional response conditioned by that state and target-specific update geometry. Learning is the persistent reorganization of distributed functional support by these responses; capability formation, maintenance, decline or recovery becomes observable when target-specific states are evaluated against their readout boundaries. Three primary coordinates - target-boundary state, target-specific update geometry and parameter-Adam receiving state - yield a second-order predictor operating before post-update outputs are read. On held-out runs, it achieved 91.43% accuracy and 91.49% macro-averaged recall across four transitions. We further establish inference as a frozen projection of training-learning dynamics. Component gating and rollback show causal recruitment and non-additive combination of query-conditioned support formed during training, deriving organizational conditions realized by Attention. Controlled feedback indicates possible double-edged reinforcement effects. ResNet/CIFAR-100 and diffusion/CIFAR-10 experiments confirm receiving-state-conditioned responses, persistent support reorganization and frozen inference projection beyond nanoGPT.

39 pages, 2 figures, 3 tables. Evidence spans 22 indexed experimental programmes: held-out prediction (91.43% accuracy), causal interventions, and cross-system validation in nanoGPT, ResNet/CIFAR-100 and diffusion/CIFAR-10. Code: this https URL. Evidence: this https URL

Machine Learning (cs.LG)

arXiv:2608.20965 [cs.LG]

(or arXiv:2608.20965v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2608.20965 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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