Recoverable Learning Through Governed Semantic Logs: Algebraic Rollback, Certified Roll-Forward, and Energy Reduction

Modern learning systems typically recover from erroneous updates by restoring checkpoints followed by partial or complete retraining. Because learning is represented as irreversible parameter mutation, recovery requires reconstructing large portions of the optimization history. This paper presents a recoverable learning architecture in which model evolution is represented as a governed sequence of semantic learning operations. Each committed learning event is versioned, validated, deterministic under replay, and stored as an executable morphism. Recovery consists of four stages: (i) causal defect localization, (ii) rollback to the last validated state, (iii) certified algebraic roll-forward, and (iv) governed replay validation. Unlike conventional replay, affected learning operations are composed, normalized, and reduced before application to the recovered model. Using certified chain reduction, redundant, inverse, and absorbed learning operations are eliminated outside the model prior to execution. The resulting repair cost depends upon the governed dependency cone rather than the complete training history and admits expected-case energy reductions whenever dependency locality and semantic memoization limit the affected descendants.