Why Training Pipelines Prevent Reproducibility in Modern AI Systems Structural Limits of Stochastic Training

Reproducibility is a prerequisite for scientific credibility, engineering reliability, and legal accountability. Yet modern artificial intelligence systems - despite extensive tooling for experiment tracking, versioning, and evaluation - frequently fail to achieve strong reproducibility. This paper argues that such failures are not transient engineering limitations but arise from structural properties of contemporary training pipelines. In particular, stochastic optimization, numerical non-determinism, ambiguous or policy-defined labeling, and irreversible information compression introduce path dependence that cannot be eliminated by statistical replication alone. By modeling training as a stochastic dynamical system over an augmented training state that explicitly includes optimizer states, execution ordering, and exogenous randomness, we derive the corresponding master equation governing training evolution. We show that whenever the effective transition kernel is non-degenerate on reachable training states, exact replay of training outcomes fails with positive probability across independent reruns, unless all latent variables inducing that non-determinism are fully captured and replayed. Crucially, these failures arise during training rather than inference and therefore cannot be repaired post hoc. The analysis applies across modern training regimes, including large-scale distributed optimization, reinforcement learning, and feedback-driven or human-in-the-loop labeling pipelines. These results imply that reproducibility in contemporary AI is a structural property of computation, not merely a statistical or procedural concern, with direct consequences for auditability, reliability, and the deployment of AI systems in regulated and safety-critical domains.