Reproducibility Is a Semantic Property of Computation Why Determinism and Replay Are Required for Machine Learning

Machine learning pipelines-spanning data preprocessing, training, evaluation, and deployment-frequently fail to reproduce results under nominally identical conditions. This failure undermines scientific falsifiability, blocks certification in regulated domains, and weakens legal and operational auditability. We show that the root cause is not inadequate experimental practice or randomness alone, but nondeterministic computational semantics arising from parallel execution, floating-point non-associativity, asynchronous data pipelines, and environment-dependent kernels. This paper provides a formal theory of reproducibility in machine learning. We define a hierarchy of reproducibility notions-statistical, numerical, bitwise, and replay reproducibility-and prove that common best practices such as seed fixing and checkpointing are insufficient to guarantee strong reproducibility. We establish an impossibility result showing that replay reproducibility is unattainable under nondeterministic transition semantics. We then introduce a deterministic computation framework based on canonicalization of inputs and histories, deterministic state transition operators, and derived randomness. We prove that this framework yields necessary and sufficient conditions for replay reproducibility and enables cryptographic identity of results. While compression-based learning objectives may explain how internal structure is discovered, we show that reproducibility is governed by execution semantics rather than by learning dynamics. Together, these results demonstrate that reproducibility is not an experimental afterthought but a semantic property of computation, with direct implications for scientific validity, auditability, and governance of machine learning systems.