Modern deep learning systems rely heavily on numerical approximations, including reduced precision, quantization, non-deterministic execution orderings, and parallel computation. These choices do not merely introduce “negligible noise”; they can fundamentally alter optimization dynamics, learned representations, training behavior, stability, and, in some cases, the functional behavior of neural networks. This presentation sheds light on the tensions between determinism, reproducibility, and predictability, and questions the actual role of numerical precision in the design, analysis, and certification of modern machine learning models.