Current AI code generation systems suffer from significant latency bottlenecks due to CPU-GPU data transfers during compilation, execution, and testing phases. We establish theoretical foundations for three complementary approaches to GPU-native compilation that eliminate these transfers: (1) parallel traditional compilation adapted for GPU execution, (2) neural compilation using learned sequence-to-sequence translation with probabilistic verification, and (3) hybrid architectures combining both strategies. We derive latency and energy bounds demonstrating potential speedups of 10-100x for code iteration cycles. Our analysis shows that traditional GPU compilation provides 2-5x improvements through transfer elimination, neural compilation achieves 10-100x speedups via massive parallelism, and hybrid approaches offer practical deployment paths with guaranteed correctness. We formalize the probabilistic verification framework that enables trading compilation accuracy for parallel exploration, and discuss implications for self-improving AI systems and future analog computing substrates.