This paper introduces the Native Differentiable Virtual Machine (NDVM), a runtime representation for differentiating executable programs without compiling every candidate into a separate graph. Symbolic elements such as tags, environments, and control flow remain native runtime data, while numeric state is stored in dense batched buffers. Exact reverse-mode gradients are recorded along the realized execution trace. The authors report forward and gradient equivalence to a reference backend, roughly 60x per-lane batch amortization, near-linear multicore scaling, and approximately 24x faster attainment of high-quality solutions in fixed-budget co-search with LLM-proposed programs.
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