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arXiv · 2607.03574

Differentiate the Evaluator, Not the Program: An Efficient Runtime Representation for Neuro-Symbolic Learning

Lucas Sheneman
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Abstract

AI systems increasingly propose executable scientific models whose value depends on both their symbolic structure and their fitted continuous parameters. This makes parameter calibration the bottleneck of program-and-parameter co-search: an outer loop can generate thousands of candidate programs, but each needs an inner gradient-based optimization before it can be assessed. Staging each candidate into its own differentiable graph makes individual models fast but sacrifices the program-as-data property that keeps search fluid; interpreter-based approaches preserve programs as runtime data but pay interpreter overhead that dominates the numerical work. We present the Native Differentiable Virtual Machine (NDVM), a runtime representation that differentiates executable programs without compiling each candidate into a separate graph. NDVM separates symbolic structure from differentiable numeric state: tags, symbols, environments, and control remain native runtime data, while numeric payloads live in dense batched buffers with exact reverse-mode gradients recorded along the realized execution trace, so one evaluator walk is amortized across large populations of parameter vectors. A locked cost model of a real differentiable self-hosted Scheme interpreter motivates the design. We realize NDVM as a native runtime with forward and gradient equivalence to the reference backend, about 60x per-lane batch amortization, near-linear multicore scaling, and two independent front ends. In fixed-budget co-search over LLM-proposed programs, NDVM reaches high-quality solutions about 24x sooner in wall-clock time, suggesting runtime differentiation as a practical systems foundation for scientific discovery workflows.

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Lucas Sheneman. 2026-07-03. Differentiate the Evaluator, Not the Program: An Efficient Runtime Representation for Neuro-Symbolic Learning. https://arxiv.org/abs/2607.03574

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