Differentiable Meta-Circular Interpreter Enables Gradient-Based Optimization of Executable Programs
Researchers have built a compiler that translates a self-hosting subset of Scheme into differentiable computation graphs, enabling gradient-based optimization of programs treated as scientific models. The system, called Differentiable Meta-Circular Interpretation (DMCI), compiles a Scheme interpreter once so that any program it subsequently executes inherits differentiability without recompilation. This extends symbolic regression and neurosymbolic search beyond closed-form expressions to stateful, executable programs, potentially allowing model-generated code to be directly optimized against real-world data.
A preprint posted to arXiv introduces DMCI, a compiler that converts a self-hosting subset of the Scheme programming language into differentiable computation graphs compatible with standard autograd backends. Because the subset is expressive enough to compile its own evaluator, the resulting interpreter can execute arbitrary programs supplied as data while reverse-mode automatic differentiation propagates gradients back to continuous constants embedded in those programs. The authors prove that gradients through the compiled interpreter are correct almost everywhere and validate them against direct compilation across 171 recursive and higher-order program-seed pairs. In practical demonstrations, DMCI is paired with a large language model in a program-and-parameter co-search loop: the LLM proposes discrete Scheme program structures while DMCI calibrates their continuous parameters via exact gradients through a single frozen interpreter. On a battery capacity-fade dataset, the approach recovers a physically meaningful degradation structure and outperforms hand-crafted baselines on an early-extrapolation split; on a high-dimensional El Niño inverse problem, DMCI successfully optimizes an interpreted Kalman-filter likelihood where gradient-free methods fail. The work positions executable, stateful programs—including those with closures, recursion, and data structures—as first-class learnable scientific models.
What's missing
The paper is a preprint and has not yet undergone peer review. Key open questions include scalability to larger or more complex programs, the computational overhead of differentiating through interpretation compared to direct compilation, and whether the approach generalizes beyond the demonstrated Scheme subset to other languages or richer program structures. The battery and El Niño experiments are relatively small-scale demonstrations rather than comprehensive benchmarks.
What different sources said
- arXiv cs.LGCenter
Compile Once, Differentiate Everywhere: A Differentiable Meta-Circular Interpreter
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