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This paper theoretically and empirically explains why inference-time harnesses (scaffolds) outperform distilled student models: harnesses can compute closures that are NL-complete even from trivial AC0 primitives, a representational power no fixed-depth forward pass can replicate under standard complexity assumptions. The authors verify that enlarging the model, simplifying the task, or lengthening chain-of-thought can close this gap, including on competition math with agentic harnesses.
This paper introduces Code-Guided Reasoning (CGR), an evaluation protocol for measuring how executable reasoning scaffolds improve small language model performance on multiple-choice question answering tasks, showing a significant accuracy improvement over direct answering.