Reasoning Scaffolding: Distilling the Flow of Thought from LLMs

The prevailing approach to distilling reasoning from Large Language Models (LLMs)-behavioral cloning from textual rationales-is fundamentally limited. It teaches Small Language Models (SLMs) to mimic surface-level patterns rather than the underlying algorithmic structure of thought, resulting in a critical lack of logical robustness. We argue that instead of cloning text, distillation should transfer this algorithmic structure directly. We introduce Reasoning Scaffolding}, a framework that reframes reasoning as a structured generation process. Our method first abstracts the teacher's thought process into a sequence of discrete, interpretable semantic signals (e.g., Contrast, Addition) that act as a scaffold. The student model is then trained via a multi-task objective to both (1)predict the next semantic signal, anticipating the reasoning flow, and (2)generate the corresponding step, conditioned on that signal. This multi-task scheme acts as a powerful regularizer, compelling the student to internalize the computational patterns of coherent reasoning. On a suite of challenging reasoning benchmarks, our method significantly outperforms state-of-the-art distillation in both accuracy and logical consistency, providing a path towards creating smaller models that are genuine reasoners, not just fluent mimics.