Revealing Procedural Reasoning Structures in Chain-of-Thought Training via Span-Level Gradient Organization

Chain-of-Thought (CoT) prompting enables large language models to produce multi-step reasoning, yet how such reasoning-related structure is expressed during training remains poorly understood. We present Gradient-based Structural Developer (GSD), an unsupervised framework with a principled gradient aggregation view that tracks span-level gradient during fine-tuning on reasoning benchmarks to understand how models develop structured, stepby-step reasoning capabilities. Our analysis shows that while gradients at the level of individual tokens are often noisy, aggregating gradients over contiguous reasoning-related spans reveals stable and recurring directional alignment across samples. We refer to these directionally aligned patterns as aligned sequential stresses, reflecting consistent gradient organization associated with similar reasoning procedures. Beyond capturing semantically similar reasoning instances, such gradient alignment also reveals structurally similar but semantically diverse cases that share common procedural organization. These findings position GSD as a diagnostic framework for analyzing how procedural reasoning structures emerge during training, with downstream selection results serving as auxiliary evidence correlating gradient alignment with adaptation efficiency.