Can Structured Templates Facilitate LLMs in Tackling Harder Tasks? : An Exploration of Scaling Laws by Difficulty
It addresses the problem of enhancing procedural reasoning in LLMs for mathematics, with incremental improvements in performance on specific tasks.
The paper tackles the limitation of LLMs in procedural reasoning on complex tasks by discovering a Scaling Law by Difficulty, showing a U-shaped performance curve with data complexity, and proposes the Structured Solution Template (SST) framework, which improves accuracy and efficiency on benchmarks like GSM8K and AIME24.
Structured, procedural reasoning is essential for Large Language Models (LLMs), especially in mathematics. While post-training methods have improved LLM performance, they still fall short in capturing deep procedural logic on complex tasks. To tackle the issue, in this paper, we first investigate this limitation and uncover a novel finding: a Scaling Law by Difficulty, which reveals that model performance follows a U-shaped curve with respect to training data complexity -- excessive low-difficulty data impedes abstraction, while high-difficulty data significantly enhances reasoning ability. Motivated by this, we propose the Structured Solution Template (SST) framework, which uses solution templates and a curriculum of varied difficulty to explicitly teach procedural reasoning. Specifically, SST comprises (1) fine-tuning with structured solution-template chains and dynamically weighted loss to prioritize procedural logic, (2) prompt-time injection of solution templates as cognitive scaffolds to guide inference, and (3) integrated curriculum fine-tuning that explicitly teaches the model to self-plan - execute - self-correct. Experiments on GSM8K, AIME24, and new Dynamic En benchmark show that SST significantly improves both accuracy and efficiency, especially on harder problems.