Can Structured Templates Facilitate LLMs in Tackling Harder Tasks? : An Exploration of Scaling Laws by Difficulty

TL;DR

This paper uncovers a U-shaped scaling law relating data difficulty to LLM performance and introduces the Structured Solution Template framework, which improves reasoning on complex tasks through curriculum learning and structured guidance.

Contribution

The paper reveals a novel Scaling Law by Difficulty for LLMs and proposes the SST framework that enhances procedural reasoning via structured templates and curriculum learning.

Findings

SST improves accuracy on GSM8K, AIME24, and Dynamic En benchmarks.

High-difficulty data enhances LLM reasoning capabilities.

Structured templates and curriculum learning lead to more efficient problem-solving.

Abstract

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.