What Makes a Good Curriculum? Disentangling the Effects of Data Ordering on LLM Mathematical Reasoning

摘要

Curriculum learning (CL), which orders training data from easy to hard, has become a popular strategy for improving reasoning in large language models (LLMs). Yet prior work employs disparate difficulty metrics and training setups, leaving open fundamental questions: When does curriculum help? Which direction—forward or reverse—is better? And does the answer depend on what we measure? We address these questions through a unified offline evaluation framework that decomposes curriculum difficulty into five complementary dimensions: Problem Difficulty, Model Surprisal, Confidence Margin, Predictive Uncertainty, and Decision Variability. Through controlled post-training experiments on mathematical reasoning benchmarks with Llama3.1-8B, Mistral-7B, and Gemma3-4B, we find that: (i) no curriculum strategy dominates universally—the relative effectiveness of forward versus reverse CL depends jointly on model capability and task complexity; (ii) even within a single metric, samples at different difficulty levels produce distinct gains depending on task demands; and (iii) Task-aligned curricula focus on shaping the model’s final representations and generalization, whereas inner-state curricula modulate internal states such as confidence and uncertainty. Our findings challenge the notion of a universal curriculum strategy and offer actionable guidance across model and task regimes, with some metrics indicating that prioritizing decision-uncertain samples can further enhance learning outcomes.