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

• URL: http://arxiv.org/abs/2510.19099v2
• Date: Fri, 24 Oct 2025 20:45:57 GMT
• Title: What Makes a Good Curriculum? Disentangling the Effects of Data Ordering on LLM Mathematical Reasoning
• Authors: Yaning Jia, Chunhui Zhang, Xingjian Diao, Xiangchi Yuan, Zhongyu Ouyang, Chiyu Ma, Soroush Vosoughi,
• Abstract summary: Curriculum learning (CL) has become a popular strategy for improving reasoning in large language models (LLMs)<n>Yet prior work employs disparate difficulty metrics and training setups, leaving open fundamental questions: When does curriculum help?<n>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.
• Score: 47.10036442634749
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Curriculum learning (CL) - ordering 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.

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