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

TL;DR

This paper investigates how different data ordering strategies in curriculum learning affect large language models' mathematical reasoning, revealing that effectiveness depends on model and task specifics, and that no single approach is universally best.

Contribution

It introduces a unified evaluation framework for curriculum difficulty and systematically analyzes the effects of data ordering on LLM reasoning performance across multiple models and metrics.

Findings

No universal curriculum strategy is optimal for all scenarios.

Effectiveness of forward vs. reverse curriculum depends on model and task complexity.

Decision-uncertain samples can enhance learning outcomes.

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.