What Makes a Good Curriculum? Disentangling the Effects of Data Ordering on LLM Mathematical Reasoning
On the map: LLM reasoning → Mathematical reasoning
Abstract (arXiv)
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.
Key facts. Cited by 10 papers in the map (data through 7 Oct 2026). Placed in Mathematical reasoning, one of 17 directions in LLM reasoning. Builds on 34 of its 55 references that are in the map. First posted on arXiv 21 Oct 2025.
Builds on
34 of 55 references.
Closest ancestors · 1
Same direction, newest first
Other references · 33
- 2024The Llama 3 Herd of Modelscited by 14,192
- 2021LoRA: Low-Rank Adaptation of Large Language Modelscited by 14,084
- 2021Training Verifiers to Solve Math Word Problemscited by 9,743
- 2022Self-Consistency Improves Chain of Thought Reasoning in Language Modelscited by 5,601
- 2021Measuring Mathematical Problem Solving With the MATH Datasetcited by 5,203
- 2023Let's Verify Step by Stepcited by 3,598
- 2023Mistral 7Bcited by 3,065
- 2025Gemma 3 Technical Reportcited by 1,686
- 2022Least-to-Most Prompting Enables Complex Reasoning in Large Language Modelscited by 1,397
- 2022STaR: Bootstrapping Reasoning With Reasoningcited by 895
- 2023MetaMath: Bootstrap Your Own Mathematical Questions for Large Language Modelscited by 724
- 2025Beyond the 80/20 Rule: High-Entropy Minority Tokens Drive Effective Reinforcement Learning for LLM Reasoningcited by 540
21 more
- 2022Formal Mathematics Statement Curriculum Learningcited by 141
- 2023Skill-it! A Data-Driven Skills Framework for Understanding and Training Language Modelscited by 120
- 2025Self-Evolving Curriculum for LLM Reasoningcited by 107
- 2024MathBench: Evaluating the Theory and Application Proficiency of LLMs with a Hierarchical Mathematics Benchmarkcited by 103
- 2025Curriculum Reinforcement Learning from Easy to Hard Tasks Improves LLM Reasoningcited by 89
- 2024Training Large Language Models for Reasoning through Reverse Curriculum Reinforcement Learningcited by 63
- 2024Let's Learn Step by Step: Enhancing In-Context Learning Ability with Curriculum Learningcited by 47
- 2025Curriculum-RLAIF: Curriculum Alignment with Reinforcement Learning from AI Feedbackcited by 30
- 2024Strategic Data Ordering: Enhancing Large Language Model Performance through Curriculum Learningcited by 28
- 2025SPEED-RL: Faster Training of Reasoning Models via Online Curriculum Learningcited by 27
- 2024Dataset Decomposition: Faster LLM Training with Variable Sequence Length Curriculumcited by 25
- 2025Beyond Random Sampling: Efficient Language Model Pretraining via Curriculum Learningcited by 25
- 2024Easy2Hard-Bench: Standardized Difficulty Labels for Profiling LLM Performance and Generalizationcited by 24
- 2025Train Long, Think Short: Curriculum Learning for Efficient Reasoningcited by 20
- 2024On the Noise Robustness of In-Context Learning for Text Generationcited by 15
- 2023CITING: Large Language Models Create Curriculum for Instruction Tuningcited by 14
- 2022Adaptive Ranking-based Sample Selection for Weakly Supervised Class-imbalanced Text Classificationcited by 7
- 2025Your Pretrained Model Tells the Difficulty Itself: A Self-Adaptive Curriculum Learning Paradigm for Natural Language Understandingcited by 3
- 2025Reasoning Steps as Curriculum: Using Depth of Thought as a Difficulty Signal for Tuning LLMscited by 3
- 2023Confidence-Aware Calibration and Scoring Functions for Curriculum Learningcited by 2
- 2025Entropy-Driven Curriculum for Multi-Task Training in Human Mobility Predictioncited by 1
Built on by
Citing papers per year: 2026: 10.
10 papers.
- 2026Behavior Knowledge Merge in Reinforced Agentic Modelscited by 10
- 2026Addressing Overthinking in Large Vision-Language Models via Gated Perception-Reasoning Optimizationcited by 6
- 2026When Linguistic and Internal Confidence Diverge in Large Language Modelscited by 2
- 2026D3: Dynamic Directional Graph-Constrained Data Scheduling for LLM Trainingcited by 0
- 2026Understanding Curriculum Learning in Large Language Models via Cross-Difficulty Optimization Dynamicscited by 0
- 2026Curriculum Learning as Transport: Understanding Curricula with Wasserstein Geodesicscited by 0
- 2026Which Tokens Should SFT Actually Learn? A Token-Trimming Perspective on Mathematical Reasoningcited by 0
- 2026Rethinking Length-Based Training: Batch Composition and Loss Normalization in Speech Token Language Modelscited by 0
- 2026The Free-Recipe Limit: Every Recipe Effect Measures Which Premise of an Idealised Learner Brokecited by 0
- 2026MetaCtrl: Your Large Language Models Can Reason Better and More Concisely with a Metacognitive Controllercited by 0
- 2026MetaCtrl: Your Large Language Models Can Reason Better and More Concisely with a Metacognitive Controller29 Sep 2026
- 2026Rethinking Length-Based Training: Batch Composition and Loss Normalization in Speech Token Language Models22 Sep 2026
- 2026Which Tokens Should SFT Actually Learn? A Token-Trimming Perspective on Mathematical Reasoning9 Sep 2026
- 2026Curriculum Learning as Transport: Understanding Curricula with Wasserstein Geodesics8 Sep 2026
- 2026When Linguistic and Internal Confidence Diverge in Large Language Models28 Aug 2026
- 2026Understanding Curriculum Learning in Large Language Models via Cross-Difficulty Optimization Dynamics18 Aug 2026
- 2026The Free-Recipe Limit: Every Recipe Effect Measures Which Premise of an Idealised Learner Broke9 Aug 2026
- 2026D3: Dynamic Directional Graph-Constrained Data Scheduling for LLM Training29 May 2026
- 2026Behavior Knowledge Merge in Reinforced Agentic Models20 Jan 2026
- 2026Addressing Overthinking in Large Vision-Language Models via Gated Perception-Reasoning Optimization7 Jan 2026
Similar, not cited
Close in wording, no citation either way
- 2026Rethinking Easy-to-Hard: Limits of Curriculum Learning in Post-Training for Deductive Reasoning
- 2024From Next-Token to Mathematics: The Learning Dynamics of Mathematical Reasoning in Language Models
- 2025Progressive Mastery: Customized Curriculum Learning with Guided Prompting for Mathematical Reasoning
- 2025MathRobust-LV: Evaluation of Large Language Models' Robustness to Linguistic Variations in Mathematical Reasoning
- 2026Math Reasoning in LLMs is Organized by Approach, Not Topic
- 2025Can Structured Templates Facilitate LLMs in Tackling Harder Tasks? : An Exploration of Scaling Laws by Difficulty
- 2024Procedural Knowledge in Pretraining Drives Reasoning in Large Language Models
- 2025Does Math Reasoning Improve General LLM Capabilities? Understanding Transferability of LLM Reasoning