# What Do Learning Dynamics Reveal About Generalization in LLM Reasoning?

arXiv: https://arxiv.org/abs/2411.07681 · HTML: https://mlsanity.com/paper/2411.07681/

## Key facts

- Cited by 23 papers in the map (data through 14 Oct 2026).
- Placed in Reasoning benchmarks and evaluation, one of 17 directions in LLM reasoning.
- Builds on 30 of its 36 references that are in the map.
- First posted on arXiv 12 Nov 2024.

## Placed in

- LLM reasoning / [Reasoning benchmarks and evaluation](https://mlsanity.com/lr/reasoning-benchmarks-and-evaluation/)

## Builds on (most cited first, 30 of 30)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Extracting Training Data from Large Language Models](https://mlsanity.com/paper/2012.07805/) (2020)
- [Gemma 2: Improving Open Language Models at a Practical Size](https://mlsanity.com/paper/2408.00118/) (2024)
- [Interpretability in the Wild: a Circuit for Indirect Object Identification in GPT-2 small](https://mlsanity.com/paper/2211.00593/) (2022)
- [A Closer Look at Memorization in Deep Networks](https://mlsanity.com/paper/1706.05394/) (2017)
- [Deep Bayesian Active Learning with Image Data](https://mlsanity.com/paper/1703.02910/) (2017)
- [Quantifying Memorization Across Neural Language Models](https://mlsanity.com/paper/2202.07646/) (2022)
- [Fantastic Generalization Measures and Where to Find Them](https://mlsanity.com/paper/1912.02178/) (2019)
- [What Neural Networks Memorize and Why: Discovering the Long Tail via Influence Estimation](https://mlsanity.com/paper/2008.03703/) (2020)
- [What Makes Good Data for Alignment? A Comprehensive Study of Automatic Data Selection in Instruction Tuning](https://mlsanity.com/paper/2312.15685/) (2023)
- [Studying Large Language Model Generalization with Influence Functions](https://mlsanity.com/paper/2308.03296/) (2023)
- [Nearly-tight VC-dimension and pseudodimension bounds for piecewise linear neural networks](https://mlsanity.com/paper/1703.02930/) (2017)
- [Function Vectors in Large Language Models](https://mlsanity.com/paper/2310.15213/) (2023)
- [From Quantity to Quality: Boosting LLM Performance with Self-Guided Data Selection for Instruction Tuning](https://mlsanity.com/paper/2308.12032/) (2023)
- [Norm-Based Capacity Control in Neural Networks](https://mlsanity.com/paper/1503.00036/) (2015)
- [Memorization Without Overfitting: Analyzing the Training Dynamics of Large Language Models](https://mlsanity.com/paper/2205.10770/) (2022)
- [Leveraging Unlabeled Data to Predict Out-of-Distribution Performance](https://mlsanity.com/paper/2201.04234/) (2022)
- [Assessing Generalization of SGD via Disagreement](https://mlsanity.com/paper/2106.13799/) (2021)
- [#InsTag: Instruction Tagging for Analyzing Supervised Fine-tuning of Large Language Models](https://mlsanity.com/paper/2308.07074/) (2023)
- [DsDm: Model-Aware Dataset Selection with Datamodels](https://mlsanity.com/paper/2401.12926/) (2024)
- [RL on Incorrect Synthetic Data Scales the Efficiency of LLM Math Reasoning by Eight-Fold](https://mlsanity.com/paper/2406.14532/) (2024)
- [A Comparative Survey of Deep Active Learning](https://mlsanity.com/paper/2203.13450/) (2022)
- [Generalization in Deep Networks: The Role of Distance from Initialization](https://mlsanity.com/paper/1901.01672/) (2019)
- [Be like a Goldfish, Don't Memorize! Mitigating Memorization in Generative LLMs](https://mlsanity.com/paper/2406.10209/) (2024)
- [Active Learning Helps Pretrained Models Learn the Intended Task](https://mlsanity.com/paper/2204.08491/) (2022)
- [A Preliminary Study of the Intrinsic Relationship between Complexity and Alignment](https://mlsanity.com/paper/2308.05696/) (2023)
- [Smaller Language Models are capable of selecting Instruction-Tuning Training Data for Larger Language Models](https://mlsanity.com/paper/2402.10430/) (2024)

## Built on by (most cited first, 23 of 23)

- [SFT Memorizes, RL Generalizes: A Comparative Study of Foundation Model Post-training](https://mlsanity.com/paper/2501.17161/) (2025)
- [A Survey of Frontiers in LLM Reasoning: Inference Scaling, Learning to Reason, and Agentic Systems](https://mlsanity.com/paper/2504.09037/) (2025)
- [Training Strategies for Efficient Embodied Reasoning](https://mlsanity.com/paper/2505.08243/) (2025)
- [RL Fine-Tuning Heals OOD Forgetting in SFT](https://mlsanity.com/paper/2509.12235/) (2025)
- [Reasoning as an Adaptive Defense for Safety](https://mlsanity.com/paper/2507.00971/) (2025)
- [Shuffle-R1: Efficient RL framework for Multimodal Large Language Models via Data-centric Dynamic Shuffle](https://mlsanity.com/paper/2508.05612/) (2025)
- [Beyond the Sampled Token: Preserving Candidate Support in RLVR](https://mlsanity.com/paper/2510.14807/) (2025)
- [Reuse your FLOPs: Scaling RL on Hard Problems by Conditioning on Very Off-Policy Prefixes](https://mlsanity.com/paper/2601.18795/) (2026)
- [Are Large Language Models Reliable AI Scientists? Assessing Reverse-Engineering of Black-Box Systems](https://mlsanity.com/paper/2505.17968/) (2025)
- [Unveiling Over-Memorization in Finetuning LLMs for Reasoning Tasks](https://mlsanity.com/paper/2508.04117/) (2025)
- [Behavior Injection: Preparing Language Models for Reinforcement Learning](https://mlsanity.com/paper/2505.18917/) (2025)
- [A Tool for In-depth Analysis of Code Execution Reasoning of Large Language Models](https://mlsanity.com/paper/2501.18482/) (2025)
- [Style over Substance: Distilled Language Models Reason Via Stylistic Replication](https://mlsanity.com/paper/2504.01738/) (2025)
- [Reason to Rote: Rethinking Memorization in Reasoning](https://mlsanity.com/paper/2507.04782/) (2025)
- [Generalization or Memorization: Dynamic Decoding for Mode Steering](https://mlsanity.com/paper/2510.22099/) (2025)
- [Rotation-Preserving Supervised Fine-Tuning](https://mlsanity.com/paper/2605.10973/) (2026)
- [Adaptive Multi-Agent Reasoning via Automated Workflow Generation](https://mlsanity.com/paper/2507.14393/) (2025)
- [ML For Hardware Design Interpretability: Challenges and Opportunities](https://mlsanity.com/paper/2504.08852/) (2025)
- [Answer-Centric or Reasoning-Driven? Uncovering the Latent Memory Anchor in LLMs](https://mlsanity.com/paper/2506.17630/) (2025)
- [ExpRL: Exploratory RL for LLM Mid-Training](https://mlsanity.com/paper/2606.17024/) (2026)
- [Towards Precision Therapy in Hepatocellular Carcinoma: A Clinical-Reasoning LLM for Risk Stratification and Treatment Guidance](https://mlsanity.com/paper/2607.08602/) (2026)
- [Large Language Models Threaten Double-blind Review](https://mlsanity.com/paper/2608.05157/) (2026)
- [Training Language Models To Be Coherent Decision-Makers](https://mlsanity.com/paper/2610.09164/) (2026)

## Abstract (arXiv)

Despite the remarkable capabilities of modern large language models (LLMs), the mechanisms behind their problem-solving abilities remain elusive. In this work, we aim to better understand how the learning dynamics of LLM finetuning shapes downstream generalization. Our analysis focuses on reasoning tasks, whose problem structure allows us to distinguish between memorization (the exact replication of reasoning steps from the training data) and performance (the correctness of the final solution). We find that a model's generalization behavior can be effectively characterized by a training metric we call pre-memorization train accuracy: the accuracy of model samples on training queries before they begin to copy the exact reasoning steps from the training set. On the dataset level, this metric is able to reliably predict test accuracy, achieving R2 of around or exceeding 0.9 across various models (Llama3 8, Gemma2 9B), datasets (GSM8k, MATH), and training configurations. On a per-example level, this metric is also indicative of whether individual model predictions are robust to perturbations in the training query. By connecting a model's learning behavior to its generalization, pre-memorization train accuracy can guide targeted improvements to training strategies. We focus on data curation as an example, and show that prioritizing examples with low pre-memorization accuracy leads to 1.5-2x improvements in data efficiency compared to i.i.d. data scaling, and outperforms other standard data curation techniques.