# Learning Dynamics in Continual Pre-Training for Large Language Models

arXiv: https://arxiv.org/abs/2505.07796 · HTML: https://mlsanity.com/paper/2505.07796/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 30 of its 42 references that are in the map.
- First posted on arXiv 12 May 2025.

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

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [Training Compute-Optimal Large Language Models](https://mlsanity.com/paper/2203.15556/) (2022)
- [The Pile: An 800GB Dataset of Diverse Text for Language Modeling](https://mlsanity.com/paper/2101.00027/) (2020)
- [The FineWeb Datasets: Decanting the Web for the Finest Text Data at Scale](https://mlsanity.com/paper/2406.17557/) (2024)
- [Learning to Prompt for Continual Learning](https://mlsanity.com/paper/2112.08654/) (2021)
- [MiniCPM: Unveiling the Potential of Small Language Models with Scalable Training Strategies](https://mlsanity.com/paper/2404.06395/) (2024)
- [Scaling Laws for Transfer](https://mlsanity.com/paper/2102.01293/) (2021)
- [Continual Learning of Large Language Models: A Comprehensive Survey](https://mlsanity.com/paper/2404.16789/) (2024)
- [Data Mixing Laws: Optimizing Data Mixtures by Predicting Language Modeling Performance](https://mlsanity.com/paper/2403.16952/) (2024)
- [RedPajama: an Open Dataset for Training Large Language Models](https://mlsanity.com/paper/2411.12372/) (2024)
- [RegMix: Data Mixture as Regression for Language Model Pre-training](https://mlsanity.com/paper/2407.01492/) (2024)
- [Continual Pre-Training of Large Language Models: How to (re)warm your model?](https://mlsanity.com/paper/2308.04014/) (2023)
- [Simple and Scalable Strategies to Continually Pre-train Large Language Models](https://mlsanity.com/paper/2403.08763/) (2024)
- [Pile of Law: Learning Responsible Data Filtering from the Law and a 256GB Open-Source Legal Dataset](https://mlsanity.com/paper/2207.00220/) (2022)
- [Reuse, Don't Retrain: A Recipe for Continued Pretraining of Language Models](https://mlsanity.com/paper/2407.07263/) (2024)
- [Lifelong Language Pretraining with Distribution-Specialized Experts](https://mlsanity.com/paper/2305.12281/) (2023)
- [Investigating Continual Pretraining in Large Language Models: Insights and Implications](https://mlsanity.com/paper/2402.17400/) (2024)
- [Continual evaluation for lifelong learning: Identifying the stability gap](https://mlsanity.com/paper/2205.13452/) (2022)
- [D-CPT Law: Domain-specific Continual Pre-Training Scaling Law for Large Language Models](https://mlsanity.com/paper/2406.01375/) (2024)
- [Scaling Law with Learning Rate Annealing](https://mlsanity.com/paper/2408.11029/) (2024)
- [CMR Scaling Law: Predicting Critical Mixture Ratios for Continual Pre-training of Language Models](https://mlsanity.com/paper/2407.17467/) (2024)
- [A Multi-Power Law for Loss Curve Prediction Across Learning Rate Schedules](https://mlsanity.com/paper/2503.12811/) (2025)
- [Data Mixture Inference: What do BPE Tokenizers Reveal about their Training Data?](https://mlsanity.com/paper/2407.16607/) (2024)
- [Unearthing Large Scale Domain-Specific Knowledge from Public Corpora](https://mlsanity.com/paper/2401.14624/) (2024)
- [An Empirical Study of Scaling Laws for Transfer](https://mlsanity.com/paper/2408.16947/) (2024)
- [Optimization Hyper-parameter Laws for Large Language Models](https://mlsanity.com/paper/2409.04777/) (2024)
- [A Learning Rate Path Switching Training Paradigm for Version Updates of Large Language Models](https://mlsanity.com/paper/2410.04103/) (2024)

## Built on by (most cited first, 5 of 5)

- [Reinforcement Fine-Tuning Naturally Mitigates Forgetting in Continual Post-Training](https://mlsanity.com/paper/2507.05386/) (2025)
- [Pre-training LLM without Learning Rate Decay Enhances Supervised Fine-Tuning](https://mlsanity.com/paper/2603.16127/) (2026)
- [LegalOne: A Family of Foundation Models for Reliable Legal Reasoning](https://mlsanity.com/paper/2602.00642/) (2026)
- [Reusing Overtrained Language Models Saturates Scaling](https://mlsanity.com/paper/2510.06548/) (2025)
- [Understanding the Weight Averaging Mechanism in LLM Training for Post-Training Quantization](https://mlsanity.com/paper/2610.05329/) (2026)

## Abstract (arXiv)

Continual Pre-Training (CPT) has become a popular and effective method to apply strong foundation models to specific downstream tasks. In this work, we explore the learning dynamics throughout the CPT process for large language models. We specifically focus on how general and downstream domain performance evolves at each training step, with domain performance measured via validation losses. We have observed that the CPT loss curve fundamentally characterizes the transition from one curve to another hidden curve, and could be described by decoupling the effects of distribution shift and learning rate annealing. We derive a CPT scaling law that combines the two factors, enabling the prediction of loss at any (continual) training steps and across learning rate schedules (LRS) in CPT. Our formulation presents a comprehensive understanding of several critical factors in CPT, including loss potential, peak learning rate, training steps, replay ratio, etc. Moreover, our approach can be adapted to customize training hyper-parameters to different CPT goals such as balancing general and domain-specific performance. Extensive experiments demonstrate that our scaling law holds across various CPT datasets and training hyper-parameters.