# Selecting Large Language Model to Fine-tune via Rectified Scaling Law

arXiv: https://arxiv.org/abs/2402.02314 · HTML: https://mlsanity.com/paper/2402.02314/

## Key facts

- Cited by 33 papers in the map (data through 14 Oct 2026).
- Builds on 55 of its 73 references that are in the map.
- First posted on arXiv 4 Feb 2024.

## Builds on (most cited first, 30 of 55)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [RoBERTa: A Robustly Optimized BERT Pretraining Approach](https://mlsanity.com/paper/1907.11692/) (2019)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [BART: Denoising Sequence-to-Sequence Pre-training for Natural Language Generation, Translation, and Comprehension](https://mlsanity.com/paper/1910.13461/) (2019)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [Deep reinforcement learning from human preferences](https://mlsanity.com/paper/1706.03741/) (2017)
- [Finetuned Language Models Are Zero-Shot Learners](https://mlsanity.com/paper/2109.01652/) (2021)
- [OPT: Open Pre-trained Transformer Language Models](https://mlsanity.com/paper/2205.01068/) (2022)
- [Switch Transformers: Scaling to Trillion Parameter Models with Simple and Efficient Sparsity](https://mlsanity.com/paper/2101.03961/) (2021)
- [Training Compute-Optimal Large Language Models](https://mlsanity.com/paper/2203.15556/) (2022)
- [Large Language Models Encode Clinical Knowledge](https://mlsanity.com/paper/2212.13138/) (2022)
- [mT5: A massively multilingual pre-trained text-to-text transformer](https://mlsanity.com/paper/2010.11934/) (2020)
- [Large Language Models](https://mlsanity.com/paper/2307.05782/) (2023)
- [The Flan Collection: Designing Data and Methods for Effective Instruction Tuning](https://mlsanity.com/paper/2301.13688/) (2023)
- [DeepSeek LLM: Scaling Open-Source Language Models with Longtermism](https://mlsanity.com/paper/2401.02954/) (2024)
- [Textbooks Are All You Need II: phi-1.5 technical report](https://mlsanity.com/paper/2309.05463/) (2023)
- [Generating Sequences With Recurrent Neural Networks](https://mlsanity.com/paper/1308.0850/) (2013)
- [Are Emergent Abilities of Large Language Models a Mirage?](https://mlsanity.com/paper/2304.15004/) (2023)
- [Scaling Laws for Autoregressive Generative Modeling](https://mlsanity.com/paper/2010.14701/) (2020)
- [Scaling Data-Constrained Language Models](https://mlsanity.com/paper/2305.16264/) (2023)
- [A Neural Attention Model for Abstractive Sentence Summarization](https://mlsanity.com/paper/1509.00685/) (2015)
- [Explaining Neural Scaling Laws](https://mlsanity.com/paper/2102.06701/) (2021)
- [Scaling Laws for Transfer](https://mlsanity.com/paper/2102.01293/) (2021)
- [Towards Understanding Grokking: An Effective Theory of Representation Learning](https://mlsanity.com/paper/2205.10343/) (2022)
- [A Constructive Prediction of the Generalization Error Across Scales](https://mlsanity.com/paper/1909.12673/) (2019)

## Built on by (most cited first, 30 of 33)

- [Inference Scaling Laws: An Empirical Analysis of Compute-Optimal Inference for Problem-Solving with Language Models](https://mlsanity.com/paper/2408.00724/) (2024)
- [RAT: Retrieval Augmented Thoughts Elicit Context-Aware Reasoning in Long-Horizon Generation](https://mlsanity.com/paper/2403.05313/) (2024)
- [Scaling Laws for Predicting Downstream Performance in LLMs](https://mlsanity.com/paper/2410.08527/) (2024)
- [Scaling Laws of Synthetic Data for Language Models](https://mlsanity.com/paper/2503.19551/) (2025)
- [Scaling Optimal LR Across Token Horizons](https://mlsanity.com/paper/2409.19913/) (2024)
- [OmniJARVIS: Unified Vision-Language-Action Tokenization Enables Open-World Instruction Following Agents](https://mlsanity.com/paper/2407.00114/) (2024)
- [JARVIS-VLA: Post-Training Large-Scale Vision Language Models to Play Visual Games with Keyboards and Mouse](https://mlsanity.com/paper/2503.16365/) (2025)
- [CMR Scaling Law: Predicting Critical Mixture Ratios for Continual Pre-training of Language Models](https://mlsanity.com/paper/2407.17467/) (2024)
- [Empirical Guidelines for Deploying LLMs onto Resource-constrained Edge Devices](https://mlsanity.com/paper/2406.03777/) (2024)
- [LENSLLM: Unveiling Fine-Tuning Dynamics for LLM Selection](https://mlsanity.com/paper/2505.03793/) (2025)
- [Can Language Models Discover Scaling Laws?](https://mlsanity.com/paper/2507.21184/) (2025)
- [Compute-Constrained Data Selection](https://mlsanity.com/paper/2410.16208/) (2024)
- [Train-before-Test Harmonizes Language Model Rankings](https://mlsanity.com/paper/2507.05195/) (2025)
- [PatentGPT: A Large Language Model for Intellectual Property](https://mlsanity.com/paper/2404.18255/) (2024)
- [Learning Shrinks the Hard Tail: Training-Dependent Inference Scaling in a Solvable Linear Model](https://mlsanity.com/paper/2601.03764/) (2026)
- [CLoG: Benchmarking Continual Learning of Image Generation Models](https://mlsanity.com/paper/2406.04584/) (2024)
- [TFG-Flow: Training-free Guidance in Multimodal Generative Flow](https://mlsanity.com/paper/2501.14216/) (2025)
- [How to Upscale Neural Networks with Scaling Law? A Survey and Practical Guidelines](https://mlsanity.com/paper/2502.12051/) (2025)
- [Towards Alignment-Centric Paradigm: A Survey of Instruction Tuning in Large Language Models](https://mlsanity.com/paper/2508.17184/) (2025)
- [Rethinking Model Selection in VLM Through the Lens of Gromov-Wasserstein Distance](https://mlsanity.com/paper/2605.01325/) (2026)
- [Spend Less, Fit Better: Budget-Efficient Scaling Law Fitting via Active Experiment Selection](https://mlsanity.com/paper/2604.22753/) (2026)
- [Estimating Time Series Foundation Model Transferability via In-Context Learning](https://mlsanity.com/paper/2509.23695/) (2025)
- [Decoding Linguistic Representations of Human Brain](https://mlsanity.com/paper/2407.20622/) (2024)
- [Prescriptive Scaling Reveals the Evolution of Language Model Capabilities](https://mlsanity.com/paper/2602.15327/) (2026)
- [TuneAhead: Predicting Fine-tuning Performance Before Full Training Begins](https://mlsanity.com/paper/2606.17660/) (2026)
- [Empowering Large Language Models in Wireless Communication: A Novel Dataset and Fine-Tuning Framework](https://mlsanity.com/paper/2501.09631/) (2025)
- [Mordal: Automated Pretrained Model Selection for Vision Language Models](https://mlsanity.com/paper/2502.00241/) (2025)
- [Fisher-Guided Progressive Parameter Selection for Adaptive Fine-Tuning](https://mlsanity.com/paper/2606.10196/) (2026)
- [Soft-Prompt Tuning for Fair and Efficient LLM Benchmark Evaluation](https://mlsanity.com/paper/2606.12117/) (2026)
- [A Risk Decomposition Framework for Pre-Hoc Fine-Tuning Prediction](https://mlsanity.com/paper/2606.17649/) (2026)

## Abstract (arXiv)

The ever-growing ecosystem of LLMs has posed a challenge in selecting the most appropriate pre-trained model to fine-tune amidst a sea of options. Given constrained resources, fine-tuning all models and making selections afterward is unrealistic. In this work, we formulate this resource-constrained selection task into predicting fine-tuning performance and illustrate its natural connection with Scaling Law. Unlike pre-training, we find that the fine-tuning scaling curve includes not just the well-known "power phase" but also the previously unobserved "pre-power phase". We also explain why existing Scaling Law fails to capture this phase transition phenomenon both theoretically and empirically. To address this, we introduce the concept of "pre-learned data size" into our Rectified Scaling Law, which overcomes theoretical limitations and fits experimental results much better. By leveraging our law, we propose a novel LLM selection algorithm that selects the near-optimal model with hundreds of times less resource consumption, while other methods may provide negatively correlated selection. The project page is available at rectified-scaling-law.github.io.