# Beyond Chinchilla-Optimal: Accounting for Inference in Language Model Scaling Laws

arXiv: https://arxiv.org/abs/2401.00448 · HTML: https://mlsanity.com/paper/2401.00448/

## Key facts

- Cited by 159 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 61 references that are in the map.
- First posted on arXiv 31 Dec 2023.

## Builds on (most cited first, 30 of 32)

- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [SQuAD: 100,000+ Questions for Machine Comprehension of Text](https://mlsanity.com/paper/1606.05250/) (2016)
- [HellaSwag: Can a Machine Really Finish Your Sentence?](https://mlsanity.com/paper/1905.07830/) (2019)
- [PIQA: Reasoning about Physical Commonsense in Natural Language](https://mlsanity.com/paper/1911.11641/) (2019)
- [BoolQ: Exploring the Surprising Difficulty of Natural Yes/No Questions](https://mlsanity.com/paper/1905.10044/) (2019)
- [Can a Suit of Armor Conduct Electricity? A New Dataset for Open Book Question Answering](https://mlsanity.com/paper/1809.02789/) (2018)
- [Beyond the Imitation Game: Quantifying and extrapolating the capabilities of language models](https://mlsanity.com/paper/2206.04615/) (2022)
- [GPTQ: Accurate Post-Training Quantization for Generative Pre-trained Transformers](https://mlsanity.com/paper/2210.17323/) (2022)
- [CommonsenseQA: A Question Answering Challenge Targeting Commonsense Knowledge](https://mlsanity.com/paper/1811.00937/) (2018)
- [Train Short, Test Long: Attention with Linear Biases Enables Input Length Extrapolation](https://mlsanity.com/paper/2108.12409/) (2021)
- [The LAMBADA dataset: Word prediction requiring a broad discourse context](https://mlsanity.com/paper/1606.06031/) (2016)
- [Are NLP Models really able to Solve Simple Math Word Problems?](https://mlsanity.com/paper/2103.07191/) (2021)
- [AGIEval: A Human-Centric Benchmark for Evaluating Foundation Models](https://mlsanity.com/paper/2304.06364/) (2023)
- [CoQA: A Conversational Question Answering Challenge](https://mlsanity.com/paper/1808.07042/) (2018)
- [MathQA: Towards Interpretable Math Word Problem Solving with Operation-Based Formalisms](https://mlsanity.com/paper/1905.13319/) (2019)
- [Deep Learning Scaling is Predictable, Empirically](https://mlsanity.com/paper/1712.00409/) (2017)
- [Beyond neural scaling laws: beating power law scaling via data pruning](https://mlsanity.com/paper/2206.14486/) (2022)
- [Scaling Laws for Autoregressive Generative Modeling](https://mlsanity.com/paper/2010.14701/) (2020)
- [LMSYS-Chat-1M: A Large-Scale Real-World LLM Conversation Dataset](https://mlsanity.com/paper/2309.11998/) (2023)
- [Reducing Activation Recomputation in Large Transformer Models](https://mlsanity.com/paper/2205.05198/) (2022)
- [Scaling Laws for Transfer](https://mlsanity.com/paper/2102.01293/) (2021)
- [A Constructive Prediction of the Generalization Error Across Scales](https://mlsanity.com/paper/1909.12673/) (2019)
- [The Quantization Model of Neural Scaling](https://mlsanity.com/paper/2303.13506/) (2023)
- [Broken Neural Scaling Laws](https://mlsanity.com/paper/2210.14891/) (2022)
- [Exploring the Limits of Large Scale Pre-training](https://mlsanity.com/paper/2110.02095/) (2021)

## Built on by (most cited first, 30 of 159)

- [Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters](https://mlsanity.com/paper/2408.03314/) (2024)
- [MiniCPM: Unveiling the Potential of Small Language Models with Scalable Training Strategies](https://mlsanity.com/paper/2404.06395/) (2024)
- [Yi: Open Foundation Models by 01.AI](https://mlsanity.com/paper/2403.04652/) (2024)
- [Inference Scaling Laws: An Empirical Analysis of Compute-Optimal Inference for Problem-Solving with Language Models](https://mlsanity.com/paper/2408.00724/) (2024)
- [The Unreasonable Ineffectiveness of the Deeper Layers](https://mlsanity.com/paper/2403.17887/) (2024)
- [Scaling Laws and Compute-Optimal Training Beyond Fixed Training Durations](https://mlsanity.com/paper/2405.18392/) (2024)
- [The Unreasonable Effectiveness of Entropy Minimization in LLM Reasoning](https://mlsanity.com/paper/2505.15134/) (2025)
- [O1 Replication Journey: A Strategic Progress Report -- Part 1](https://mlsanity.com/paper/2410.18982/) (2024)
- [Scaling Laws with Vocabulary: Larger Models Deserve Larger Vocabularies](https://mlsanity.com/paper/2407.13623/) (2024)
- [Language models scale reliably with over-training and on downstream tasks](https://mlsanity.com/paper/2403.08540/) (2024)
- [Multi-Agent Collaboration via Evolving Orchestration](https://mlsanity.com/paper/2505.19591/) (2025)
- [Reward-Guided Speculative Decoding for Efficient LLM Reasoning](https://mlsanity.com/paper/2501.19324/) (2025)
- [Scaling Laws for Precision](https://mlsanity.com/paper/2411.04330/) (2024)
- [Resolving Discrepancies in Compute-Optimal Scaling of Language Models](https://mlsanity.com/paper/2406.19146/) (2024)
- [Scaling Test-Time Compute Without Verification or RL is Suboptimal](https://mlsanity.com/paper/2502.12118/) (2025)
- [Scaling Laws for Data Filtering -- Data Curation cannot be Compute Agnostic](https://mlsanity.com/paper/2404.07177/) (2024)
- [Chinchilla Scaling: A replication attempt](https://mlsanity.com/paper/2404.10102/) (2024)
- [BREAD: Branched Rollouts from Expert Anchors Bridge SFT & RL for Reasoning](https://mlsanity.com/paper/2506.17211/) (2025)
- [Mechanistic Design and Scaling of Hybrid Architectures](https://mlsanity.com/paper/2403.17844/) (2024)
- [CroissantLLM: A Truly Bilingual French-English Language Model](https://mlsanity.com/paper/2402.00786/) (2024)
- [Crosslingual Reasoning through Test-Time Scaling](https://mlsanity.com/paper/2505.05408/) (2025)
- [Towards Greater Leverage: Scaling Laws for Efficient Mixture-of-Experts Language Models](https://mlsanity.com/paper/2507.17702/) (2025)
- [How Do Large Language Monkeys Get Their Power (Laws)?](https://mlsanity.com/paper/2502.17578/) (2025)
- [Scaling Optimal LR Across Token Horizons](https://mlsanity.com/paper/2409.19913/) (2024)
- [Densing Law of LLMs](https://mlsanity.com/paper/2412.04315/) (2024)
- [Unveiling the Secret Recipe: A Guide For Supervised Fine-Tuning Small LLMs](https://mlsanity.com/paper/2412.13337/) (2024)
- [Quartet: Native FP4 Training Can Be Optimal for Large Language Models](https://mlsanity.com/paper/2505.14669/) (2025)
- [Towards Neural Scaling Laws for Time Series Foundation Models](https://mlsanity.com/paper/2410.12360/) (2024)
- [Joint MoE Scaling Laws: Mixture of Experts Can Be Memory Efficient](https://mlsanity.com/paper/2502.05172/) (2025)
- [The Future of Large Language Model Pre-training is Federated](https://mlsanity.com/paper/2405.10853/) (2024)

## Abstract (arXiv)

Large language model (LLM) scaling laws are empirical formulas that estimate changes in model quality as a result of increasing parameter count and training data. However, these formulas, including the popular Deepmind Chinchilla scaling laws, neglect to include the cost of inference. We modify the Chinchilla scaling laws to calculate the optimal LLM parameter count and pre-training data size to train and deploy a model of a given quality and inference demand. We conduct our analysis both in terms of a compute budget and real-world costs and find that LLM researchers expecting reasonably large inference demand (~1B requests) should train models smaller and longer than Chinchilla-optimal. Furthermore, we train 47 models of varying sizes and parameter counts to validate our formula and find that model quality continues to improve as we scale tokens per parameter to extreme ranges (up to 10,000). Finally, we ablate the procedure used to fit the Chinchilla scaling law coefficients and find that developing scaling laws only from data collected at typical token/parameter ratios overestimates the impact of additional tokens at these extreme ranges.