# Skaling: Chinchilla's Exponents Meet Kaplan's Coupling

arXiv: https://arxiv.org/abs/2608.07222 · HTML: https://mlsanity.com/paper/2608.07222/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 18 references that are in the map.
- First posted on arXiv 7 Aug 2026.

## Builds on (most cited first, 16 of 16)

- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [Training Compute-Optimal Large Language Models](https://mlsanity.com/paper/2203.15556/) (2022)
- [DeepSeek LLM: Scaling Open-Source Language Models with Longtermism](https://mlsanity.com/paper/2401.02954/) (2024)
- [Deep Learning Scaling is Predictable, Empirically](https://mlsanity.com/paper/1712.00409/) (2017)
- [Scaling Data-Constrained Language Models](https://mlsanity.com/paper/2305.16264/) (2023)
- [DataComp-LM: In search of the next generation of training sets for language models](https://mlsanity.com/paper/2406.11794/) (2024)
- [The CMA Evolution Strategy: A Tutorial](https://mlsanity.com/paper/1604.00772/) (2016)
- [A Constructive Prediction of the Generalization Error Across Scales](https://mlsanity.com/paper/1909.12673/) (2019)
- [Data Mixing Laws: Optimizing Data Mixtures by Predicting Language Modeling Performance](https://mlsanity.com/paper/2403.16952/) (2024)
- [Resolving Discrepancies in Compute-Optimal Scaling of Language Models](https://mlsanity.com/paper/2406.19146/) (2024)
- [Chinchilla Scaling: A replication attempt](https://mlsanity.com/paper/2404.10102/) (2024)
- [Distillation Scaling Laws](https://mlsanity.com/paper/2502.08606/) (2025)
- [Scaling Laws for Optimal Data Mixtures](https://mlsanity.com/paper/2507.09404/) (2025)
- [Reconciling Kaplan and Chinchilla Scaling Laws](https://mlsanity.com/paper/2406.12907/) (2024)
- [Predictable Scale: Part I, Step Law -- Optimal Hyperparameter Scaling Law in Large Language Model Pretraining](https://mlsanity.com/paper/2503.04715/) (2025)
- [Predictable Scale: Part II, Farseer: A Refined Scaling Law in Large Language Models](https://mlsanity.com/paper/2506.10972/) (2025)

## Built on by (most cited first, 3 of 3)

- [Deriving Scaling Laws for OpenEuroLLM Models: Learning Rate, Batch Size and Loss](https://mlsanity.com/paper/2608.28308/) (2026)
- [Optimizer Memory Schedules for Outscaling the Overtraining Axis](https://mlsanity.com/paper/2609.04577/) (2026)
- [Mixed Precision Scaling Laws for Quantized Pretraining](https://mlsanity.com/paper/2610.17637/) (2026)

## Abstract (arXiv)

Neural scaling laws are foundational for language model development, yet standard formulations systematically under- and overestimate loss at data-scarce and overtraining extremes. This failure originates in the underlying assumption that model size and training data impact the loss independently. To address this, we introduce the Skaling law, a generalized functional form that couples model capacity and data through a single interaction exponent. This simple extension reduces the Mean Absolute Percentage Error (MAPE) by 1.5-3x across both interpolation and extrapolation regimes. When paired with a sparse grid strategy restricted to low-compute regimes, the Skaling law achieves accurate full-grid extrapolation using approximately 10x less compute than uniform sweeps. By enabling reliable performance prediction from small-scale experiments, the Skaling law provides a more robust and resource-efficient framework for allocating compute budgets in next-generation model training.