@misc{sharma2020neural,
  title = {A Neural Scaling Law from the Dimension of the Data Manifold},
  author = {Utkarsh Sharma and J. Kaplan},
  year = {2020},
  howpublished = {arXiv.org},
  url = {https://arxiv.org/abs/2004.10802},
  abstract = {When data is plentiful, the loss achieved by well-trained neural networks scales as a power-law $L \propto N^{-\alpha}$ in the number of network parameters $N$. This empirical scaling law holds for a wide variety of data modalities, and may persist over many orders of magnitude. The scaling law can be explained if neural models are effectively just performing regression on a data manifold of intrinsic dimension $d$. This simple theory predicts that the scaling exponents $\alpha \approx 4/d$ for cross-entropy and mean-squared error losses. We confirm the theory by independently measuring the intrinsic dimension and the scaling exponents in a teacher/student framework, where we can study a variety of $d$ and $\alpha$ by dialing the properties of random teacher networks. We also test the theory with CNN image classifiers on several datasets and with GPT-type language models.}
}