A Neural Scaling Law from the Dimension of the Data Manifold
| Autor: | Sharma, Utkarsh, Kaplan, Jared |
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| Rok vydání: | 2020 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: 16+12 pages, 11+11 figures |
| Databáze: | arXiv |
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