  We identify empirical scaling laws for the cross-entropy loss in four
domains: generative image modeling, video modeling, multimodal
image$\leftrightarrow$text models, and mathematical problem solving. In all
cases autoregressive Transformers smoothly improve in performance as model size
and compute budgets increase, following a power-law plus constant scaling law.
The optimal model size also depends on the compute budget through a power-law,
with exponents that are nearly universal across all data domains.
  The cross-entropy loss has an information theoretic interpretation as
$S($True$) + D_{\mathrm{KL}}($True$||$Model$)$, and the empirical scaling laws
suggest a prediction for both the true data distribution's entropy and the KL
divergence between the true and model distributions. With this interpretation,
billion-parameter Transformers are nearly perfect models of the YFCC100M image
distribution downsampled to an $8\times 8$ resolution, and we can forecast the
model size needed to achieve any given reducible loss (ie $D_{\mathrm{KL}}$) in
nats/image for other resolutions.
  We find a number of additional scaling laws in specific domains: (a) we
identify a scaling relation for the mutual information between captions and
images in multimodal models, and show how to answer the question "Is a picture
worth a thousand words?"; (b) in the case of mathematical problem solving, we
identify scaling laws for model performance when extrapolating beyond the
training distribution; (c) we finetune generative image models for ImageNet
classification and find smooth scaling of the classification loss and error
rate, even as the generative loss levels off. Taken together, these results
strengthen the case that scaling laws have important implications for neural
network performance, including on downstream tasks.
