Scaling Laws for Autoregressive Generative Modeling (2010.14701v2)

Abstract: 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.

Analytical Perspective on Scaling Laws for Autoregressive Generative Modeling

The paper "Scaling Laws for Autoregressive Generative Modeling" presents a comprehensive examination of the scalability of autoregressive Transformer models across various domains, specifically focusing on generative image modeling, video modeling, multimodal image-text models, and mathematical problem solving. The paper identifies consistent empirical scaling laws linked to model performance, particularly cross-entropy loss, as model size and compute resources increase.

The authors substantiate the hypothesis that autoregressive Transformers exhibit predictable performance improvements across different domains with increasing model size and computational budgets, adhering to a power-law plus constant framework. The cross-entropy loss is interpreted within an information-theoretic context, representing the true data distribution's entropy and the KL divergence between the model and true distributions. Notably, the paper claims that billion-parameter Transformers approximate the YFCC100M image distribution quite accurately, illustrating the model's efficacy at an exceptional level. This ability opens avenues for forecasting model requirements to achieve predefined reducible losses for varying image resolutions.

The paper extends the discussion to domain-specific scaling laws, highlighting the mutual information potential in multimodal models and interpreting whether a picture's worth can equate to a thousand words through numerical experimentation. Furthermore, the scaling laws reveal insights into the models' performance on mathematical problem-solving tasks where extrapolation beyond the training distribution was considered. The results emphasize the fine-tuned classification of generative image models, maintaining a consistent scaling of classification loss and error rates, indicating robust neural network performance implications even as generative losses stabilize.

Another salient feature of the analysis is the remarkable universality observed in the power-law exponents across different data modalities. These exponents suggest there's a coherent scaling aspect relative to the compute budget, hinting at an optimal model size that suggests a profound implication where optimality in model scale is nearly invariant across data types examined.

The paper positions the scaling laws within a wider narrative about the potential universal applicability of the Transformer architecture. By doing so, it encapsulates emergent understanding and consistency in performance gains as model sizes expand, becoming both more efficient and capable. Although findings confirm alignment with theoretical predictions, the authors acknowledge subtle inconsistencies that demand additional exploration, such as those concerning supervised data size scaling.

Taken as a whole, this exploration informs prospective theoretical frameworks in machine learning, motivating further paper. Furthermore, these laws encourage strategic considerations on resource allocation, suggesting that investing in more extensive models brings substantial returns compared to merely enlarging training datasets. Looking forward, this paper hints at paradigm shifts in AI, suggesting attention toward scaling and architecture must harmonize with evolving complexities in data landscapes and task formulations. The implications are manifold for advancing AI with greater efficacy, speed, and representational fidelity.