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Register a new userScaling Laws for Autoregressive Generative Modeling
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Samuel McCandlish
Publication date
2020
fields
Informatics Engineering
and research's language is
English
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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 distributions 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 $8times 8$ 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.
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There is a recent trend in machine learning to increase model quality by growing models to sizes previously thought to be unreasonable. Recent work has shown that autoregressive generative models with cross-entropy objective functions exhibit smooth power-law relationships, or scaling laws, that predict model quality from model size, training set size, and the available compute budget. These scaling laws allow one to choose nearly optimal hyper-parameters given constraints on available training data, model parameter count, or training computation budget. In this paper, we demonstrate that acoustic models trained with an auto-predictive coding loss behave as if they are subject to similar scaling laws. We extend previous work to jointly predict loss due to model size, to training set size, and to the inherent irreducible loss of the task. We find that the scaling laws accurately match model performance over two orders of magnitude in both model size and training set size, and make predictions about the limits of model performance.
Self attention mechanisms have become a key building block in many state-of-the-art language understanding models. In this paper, we show that the self attention operator can be formulated in terms of 1x1 convolution operations. Following this observation, we propose several novel operators: First, we introduce a 2D version of self attention that is applicable for 2D signals such as images. Second, we present the 1D and 2D Self Attentive Convolutions (SAC) operator that generalizes self attention beyond 1x1 convolutions to 1xm and nxm convolutions, respectively. While 1D and 2D self attention operate on individual words and pixels, SAC operates on m-grams and image patches, respectively. Third, we present a multiscale version of SAC (MSAC) which analyzes the input by employing multiple SAC operators that vary by filter size, in parallel. Finally, we explain how MSAC can be utilized for vision and language modeling, and further harness MSAC to form a cross attentive image similarity machinery.
We study empirical scaling laws for language model performance on the cross-entropy loss. The loss scales as a power-law with model size, dataset size, and the amount of compute used for training, with some trends spanning more than seven orders of magnitude. Other architectural details such as network width or depth have minimal effects within a wide range. Simple equations govern the dependence of overfitting on model/dataset size and the dependence of training speed on model size. These relationships allow us to determine the optimal allocation of a fixed compute budget. Larger models are significantly more sample-efficient, such that optimally compute-efficient training involves training very large models on a relatively modest amount of data and stopping significantly before convergence.
We present an empirical study of scaling properties of encoder-decoder Transformer models used in neural machine translation (NMT). We show that cross-entropy loss as a function of model size follows a certain scaling law. Specifically (i) We propose a formula which describes the scaling behavior of cross-entropy loss as a bivariate function of encoder and decoder size, and show that it gives accurate predictions under a variety of scaling approaches and languages; we show that the total number of parameters alone is not sufficient for such purposes. (ii) We observe different power law exponents when scaling the decoder vs scaling the encoder, and provide recommendations for optimal allocation of encoder/decoder capacity based on this observation. (iii) We also report that the scaling behavior of the model is acutely influenced by composition bias of the train/test sets, which we define as any deviation from naturally generated text (either via machine generated or human translated text). We observe that natural text on the target side enjoys scaling, which manifests as successful reduction of the cross-entropy loss. (iv) Finally, we investigate the relationship between the cross-entropy loss and the quality of the generated translations. We find two different behaviors, depending on the nature of the test data. For test sets which were originally translated from target language to source language, both loss and BLEU score improve as model size increases. In contrast, for test sets originally translated from source language to target language, the loss improves, but the BLEU score stops improving after a certain threshold. We release generated text from all models used in this study.
While autoregressive models excel at image compression, their sample quality is often lacking. Although not realistic, generated images often have high likelihood according to the model, resembling the case of adversarial examples. Inspired by a successful adversarial defense method, we incorporate randomized smoothing into autoregressive generative modeling. We first model a smoothed version of the data distribution, and then reverse the smoothing process to recover the original data distribution. This procedure drastically improves the sample quality of existing autoregressive models on several synthetic and real-world image datasets while obtaining competitive likelihoods on synthetic datasets.
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