Explaining Neural Scaling Laws

• URL: http://arxiv.org/abs/2102.06701v2
• Date: Mon, 29 Apr 2024 00:55:09 GMT
• Title: Explaining Neural Scaling Laws
• Authors: Yasaman Bahri, Ethan Dyer, Jared Kaplan, Jaehoon Lee, Utkarsh Sharma,
• Abstract summary: Population loss of trained deep neural networks often follows precise power-law scaling relations. We propose a theory that explains the origins of and connects these scaling laws. We identify variance-limited and resolution-limited scaling behavior for both dataset and model size.
• Score: 17.115592382420626
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The population loss of trained deep neural networks often follows precise power-law scaling relations with either the size of the training dataset or the number of parameters in the network. We propose a theory that explains the origins of and connects these scaling laws. We identify variance-limited and resolution-limited scaling behavior for both dataset and model size, for a total of four scaling regimes. The variance-limited scaling follows simply from the existence of a well-behaved infinite data or infinite width limit, while the resolution-limited regime can be explained by positing that models are effectively resolving a smooth data manifold. In the large width limit, this can be equivalently obtained from the spectrum of certain kernels, and we present evidence that large width and large dataset resolution-limited scaling exponents are related by a duality. We exhibit all four scaling regimes in the controlled setting of large random feature and pretrained models and test the predictions empirically on a range of standard architectures and datasets. We also observe several empirical relationships between datasets and scaling exponents under modifications of task and architecture aspect ratio. Our work provides a taxonomy for classifying different scaling regimes, underscores that there can be different mechanisms driving improvements in loss, and lends insight into the microscopic origins of and relationships between scaling exponents.

Related papers

• Unified Neural Network Scaling Laws and Scale-time Equivalence [10.918504301310753]
  We present a novel theoretical characterization of how three factors -- model size, training time, and data volume -- interact to determine the performance of deep neural networks. We first establish a theoretical and empirical equivalence between scaling the size of a neural network and increasing its training time proportionally. We then combine scale-time equivalence with a linear model analysis of double descent to obtain a unified theoretical scaling law.
  arXiv  Detail & Related papers  (2024-09-09T16:45:26Z)
• Information-Theoretic Foundations for Neural Scaling Laws [20.617552198581024]
  We develop information-theoretic foundations for neural scaling laws. We observe that the optimal relation between data and model size is linear, up to logarithmic factors.
  arXiv  Detail & Related papers  (2024-06-28T02:20:54Z)
• Scaling Laws for the Value of Individual Data Points in Machine Learning [55.596413470429475]
  We introduce a new perspective by investigating scaling behavior for the value of individual data points. We provide learning theory to support our scaling law, and we observe empirically that it holds across diverse model classes. Our work represents a first step towards understanding and utilizing scaling properties for the value of individual data points.
  arXiv  Detail & Related papers  (2024-05-30T20:10:24Z)
• Neural Scaling Laws on Graphs [54.435688297561015]
  We study neural scaling laws on graphs from both model and data perspectives. For model scaling, we investigate the phenomenon of scaling law collapse and identify overfitting as the potential reason. For data scaling, we suggest that the number of graphs can not effectively metric the graph data volume in scaling law since the sizes of different graphs are highly irregular.
  arXiv  Detail & Related papers  (2024-02-03T06:17:21Z)
• A Dynamical Model of Neural Scaling Laws [79.59705237659547]
  We analyze a random feature model trained with gradient descent as a solvable model of network training and generalization. Our theory shows how the gap between training and test loss can gradually build up over time due to repeated reuse of data.
  arXiv  Detail & Related papers  (2024-02-02T01:41:38Z)
• Feature-Learning Networks Are Consistent Across Widths At Realistic Scales [72.27228085606147]
  We study the effect of width on the dynamics of feature-learning neural networks across a variety of architectures and datasets. Early in training, wide neural networks trained on online data have not only identical loss curves but also agree in their point-wise test predictions throughout training. We observe, however, that ensembles of narrower networks perform worse than a single wide network.
  arXiv  Detail & Related papers  (2023-05-28T17:09:32Z)
• A Solvable Model of Neural Scaling Laws [72.8349503901712]
  Large language models with a huge number of parameters, when trained on near internet-sized number of tokens, have been empirically shown to obey neural scaling laws. We propose a statistical model -- a joint generative data model and random feature model -- that captures this neural scaling phenomenology. Key findings are the manner in which the power laws that occur in the statistics of natural datasets are extended by nonlinear random feature maps.
  arXiv  Detail & Related papers  (2022-10-30T15:13:18Z)
• Post-mortem on a deep learning contest: a Simpson's paradox and the complementary roles of scale metrics versus shape metrics [61.49826776409194]
  We analyze a corpus of models made publicly-available for a contest to predict the generalization accuracy of neural network (NN) models. We identify what amounts to a Simpson's paradox: where "scale" metrics perform well overall but perform poorly on sub partitions of the data. We present two novel shape metrics, one data-independent, and the other data-dependent, which can predict trends in the test accuracy of a series of NNs.
  arXiv  Detail & Related papers  (2021-06-01T19:19:49Z)
• On the Predictability of Pruning Across Scales [29.94870276983399]
  We show that the error of magnitude-pruned networks empirically follows a scaling law with interpretable coefficients that depend on the architecture and task. As neural networks become ever larger and costlier to train, our findings suggest a framework for reasoning conceptually and analytically about a standard method for unstructured pruning.
  arXiv  Detail & Related papers  (2020-06-18T15:41:46Z)
• Scaling Laws for Neural Language Models [14.472857826717613]
  We study 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.
  arXiv  Detail & Related papers  (2020-01-23T03:59:20Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.