Log In Sign Up

Dynamically Stable Infinite-Width Limits of Neural Classifiers

by   Eugene. A. Golikov, et al.

Recent research has been focused on two different approaches to studying neural networks training in the limit of infinite width (1) a mean-field (MF) and (2) a constant neural tangent kernel (NTK) approximations. These two approaches have different scaling of hyperparameters with a width of a network layer and as a result different infinite width limit models. We propose a general framework to study how the limit behavior of neural models depends on the scaling of hyperparameters with a network width. Our framework allows us to derive scaling for existing MF and NTK limits, as well as an uncountable number of other scalings that lead to a dynamically stable limit behavior of corresponding models. However, only a finite number of distinct limit models are induced by these scalings. Each distinct limit model corresponds to a unique combination of such properties as boundedness of logits and tangent kernels at initialization or stationarity of tangent kernels. Existing MF and NTK limit models, as well as one novel limit model, satisfy most of the properties demonstrated by finite-width models. We also propose a novel initialization-corrected mean-field limit that satisfies all properties noted above, and its corresponding model is a simple modification for a finite-width model. Source code to reproduce all the reported results is available on GitHub.


page 1

page 2

page 3

page 4


Towards a General Theory of Infinite-Width Limits of Neural Classifiers

Obtaining theoretical guarantees for neural networks training appears to...

Meta-Principled Family of Hyperparameter Scaling Strategies

In this note, we first derive a one-parameter family of hyperparameter s...

Feature Learning in Infinite-Width Neural Networks

As its width tends to infinity, a deep neural network's behavior under g...

Training Integrable Parameterizations of Deep Neural Networks in the Infinite-Width Limit

To theoretically understand the behavior of trained deep neural networks...

Neural Tangent Kernel Beyond the Infinite-Width Limit: Effects of Depth and Initialization

Neural Tangent Kernel (NTK) is widely used to analyze overparametrized n...

Nonperturbative renormalization for the neural network-QFT correspondence

In a recent work arXiv:2008.08601, Halverson, Maiti and Stoner proposed ...

Unified Field Theory for Deep and Recurrent Neural Networks

Understanding capabilities and limitations of different network architec...