Analyzing Finite Neural Networks: Can We Trust Neural Tangent Kernel Theory?

• URL: http://arxiv.org/abs/2012.04477v2
• Date: Wed, 31 Mar 2021 19:06:43 GMT
• Title: Analyzing Finite Neural Networks: Can We Trust Neural Tangent Kernel Theory?
• Authors: Mariia Seleznova and Gitta Kutyniok
• Abstract summary: Neural Kernel (NTK) theory is widely used to study the dynamics of infinitely-wide deep neural networks (DNNs) under gradient descent. We study empirically when NTK theory is valid in practice for fully-connected ReLU and sigmoid DNNs. In particular, NTK theory does not explain the behavior of sufficiently deep networks so that their gradients explode as they propagate through the network's layers.
• Score: 2.0711789781518752
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Neural Tangent Kernel (NTK) theory is widely used to study the dynamics of infinitely-wide deep neural networks (DNNs) under gradient descent. But do the results for infinitely-wide networks give us hints about the behavior of real finite-width ones? In this paper, we study empirically when NTK theory is valid in practice for fully-connected ReLU and sigmoid DNNs. We find out that whether a network is in the NTK regime depends on the hyperparameters of random initialization and the network's depth. In particular, NTK theory does not explain the behavior of sufficiently deep networks initialized so that their gradients explode as they propagate through the network's layers: the kernel is random at initialization and changes significantly during training in this case, contrary to NTK theory. On the other hand, in the case of vanishing gradients, DNNs are in the the NTK regime but become untrainable rapidly with depth. We also describe a framework to study generalization properties of DNNs, in particular the variance of network's output function, by means of NTK theory and discuss its limits.

Related papers

• Infinite Width Limits of Self Supervised Neural Networks [6.178817969919849]
  We bridge the gap between the NTK and self-supervised learning, focusing on two-layer neural networks trained under the Barlow Twins loss. We prove that the NTK of Barlow Twins indeed becomes constant as the width of the network approaches infinity.
  arXiv  Detail & Related papers  (2024-11-17T21:13:57Z)
• Novel Kernel Models and Exact Representor Theory for Neural Networks Beyond the Over-Parameterized Regime [52.00917519626559]
  This paper presents two models of neural-networks and their training applicable to neural networks of arbitrary width, depth and topology. We also present an exact novel representor theory for layer-wise neural network training with unregularized gradient descent in terms of a local-extrinsic neural kernel (LeNK) This representor theory gives insight into the role of higher-order statistics in neural network training and the effect of kernel evolution in neural-network kernel models.
  arXiv  Detail & Related papers  (2024-05-24T06:30:36Z)
• How neural networks learn to classify chaotic time series [77.34726150561087]
  We study the inner workings of neural networks trained to classify regular-versus-chaotic time series. We find that the relation between input periodicity and activation periodicity is key for the performance of LKCNN models.
  arXiv  Detail & Related papers  (2023-06-04T08:53:27Z)
• Gradient Descent in Neural Networks as Sequential Learning in RKBS [63.011641517977644]
  We construct an exact power-series representation of the neural network in a finite neighborhood of the initial weights. We prove that, regardless of width, the training sequence produced by gradient descent can be exactly replicated by regularized sequential learning.
  arXiv  Detail & Related papers  (2023-02-01T03:18:07Z)
• Neural Networks with Sparse Activation Induced by Large Bias: Tighter Analysis with Bias-Generalized NTK [86.45209429863858]
  We study training one-hidden-layer ReLU networks in the neural tangent kernel (NTK) regime. We show that the neural networks possess a different limiting kernel which we call textitbias-generalized NTK We also study various properties of the neural networks with this new kernel.
  arXiv  Detail & Related papers  (2023-01-01T02:11:39Z)
• Extrapolation and Spectral Bias of Neural Nets with Hadamard Product: a Polynomial Net Study [55.12108376616355]
  The study on NTK has been devoted to typical neural network architectures, but is incomplete for neural networks with Hadamard products (NNs-Hp) In this work, we derive the finite-width-K formulation for a special class of NNs-Hp, i.e., neural networks. We prove their equivalence to the kernel regression predictor with the associated NTK, which expands the application scope of NTK.
  arXiv  Detail & Related papers  (2022-09-16T06:36:06Z)
• Limitations of the NTK for Understanding Generalization in Deep Learning [13.44676002603497]
  We study NTKs through the lens of scaling laws, and demonstrate that they fall short of explaining important aspects of neural network generalization. We show that even if the empirical NTK is allowed to be pre-trained on a constant number of samples, the kernel scaling does not catch up to the neural network scaling.
  arXiv  Detail & Related papers  (2022-06-20T21:23:28Z)
• Neural Tangent Kernel Analysis of Deep Narrow Neural Networks [11.623483126242478]
  We present the first trainability guarantee of infinitely deep but narrow neural networks. We then extend the analysis to an infinitely deep convolutional neural network (CNN) and perform brief experiments.
  arXiv  Detail & Related papers  (2022-02-07T07:27:02Z)
• Finite Versus Infinite Neural Networks: an Empirical Study [69.07049353209463]
  kernel methods outperform fully-connected finite-width networks. Centered and ensembled finite networks have reduced posterior variance. Weight decay and the use of a large learning rate break the correspondence between finite and infinite networks.
  arXiv  Detail & Related papers  (2020-07-31T01:57:47Z)

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.