On the Disconnect Between Theory and Practice of Neural Networks: Limits of the NTK Perspective

• URL: http://arxiv.org/abs/2310.00137v2
• Date: Tue, 28 May 2024 20:59:41 GMT
• Title: On the Disconnect Between Theory and Practice of Neural Networks: Limits of the NTK Perspective
• Authors: Jonathan Wenger, Felix Dangel, Agustinus Kristiadi,
• Abstract summary: The neural tangent kernel (NTK) has garnered significant attention as a theoretical framework for describing the behavior of large-scale neural networks. Current results quantifying the rate of convergence to the kernel regime suggest that exploiting these benefits requires architectures that are orders of magnitude wider than they are deep. This paper investigates whether the limiting regime predicts practically relevant behavior of large-width architectures.
• Score: 9.753461673117362
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The neural tangent kernel (NTK) has garnered significant attention as a theoretical framework for describing the behavior of large-scale neural networks. Kernel methods are theoretically well-understood and as a result enjoy algorithmic benefits, which can be demonstrated to hold in wide synthetic neural network architectures. These advantages include faster optimization, reliable uncertainty quantification and improved continual learning. However, current results quantifying the rate of convergence to the kernel regime suggest that exploiting these benefits requires architectures that are orders of magnitude wider than they are deep. This assumption raises concerns that architectures used in practice do not exhibit behaviors as predicted by the NTK. Here, we supplement previous work on the NTK by empirically investigating whether the limiting regime predicts practically relevant behavior of large-width architectures. Our results demonstrate that this is not the case across multiple domains. This observed disconnect between theory and practice further calls into question to what degree NTK theory should inform architectural and algorithmic choices.

Related papers

• Efficient kernel surrogates for neural network-based regression [0.8030359871216615]
  We study the performance of the Conjugate Kernel (CK), an efficient approximation to the Neural Tangent Kernel (NTK) We show that the CK performance is only marginally worse than that of the NTK and, in certain cases, is shown to be superior. In addition to providing a theoretical grounding for using CKs instead of NTKs, our framework suggests a recipe for improving DNN accuracy inexpensively.
  arXiv  Detail & Related papers  (2023-10-28T06:41:47Z)
• 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)
• What Can the Neural Tangent Kernel Tell Us About Adversarial Robustness? [0.0]
  We study adversarial examples of trained neural networks through analytical tools afforded by recent theory advances connecting neural networks and kernel methods. We show how NTKs allow to generate adversarial examples in a training-free'' fashion, and demonstrate that they transfer to fool their finite-width neural net counterparts in the lazy'' regime.
  arXiv  Detail & Related papers  (2022-10-11T16:11:48Z)
• Knowledge Enhanced Neural Networks for relational domains [83.9217787335878]
  We focus on a specific method, KENN, a Neural-Symbolic architecture that injects prior logical knowledge into a neural network. In this paper, we propose an extension of KENN for relational data.
  arXiv  Detail & Related papers  (2022-05-31T13:00:34Z)
• Deep Architecture Connectivity Matters for Its Convergence: A Fine-Grained Analysis [94.64007376939735]
  We theoretically characterize the impact of connectivity patterns on the convergence of deep neural networks (DNNs) under gradient descent training. We show that by a simple filtration on "unpromising" connectivity patterns, we can trim down the number of models to evaluate.
  arXiv  Detail & Related papers  (2022-05-11T17:43:54Z)
• Extended critical regimes of deep neural networks [0.0]
  We show that heavy-tailed weights enable the emergence of an extended critical regime without fine-tuning parameters. In this extended critical regime, DNNs exhibit rich and complex propagation dynamics across layers. We provide a theoretical guide for the design of efficient neural architectures.
  arXiv  Detail & Related papers  (2022-03-24T10:15:50Z)
• What can linearized neural networks actually say about generalization? [67.83999394554621]
  In certain infinitely-wide neural networks, the neural tangent kernel (NTK) theory fully characterizes generalization. We show that the linear approximations can indeed rank the learning complexity of certain tasks for neural networks. Our work provides concrete examples of novel deep learning phenomena which can inspire future theoretical research.
  arXiv  Detail & Related papers  (2021-06-12T13:05:11Z)
• A Convergence Theory Towards Practical Over-parameterized Deep Neural Networks [56.084798078072396]
  We take a step towards closing the gap between theory and practice by significantly improving the known theoretical bounds on both the network width and the convergence time. We show that convergence to a global minimum is guaranteed for networks with quadratic widths in the sample size and linear in their depth at a time logarithmic in both. Our analysis and convergence bounds are derived via the construction of a surrogate network with fixed activation patterns that can be transformed at any time to an equivalent ReLU network of a reasonable size.
  arXiv  Detail & Related papers  (2021-01-12T00:40:45Z)
• 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)
• On the Empirical Neural Tangent Kernel of Standard Finite-Width Convolutional Neural Network Architectures [3.4698840925433765]
  It remains an open question how well NTK theory models standard neural network architectures of widths common in practice. We study this question empirically for two well-known convolutional neural network architectures, namely AlexNet and LeNet. For wider versions of these networks, where the number of channels and widths of fully-connected layers are increased, the deviation decreases.
  arXiv  Detail & Related papers  (2020-06-24T11:40:36Z)

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.