Fast Adaptation with Linearized Neural Networks

• URL: http://arxiv.org/abs/2103.01439v1
• Date: Tue, 2 Mar 2021 03:23:03 GMT
• Title: Fast Adaptation with Linearized Neural Networks
• Authors: Wesley J. Maddox, Shuai Tang, Pablo Garcia Moreno, Andrew Gordon Wilson, Andreas Damianou
• Abstract summary: We study the inductive biases of linearizations of neural networks, which we show to be surprisingly good summaries of the full network functions. Inspired by this finding, we propose a technique for embedding these inductive biases into Gaussian processes through a kernel designed from the Jacobian of the network. In this setting, domain adaptation takes the form of interpretable posterior inference, with accompanying uncertainty estimation.
• Score: 35.43406281230279
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The inductive biases of trained neural networks are difficult to understand and, consequently, to adapt to new settings. We study the inductive biases of linearizations of neural networks, which we show to be surprisingly good summaries of the full network functions. Inspired by this finding, we propose a technique for embedding these inductive biases into Gaussian processes through a kernel designed from the Jacobian of the network. In this setting, domain adaptation takes the form of interpretable posterior inference, with accompanying uncertainty estimation. This inference is analytic and free of local optima issues found in standard techniques such as fine-tuning neural network weights to a new task. We develop significant computational speed-ups based on matrix multiplies, including a novel implementation for scalable Fisher vector products. Our experiments on both image classification and regression demonstrate the promise and convenience of this framework for transfer learning, compared to neural network fine-tuning. Code is available at https://github.com/amzn/xfer/tree/master/finite_ntk.

Related papers

• Graph Neural Networks for Learning Equivariant Representations of Neural Networks [55.04145324152541]
  We propose to represent neural networks as computational graphs of parameters. Our approach enables a single model to encode neural computational graphs with diverse architectures. We showcase the effectiveness of our method on a wide range of tasks, including classification and editing of implicit neural representations.
  arXiv  Detail & Related papers  (2024-03-18T18:01:01Z)
• When Deep Learning Meets Polyhedral Theory: A Survey [6.899761345257773]
  In the past decade, deep became the prevalent methodology for predictive modeling thanks to the remarkable accuracy of deep neural learning. Meanwhile, the structure of neural networks converged back to simplerwise and linear functions.
  arXiv  Detail & Related papers  (2023-04-29T11:46:53Z)
• 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)
• Simple initialization and parametrization of sinusoidal networks via their kernel bandwidth [92.25666446274188]
  sinusoidal neural networks with activations have been proposed as an alternative to networks with traditional activation functions. We first propose a simplified version of such sinusoidal neural networks, which allows both for easier practical implementation and simpler theoretical analysis. We then analyze the behavior of these networks from the neural tangent kernel perspective and demonstrate that their kernel approximates a low-pass filter with an adjustable bandwidth.
  arXiv  Detail & Related papers  (2022-11-26T07:41:48Z)
• Lifted Bregman Training of Neural Networks [28.03724379169264]
  We introduce a novel mathematical formulation for the training of feed-forward neural networks with (potentially non-smooth) proximal maps as activation functions. This formulation is based on Bregman and a key advantage is that its partial derivatives with respect to the network's parameters do not require the computation of derivatives of the network's activation functions. We present several numerical results that demonstrate that these training approaches can be equally well or even better suited for the training of neural network-based classifiers and (denoising) autoencoders with sparse coding.
  arXiv  Detail & Related papers  (2022-08-18T11:12:52Z)
• Data-driven emergence of convolutional structure in neural networks [83.4920717252233]
  We show how fully-connected neural networks solving a discrimination task can learn a convolutional structure directly from their inputs. By carefully designing data models, we show that the emergence of this pattern is triggered by the non-Gaussian, higher-order local structure of the inputs.
  arXiv  Detail & Related papers  (2022-02-01T17:11:13Z)
• Stochastic Neural Networks with Infinite Width are Deterministic [7.07065078444922]
  We study neural networks, a main type of neural network in use. We prove that as the width of an optimized neural network tends to infinity, its predictive variance on the training set decreases to zero.
  arXiv  Detail & Related papers  (2022-01-30T04:52:31Z)
• Neural Capacitance: A New Perspective of Neural Network Selection via Edge Dynamics [85.31710759801705]
  Current practice requires expensive computational costs in model training for performance prediction. We propose a novel framework for neural network selection by analyzing the governing dynamics over synaptic connections (edges) during training. Our framework is built on the fact that back-propagation during neural network training is equivalent to the dynamical evolution of synaptic connections.
  arXiv  Detail & Related papers  (2022-01-11T20:53:15Z)
• Local Critic Training for Model-Parallel Learning of Deep Neural Networks [94.69202357137452]
  We propose a novel model-parallel learning method, called local critic training. We show that the proposed approach successfully decouples the update process of the layer groups for both convolutional neural networks (CNNs) and recurrent neural networks (RNNs) We also show that trained networks by the proposed method can be used for structural optimization.
  arXiv  Detail & Related papers  (2021-02-03T09:30:45Z)
• A Deep Conditioning Treatment of Neural Networks [37.192369308257504]
  We show that depth improves trainability of neural networks by improving the conditioning of certain kernel matrices of the input data. We provide versions of the result that hold for training just the top layer of the neural network, as well as for training all layers via the neural tangent kernel.
  arXiv  Detail & Related papers  (2020-02-04T20:21:36Z)

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.