Gradient-trained Weights in Wide Neural Networks Align Layerwise to Error-scaled Input Correlations

• URL: http://arxiv.org/abs/2106.08453v1
• Date: Tue, 15 Jun 2021 21:56:38 GMT
• Title: Gradient-trained Weights in Wide Neural Networks Align Layerwise to Error-scaled Input Correlations
• Authors: Akhilan Boopathy, Ila Fiete
• Abstract summary: We derive the layerwise weight dynamics of infinite-width neural networks with nonlinear activations trained by gradient descent. We formulate backpropagation-free learning rules, named Align-zero and Align-ada, that theoretically achieve the same alignment as backpropagation.
• Score: 11.176824373696324
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Recent works have examined how deep neural networks, which can solve a variety of difficult problems, incorporate the statistics of training data to achieve their success. However, existing results have been established only in limited settings. In this work, we derive the layerwise weight dynamics of infinite-width neural networks with nonlinear activations trained by gradient descent. We show theoretically that weight updates are aligned with input correlations from intermediate layers weighted by error, and demonstrate empirically that the result also holds in finite-width wide networks. The alignment result allows us to formulate backpropagation-free learning rules, named Align-zero and Align-ada, that theoretically achieve the same alignment as backpropagation. Finally, we test these learning rules on benchmark problems in feedforward and recurrent neural networks and demonstrate, in wide networks, comparable performance to backpropagation.

Related papers

• Concurrent Training and Layer Pruning of Deep Neural Networks [0.0]
  We propose an algorithm capable of identifying and eliminating irrelevant layers of a neural network during the early stages of training. We employ a structure using residual connections around nonlinear network sections that allow the flow of information through the network once a nonlinear section is pruned.
  arXiv  Detail & Related papers  (2024-06-06T23:19:57Z)
• Globally Optimal Training of Neural Networks with Threshold Activation Functions [63.03759813952481]
  We study weight decay regularized training problems of deep neural networks with threshold activations. We derive a simplified convex optimization formulation when the dataset can be shattered at a certain layer of the network.
  arXiv  Detail & Related papers  (2023-03-06T18:59:13Z)
• Slimmable Networks for Contrastive Self-supervised Learning [67.21528544724546]
  Self-supervised learning makes significant progress in pre-training large models, but struggles with small models. We present a one-stage solution to obtain pre-trained small models without the need for extra teachers. A slimmable network consists of a full network and several weight-sharing sub-networks, which can be pre-trained once to obtain various networks.
  arXiv  Detail & Related papers  (2022-09-30T15:15:05Z)
• Adversarial Reprogramming Revisited [0.15229257192293197]
  Adversarial reprogramming seeks to repurpose a neural network to perform a different task. We prove that two-layer ReLU neural networks with random weights can be adversarially reprogrammed to achieve arbitrarily high accuracy.
  arXiv  Detail & Related papers  (2022-06-07T17:37:22Z)
• Compact representations of convolutional neural networks via weight pruning and quantization [63.417651529192014]
  We propose a novel storage format for convolutional neural networks (CNNs) based on source coding and leveraging both weight pruning and quantization. We achieve a reduction of space occupancy up to 0.6% on fully connected layers and 5.44% on the whole network, while performing at least as competitive as the baseline.
  arXiv  Detail & Related papers  (2021-08-28T20:39:54Z)
• Backward Gradient Normalization in Deep Neural Networks [68.8204255655161]
  We introduce a new technique for gradient normalization during neural network training. The gradients are rescaled during the backward pass using normalization layers introduced at certain points within the network architecture. Results on tests with very deep neural networks show that the new technique can do an effective control of the gradient norm.
  arXiv  Detail & Related papers  (2021-06-17T13:24:43Z)
• Fast Adaptation with Linearized Neural Networks [35.43406281230279]
  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.
  arXiv  Detail & Related papers  (2021-03-02T03:23:03Z)
• Statistical Mechanics of Deep Linear Neural Networks: The Back-Propagating Renormalization Group [4.56877715768796]
  We study the statistical mechanics of learning in Deep Linear Neural Networks (DLNNs) in which the input-output function of an individual unit is linear. We solve exactly the network properties following supervised learning using an equilibrium Gibbs distribution in the weight space. Our numerical simulations reveal that despite the nonlinearity, the predictions of our theory are largely shared by ReLU networks with modest depth.
  arXiv  Detail & Related papers  (2020-12-07T20:08:31Z)
• Revisiting Initialization of Neural Networks [72.24615341588846]
  We propose a rigorous estimation of the global curvature of weights across layers by approximating and controlling the norm of their Hessian matrix. Our experiments on Word2Vec and the MNIST/CIFAR image classification tasks confirm that tracking the Hessian norm is a useful diagnostic tool.
  arXiv  Detail & Related papers  (2020-04-20T18:12:56Z)
• Distance-Based Regularisation of Deep Networks for Fine-Tuning [116.71288796019809]
  We develop an algorithm that constrains a hypothesis class to a small sphere centred on the initial pre-trained weights. Empirical evaluation shows that our algorithm works well, corroborating our theoretical results.
  arXiv  Detail & Related papers  (2020-02-19T16:00:47Z)
• Implicit Bias of Gradient Descent for Wide Two-layer Neural Networks Trained with the Logistic Loss [0.0]
  Neural networks trained to minimize the logistic (a.k.a. cross-entropy) loss with gradient-based methods are observed to perform well in many supervised classification tasks. We analyze the training and generalization behavior of infinitely wide two-layer neural networks with homogeneous activations.
  arXiv  Detail & Related papers  (2020-02-11T15:42:09Z)

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.