Finding Everything within Random Binary Networks

• URL: http://arxiv.org/abs/2110.08996v1
• Date: Mon, 18 Oct 2021 03:19:25 GMT
• Title: Finding Everything within Random Binary Networks
• Authors: Kartik Sreenivasan, Shashank Rajput, Jy-yong Sohn and Dimitris Papailiopoulos
• Abstract summary: We prove that a random network can be approximated up to arbitrary accuracy by simply pruning a random network of binary $pm1$ weights. We prove that any target network can be approximated up to arbitrary accuracy by simply pruning a random network of binary $pm1$ weights that is only a polylogarithmic factor wider and deeper than the target network.
• Score: 11.689913953698081
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: A recent work by Ramanujan et al. (2020) provides significant empirical evidence that sufficiently overparameterized, random neural networks contain untrained subnetworks that achieve state-of-the-art accuracy on several predictive tasks. A follow-up line of theoretical work provides justification of these findings by proving that slightly overparameterized neural networks, with commonly used continuous-valued random initializations can indeed be pruned to approximate any target network. In this work, we show that the amplitude of those random weights does not even matter. We prove that any target network can be approximated up to arbitrary accuracy by simply pruning a random network of binary $\{\pm1\}$ weights that is only a polylogarithmic factor wider and deeper than the target network.

Related papers

• Trained quantum neural networks are Gaussian processes [5.439020425819001]
  We study quantum neural networks made by parametric one-qubit gates and fixed two-qubit gates in the limit of width. We analytically characterize the training of the network via gradient descent with square loss on supervised learning problems. We prove that, as long as the network is not affected by barren plateaus, the trained network can perfectly fit the training set.
  arXiv  Detail & Related papers  (2024-02-13T19:00:08Z)
• Computational Complexity of Learning Neural Networks: Smoothness and Degeneracy [52.40331776572531]
  We show that learning depth-$3$ ReLU networks under the Gaussian input distribution is hard even in the smoothed-analysis framework. Our results are under a well-studied assumption on the existence of local pseudorandom generators.
  arXiv  Detail & Related papers  (2023-02-15T02:00:26Z)
• Robust Training and Verification of Implicit Neural Networks: A Non-Euclidean Contractive Approach [64.23331120621118]
  This paper proposes a theoretical and computational framework for training and robustness verification of implicit neural networks. We introduce a related embedded network and show that the embedded network can be used to provide an $ell_infty$-norm box over-approximation of the reachable sets of the original network. We apply our algorithms to train implicit neural networks on the MNIST dataset and compare the robustness of our models with the models trained via existing approaches in the literature.
  arXiv  Detail & Related papers  (2022-08-08T03:13:24Z)
• On the Neural Tangent Kernel Analysis of Randomly Pruned Neural Networks [91.3755431537592]
  We study how random pruning of the weights affects a neural network's neural kernel (NTK) In particular, this work establishes an equivalence of the NTKs between a fully-connected neural network and its randomly pruned version.
  arXiv  Detail & Related papers  (2022-03-27T15:22:19Z)
• Why Lottery Ticket Wins? A Theoretical Perspective of Sample Complexity on Pruned Neural Networks [79.74580058178594]
  We analyze the performance of training a pruned neural network by analyzing the geometric structure of the objective function. We show that the convex region near a desirable model with guaranteed generalization enlarges as the neural network model is pruned.
  arXiv  Detail & Related papers  (2021-10-12T01:11:07Z)
• A Probabilistic Approach to Neural Network Pruning [20.001091112545065]
  We theoretically study the performance of two pruning techniques (random and magnitude-based) on FCNs and CNNs. The results establish that there exist pruned networks with expressive power within any specified bound from the target network.
  arXiv  Detail & Related papers  (2021-05-20T23:19:43Z)
• How Powerful are Shallow Neural Networks with Bandlimited Random Weights? [25.102870584507244]
  We investigate the expressive power of limited depth-2 band random neural networks. A random net is a neural network where the hidden layer parameters are frozen with random bandwidth.
  arXiv  Detail & Related papers  (2020-08-19T13:26:12Z)
• ESPN: Extremely Sparse Pruned Networks [50.436905934791035]
  We show that a simple iterative mask discovery method can achieve state-of-the-art compression of very deep networks. Our algorithm represents a hybrid approach between single shot network pruning methods and Lottery-Ticket type approaches.
  arXiv  Detail & Related papers  (2020-06-28T23:09:27Z)
• Logarithmic Pruning is All You Need [30.330326149079326]
  Lottery Ticket Hypothesis: Every large neural network contains a subnetwork that, when trained in isolation, achieves comparable performance to the large network. This latter result, however, relies on a number of strong assumptions and guarantees a factor on the size of the large network compared to the target function.
  arXiv  Detail & Related papers  (2020-06-22T11:42:30Z)
• Proving the Lottery Ticket Hypothesis: Pruning is All You Need [56.25432563818297]
  The lottery ticket hypothesis states that a randomly-d network contains a small subnetwork such that, when trained in isolation, can compete with the performance of the original network. We prove an even stronger hypothesis, showing that for every bounded distribution and every target network with bounded weights, a sufficiently over- parameterized neural network with random weights contains a subnetwork with roughly the same accuracy as the target network, without any further training.
  arXiv  Detail & Related papers  (2020-02-03T07:23:11Z)

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.