Residual Random Neural Networks

• URL: http://arxiv.org/abs/2410.19987v3
• Date: Mon, 04 Nov 2024 15:09:54 GMT
• Title: Residual Random Neural Networks
• Authors: M. Andrecut,
• Abstract summary: Single-layer feedforward neural network with random weights is a recurring motif in the neural networks literature. We show that one can obtain good classification results even if the number of hidden neurons has the same order of magnitude as the dimensionality of the data samples.
• Score: 0.0
• License:
• Abstract: The single-layer feedforward neural network with random weights is a recurring motif in the neural networks literature. The advantage of these networks is their simplified training, which reduces to solving a ridge-regression problem. A general assumption is that these networks require a large number of hidden neurons relative to the dimensionality of the data samples, in order to achieve good classification accuracy. Contrary to this assumption, here we show that one can obtain good classification results even if the number of hidden neurons has the same order of magnitude as the dimensionality of the data samples, if this dimensionality is reasonably high. Inspired by this result, we also develop an efficient iterative residual training method for such random neural networks, and we extend the algorithm to the least-squares kernel version of the neural network model. Moreover, we also describe an encryption (obfuscation) method which can be used to protect both the data and the resulted network model.

Related papers

• The sampling complexity of learning invertible residual neural networks [9.614718680817269]
  It has been shown that determining a feedforward ReLU neural network to within high uniform accuracy from point samples suffers from the curse of dimensionality. We consider the question of whether the sampling complexity can be improved by restricting the specific neural network architecture. Our main result shows that the residual neural network architecture and invertibility do not help overcome the complexity barriers encountered with simpler feedforward architectures.
  arXiv  Detail & Related papers  (2024-11-08T10:00:40Z)
• Verified Neural Compressed Sensing [58.98637799432153]
  We develop the first (to the best of our knowledge) provably correct neural networks for a precise computational task. We show that for modest problem dimensions (up to 50), we can train neural networks that provably recover a sparse vector from linear and binarized linear measurements. We show that the complexity of the network can be adapted to the problem difficulty and solve problems where traditional compressed sensing methods are not known to provably work.
  arXiv  Detail & Related papers  (2024-05-07T12:20:12Z)
• 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)
• On the Convergence of Locally Adaptive and Scalable Diffusion-Based Sampling Methods for Deep Bayesian Neural Network Posteriors [2.3265565167163906]
  Bayesian neural networks are a promising approach for modeling uncertainties in deep neural networks. generating samples from the posterior distribution of neural networks is a major challenge. One advance in that direction would be the incorporation of adaptive step sizes into Monte Carlo Markov chain sampling algorithms. In this paper, we demonstrate that these methods can have a substantial bias in the distribution they sample, even in the limit of vanishing step sizes and at full batch size.
  arXiv  Detail & Related papers  (2024-03-13T15:21:14Z)
• Sampling weights of deep neural networks [1.2370077627846041]
  We introduce a probability distribution, combined with an efficient sampling algorithm, for weights and biases of fully-connected neural networks. In a supervised learning context, no iterative optimization or gradient computations of internal network parameters are needed. We prove that sampled networks are universal approximators.
  arXiv  Detail & Related papers  (2023-06-29T10:13:36Z)
• Benign Overfitting for Two-layer ReLU Convolutional Neural Networks [60.19739010031304]
  We establish algorithm-dependent risk bounds for learning two-layer ReLU convolutional neural networks with label-flipping noise. We show that, under mild conditions, the neural network trained by gradient descent can achieve near-zero training loss and Bayes optimal test risk.
  arXiv  Detail & Related papers  (2023-03-07T18:59:38Z)
• Spiking neural network for nonlinear regression [68.8204255655161]
  Spiking neural networks carry the potential for a massive reduction in memory and energy consumption. They introduce temporal and neuronal sparsity, which can be exploited by next-generation neuromorphic hardware. A framework for regression using spiking neural networks is proposed.
  arXiv  Detail & Related papers  (2022-10-06T13:04:45Z)
• 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)
• Robust Generalization of Quadratic Neural Networks via Function Identification [19.87036824512198]
  Generalization bounds from learning theory often assume that the test distribution is close to the training distribution. We show that for quadratic neural networks, we can identify the function represented by the model even though we cannot identify its parameters.
  arXiv  Detail & Related papers  (2021-09-22T18:02:00Z)
• The Compact Support Neural Network [6.47243430672461]
  We present a neuron generalization that has the standard dot-product-based neuron and the RBF neuron as two extreme cases of a shape parameter. We show how to avoid difficulties in training a neural network with such neurons, by starting with a trained standard neural network and gradually increasing the shape parameter to the desired value.
  arXiv  Detail & Related papers  (2021-04-01T06:08:09Z)
• And/or trade-off in artificial neurons: impact on adversarial robustness [91.3755431537592]
  Presence of sufficient number of OR-like neurons in a network can lead to classification brittleness and increased vulnerability to adversarial attacks. We define AND-like neurons and propose measures to increase their proportion in the network. Experimental results on the MNIST dataset suggest that our approach holds promise as a direction for further exploration.
  arXiv  Detail & Related papers  (2021-02-15T08:19:05Z)

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.