text: Training deep neural networks results in strong learned representations that show good generalization capabilities. In most cases, training involves iterative modification of all weights in the network via back-propagation. In Extreme Learning Machines, it has been suggested to set the first layer of a network to fixed random values instead of learning it. In this paper, we propose to take this approach a step further and fix almost all layers of a deep convolutional neural network, allowing only a small portion of the weights to be learned. As our experiments show, fixing even the majority of the parameters of the network often results in performance which is on par with the performance of learning all of them. The implications of this intriguing property of deep neural networks are discussed and we suggest practical ways to harness it to create more robust and compact representations.
  @cite_28: Three important properties of a classification machinery are i) the system preserves the core information of the input data; ii) the training examples convey information about unseen data; and iii) the system is able to treat differently points from different classes. In this paper, we show that these fundamental properties are satisfied by the architecture of deep neural networks. We formally prove that these networks with random Gaussian weights perform a distance-preserving embedding of the data, with a special treatment for in-class and out-of-class data. Similar points at the input of the network are likely to have a similar output. The theoretical analysis of deep networks here presented exploits tools used in the compressed sensing and dictionary learning literature, thereby making a formal connection between these important topics. The derived results allow drawing conclusions on the metric learning properties of the network and their relation to its structure, as well as providing bounds on the required size of the training set such that the training examples would represent faithfully the unseen data. The results are validated with state-of-the-art trained networks.
  @cite_38: Extreme learning machine (ELM) has gained increasing interest from various research fields recently. In this review, we aim to report the current state of the theoretical research and practical advances on this subject. We first give an overview of ELM from the theoretical perspective, including the interpolation theory, universal approximation capability, and generalization ability. Then we focus on the various improvements made to ELM which further improve its stability, sparsity and accuracy under general or specific conditions. Apart from classification and regression, ELM has recently been extended for clustering, feature selection, representational learning and many other learning tasks. These newly emerging algorithms greatly expand the applications of ELM. From implementation aspect, hardware implementation and parallel computation techniques have substantially sped up the training of ELM, making it feasible for big data processing and real-time reasoning. Due to its remarkable efficiency, simplicity, and impressive generalization performance, ELM have been applied in a variety of domains, such as biomedical engineering, computer vision, system identification, and control and robotics. In this review, we try to provide a comprehensive view of these advances in ELM together with its future perspectives.
  @cite_33: We study the generalization properties of ridge regression with random features in the statistical learning framework. We show for the first time that @math learning bounds can be achieved with only @math random features rather than @math as suggested by previous results. Further, we prove faster learning rates and show that they might require more random features, unless they are sampled according to a possibly problem dependent distribution. Our results shed light on the statistical computational trade-offs in large scale kernelized learning, showing the potential effectiveness of random features in reducing the computational complexity while keeping optimal generalization properties.
  @cite_11: We propose a new approach to the problem of neural network expressivity, which seeks to characterize how structural properties of a neural network family affect the functions it is able to compute. Our approach is based on an interrelated set of measures of expressivity, unified by the novel notion of trajectory length, which measures how the output of a network changes as the input sweeps along a one-dimensional path. Our findings can be summarized as follows: (1) The complexity of the computed function grows exponentially with depth. (2) All weights are not equal: trained networks are more sensitive to their lower (initial) layer weights. (3) Regularizing on trajectory length (trajectory regularization) is a simpler alternative to batch normalization, with the same performance.
summary: There is a long line of research revolving around the use of randomly drawn features in machine learning. Extreme Learning Machines show the utility of keeping some layer of a neural net fixed - but this is usually done only for one or two layers, and not within layers @cite_38 or across multiple (more than two) layers. @cite_33 has shown how picking random features has merits over matching kernels to the data. @cite_28 have analytically shown useful properties of random nets with Gaussian weights. As mentioned in the work of @cite_11 , many of the theoretical works on deep neural networks assume specific conditions which are not known to hold in practice; we show empirically what happens when weights are selected randomly (and fixed) throughout various layer of the network and within layers.