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.
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.
@cite_28 @cite_38 @cite_33 @cite_11
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We study the effectiveness of learning low degree polynomials using neural networks by the gradient descent method. While neural networks have been shown to have great expressive power, and gradient descent has been widely used in practice for learning neural networks, few theoretical guarantees are known for such methods. In particular, it is well known that gradient descent can get stuck at local minima, even for simple classes of target functions. In this paper, we present several positive theoretical results to support the effectiveness of neural networks. We focus on twolayer neural networks where the bottom layer is a set of non-linear hidden nodes, and the top layer node is a linear function, similar to Barron (1993). First we show that for a randomly initialized neural network with sufficiently many hidden units, the generic gradient descent algorithm learns any low degree polynomial, assuming we initialize the weights randomly. Secondly, we show that if we use complex-valued weights (the target function can still be real), then under suitable conditions, there are no "robust local minima": the neural network can always escape a local minimum by performing a random perturbation. This property does not hold for real-valued weights. Thirdly, we discuss whether sparse polynomials can be learned with small neural networks, with the size dependent on the sparsity of the target function. Extreme learning machine (ELM) is an emerging learning algorithm for the generalized single hidden layer feedforward neural networks, of which the hidden node parameters are randomly generated and the output weights are analytically computed. However, due to its shallow architecture, feature learning using ELM may not be effective for natural signals (e.g., images videos), even with a large number of hidden nodes. To address this issue, in this paper, a new ELM-based hierarchical learning framework is proposed for multilayer perceptron. The proposed architecture is divided into two main components: 1) self-taught feature extraction followed by supervised feature classification and 2) they are bridged by random initialized hidden weights. The novelties of this paper are as follows: 1) unsupervised multilayer encoding is conducted for feature extraction, and an ELM-based sparse autoencoder is developed via l 1 constraint. By doing so, it achieves more compact and meaningful feature representations than the original ELM; 2) by exploiting the advantages of ELM random feature mapping, the hierarchically encoded outputs are randomly projected before final decision making, which leads to a better generalization with faster learning speed; and 3) unlike the greedy layerwise training of deep learning (DL), the hidden layers of the proposed framework are trained in a forward manner. Once the previous layer is established, the weights of the current layer are fixed without fine-tuning. Therefore, it has much better learning efficiency than the DL. Extensive experiments on various widely used classification data sets show that the proposed algorithm achieves better and faster convergence than the existing state-of-the-art hierarchical learning methods. Furthermore, multiple applications in computer vision further confirm the generality and capability of the proposed learning scheme. In big data fields, with increasing computing capability, artificial neural networks have shown great strength in solving data classification and regression problems. The traditional training of neural networks depends generally on the error back propagation method to iteratively tune all the parameters. When the number of hidden layers increases, this kind of training has many problems such as slow convergence, time consuming, and local minima. To avoid these problems, neural networks with random weights (NNRW) are proposed in which the weights between the hidden layer and input layer are randomly selected and the weights between the output layer and hidden layer are obtained analytically. Researchers have shown that NNRW has much lower training complexity in comparison with the traditional training of feed-forward neural networks. This paper objectively reviews the advantages and disadvantages of NNRW model, tries to reveal the essence of NNRW, gives our comments and remarks on NNRW, and provides some useful guidelines for users to choose a mechanism to train a feed-forward neural network. Artificial neural networks are most commonly trained with the back-propagation algorithm, where the gradient for learning is provided by back-propagating the error, layer by layer, from the output layer to the hidden layers. A recently discovered method called feedback-alignment shows that the weights used for propagating the error backward don't have to be symmetric with the weights used for propagation the activation forward. In fact, random feedback weights work evenly well, because the network learns how to make the feedback useful. In this work, the feedback alignment principle is used for training hidden layers more independently from the rest of the network, and from a zero initial condition. The error is propagated through fixed random feedback connections directly from the output layer to each hidden layer. This simple method is able to achieve zero training error even in convolutional networks and very deep networks, completely without error back-propagation. The method is a step towards biologically plausible machine learning because the error signal is almost local, and no symmetric or reciprocal weights are required. Experiments show that the test performance on MNIST and CIFAR is almost as good as those obtained with back-propagation for fully connected networks. If combined with dropout, the method achieves 1.45 error on the permutation invariant MNIST task.