Whereas CNNs have demonstrated immense progress in many vision problems, they suffer from a dependence on monumental amounts of labeled training data. On the other hand, dictionary learning does not scale to the size of problems that CNNs can handle, despite being very effective at low-level vision tasks such as denoising and inpainting. Recently, interest has grown in adapting dictionary learning methods for supervised tasks such as classification and inverse problems. We propose two new network layers that are based on dictionary learning: a sparse factorization layer and a convolutional sparse factorization layer, analogous to fully-connected and convolutional layers, respectively. Using our derivations, these layers can be dropped in to existing CNNs, trained together in an end-to-end fashion with back-propagation, and leverage semisupervision in ways classical CNNs cannot. We experimentally compare networks with these two new layers against a baseline CNN. Our results demonstrate that networks with either of the sparse factorization layers are able to outperform classical CNNs when supervised data are few. They also show performance improvements in certain tasks when compared to the CNN with no sparse factorization layers with the same exact number of parameters.
We relate our work to past methods that directly induce sparsity into artificial neural networks. Various methods @cite_27 @cite_17 @cite_25 have indirectly induced sparsity in the parameters or activations by incorporating sparsity-inducing penalties into network loss functions. Techniques like Dropout @cite_41 and DropConnect @cite_10 artificially simulate activation sparsity during inference to prevent redundancy and improve performance. @cite_19 argue for the use of the rectified linear unit (ReLU), a sparsifying activation function, to improve performance in CNNs. This works primarily by limiting the sensitivity of the activations to small changes in the input, thereby forming a more robust and error-tolerant network. However, these methods either lack theoretical basis, offer no means for controlling the activations' sparsity, and or require that all nonzero activations are positive, unlike our work.
@cite_41 @cite_19 @cite_27 @cite_10 @cite_25 @cite_17
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Deep neural nets with a large number of parameters are very powerful machine learning systems. However, overfitting is a serious problem in such networks. Large networks are also slow to use, making it difficult to deal with overfitting by combining the predictions of many different large neural nets at test time. Dropout is a technique for addressing this problem. The key idea is to randomly drop units (along with their connections) from the neural network during training. This prevents units from co-adapting too much. During training, dropout samples from an exponential number of different "thinned" networks. At test time, it is easy to approximate the effect of averaging the predictions of all these thinned networks by simply using a single unthinned network that has smaller weights. This significantly reduces overfitting and gives major improvements over other regularization methods. We show that dropout improves the performance of neural networks on supervised learning tasks in vision, speech recognition, document classification and computational biology, obtaining state-of-the-art results on many benchmark data sets. This article proposes the use of a penalty function for pruning feedforward neural network by weight elimination. The penalty function proposed consists of two terms. The first term is to discourage the use of unnecessary connections, and the second term is to prevent the weights of the connections from taking excessively large values. Simple criteria for eliminating weights from the network are also given. The effectiveness of this penalty function is tested on three well-known problems: the contiguity problem, the parity problems, and the monks problems. The resulting pruned networks obtained for many of these problems have fewer connections than previously reported in the literature. We introduce DropConnect, a generalization of Dropout (, 2012), for regularizing large fully-connected layers within neural networks. When training with Dropout, a randomly selected subset of activations are set to zero within each layer. DropConnect instead sets a randomly selected subset of weights within the network to zero. Each unit thus receives input from a random subset of units in the previous layer. We derive a bound on the generalization performance of both Dropout and DropConnect. We then evaluate DropConnect on a range of datasets, comparing to Dropout, and show state-of-the-art results on several image recognition benchmarks by aggregating multiple DropConnect-trained models. Unsupervised learning algorithms aim to discover the structure hidden in the data, and to learn representations that are more suitable as input to a supervised machine than the raw input. Many unsupervised methods are based on reconstructing the input from the representation, while constraining the representation to have certain desirable properties (e.g. low dimension, sparsity, etc). Others are based on approximating density by stochastically reconstructing the input from the representation. We describe a novel and efficient algorithm to learn sparse representations, and compare it theoretically and experimentally with a similar machine trained probabilistically, namely a Restricted Boltzmann Machine. We propose a simple criterion to compare and select different unsupervised machines based on the trade-off between the reconstruction error and the information content of the representation. We demonstrate this method by extracting features from a dataset of handwritten numerals, and from a dataset of natural image patches. We show that by stacking multiple levels of such machines and by training sequentially, high-order dependencies between the input observed variables can be captured. We consider supervised learning in the presence of very many irrelevant features, and study two different regularization methods for preventing overfitting. Focusing on logistic regression, we show that using L 1 regularization of the parameters, the sample complexity (i.e., the number of training examples required to learn "well,") grows only logarithmically in the number of irrelevant features. This logarithmic rate matches the best known bounds for feature selection, and indicates that L 1 regularized logistic regression can be effective even if there are exponentially many irrelevant features as there are training examples. We also give a lower-bound showing that any rotationally invariant algorithm---including logistic regression with L 2 regularization, SVMs, and neural networks trained by backpropagation---has a worst case sample complexity that grows at least linearly in the number of irrelevant features.