Dropout is commonly used to help reduce overfitting in deep neural networks. Sparsity is a potentially important property of neural networks, but is not explicitly controlled by Dropout-based regularization. In this work, we propose Sparseout a simple and efficient variant of Dropout that can be used to control the sparsity of the activations in a neural network. We theoretically prove that Sparseout is equivalent to an (L_q ) penalty on the features of a generalized linear model and that Dropout is a special case of Sparseout for neural networks. We empirically demonstrate that Sparseout is computationally inexpensive and is able to control the desired level of sparsity in the activations. We evaluated Sparseout on image classification and language modelling tasks to see the effect of sparsity on these tasks. We found that sparsity of the activations is favorable for language modelling performance while image classification benefits from denser activations. Sparseout provides a way to investigate sparsity in state-of-the-art deep learning models. Source code for Sparseout could be found at https: github.com najeebkhan sparseout.
In this paper we aim at facilitating generalization for deep networks while supporting interpretability of the learned representations. Towards this goal, we propose a clustering based regularization that encourages parsimonious representations. Our k-means style objective is easy to optimize and flexible supporting various forms of clustering, including sample and spatial clustering as well as co-clustering. We demonstrate the effectiveness of our approach on the tasks of unsupervised learning, classification, fine grained categorization and zero-shot learning. Motivated in part by the hierarchical organization of the cortex, a number of algorithms have recently been proposed that try to learn hierarchical, or "deep," structure from unlabeled data. While several authors have formally or informally compared their algorithms to computations performed in visual area V1 (and the cochlea), little attempt has been made thus far to evaluate these algorithms in terms of their fidelity for mimicking computations at deeper levels in the cortical hierarchy. This paper presents an unsupervised learning model that faithfully mimics certain properties of visual area V2. Specifically, we develop a sparse variant of the deep belief networks of (2006). We learn two layers of nodes in the network, and demonstrate that the first layer, similar to prior work on sparse coding and ICA, results in localized, oriented, edge filters, similar to the Gabor functions known to model V1 cell receptive fields. Further, the second layer in our model encodes correlations of the first layer responses in the data. Specifically, it picks up both colinear ("contour") features as well as corners and junctions. More interestingly, in a quantitative comparison, the encoding of these more complex "corner" features matches well with the results from the Ito & Komatsu's study of biological V2 responses. This suggests that our sparse variant of deep belief networks holds promise for modeling more higher-order features. The spatial receptive fields of simple cells in mammalian striate cortex have been reasonably well described physiologically and can be characterized as being localized, oriented, and ban@ass, comparable with the basis functions of wavelet transforms. Previously, we have shown that these receptive field properties may be accounted for in terms of a strategy for producing a sparse distribution of output activity in response to natural images. Here, in addition to describing this work in a more expansive fashion, we examine the neurobiological implications of sparse coding. Of particular interest is the case when the code is overcomplete--i.e., when the number of code elements is greater than the effective dimensionality of the input space. Because the basis functions are non-orthogonal and not linearly independent of each other, sparsifying the code will recruit only those basis functions necessary for representing a given input, and so the input-output function will deviate from being purely linear. These deviations from linearity provide a potential explanation for the weak forms of non-linearity observed in the response properties of cortical simple cells, and they further make predictions about the expected interactions among units in response to naturalistic stimuli. © 1997 Elsevier Science Ltd Restricted Boltzmann machines (RBMs) have been used as generative models of many different types of data. RBMs are usually trained using the contrastive divergence learning procedure. This requires a certain amount of practical experience to decide how to set the values of numerical meta-parameters. Over the last few years, the machine learning group at the University of Toronto has acquired considerable expertise at training RBMs and this guide is an attempt to share this expertise with other machine learning researchers. Sparseness is a useful regularizer for learning in a wide range of applications, in particular in neural networks. This paper proposes a model targeted at classification tasks, where sparse activity and sparse connectivity are used to enhance classification capabilities. The tool for achieving this is a sparseness-enforcing projection operator which finds the closest vector with a pre-defined sparseness for any given vector. In the theoretical part of this paper, a comprehensive theory for such a projection is developed. In conclusion, it is shown that the projection is differentiable almost everywhere and can thus be implemented as a smooth neuronal transfer function. The entire model can hence be tuned end-to-end using gradient-based methods. Experiments on the MNIST database of handwritten digits show that classification performance can be boosted by sparse activity or sparse connectivity. With a combination of both, performance can be significantly better compared to classical non-sparse approaches.