A new algorithm for training Restricted Boltzmann Machines is introduced. The algorithm, named Persistent Contrastive Divergence, is different from the standard Contrastive Divergence algorithms in that it aims to draw samples from almost exactly the model distribution. It is compared to some standard Contrastive Divergence and Pseudo-Likelihood algorithms on the tasks of modeling and classifying various types of data. The Persistent Contrastive Divergence algorithm outperforms the other algorithms, and is equally fast and simple.

Previous work has shown that the difficulties in learning deep generative or discriminative models can be overcome by an initial unsupervised learning step that maps inputs to useful intermediate representations. We introduce and motivate a new training principle for unsupervised learning of a representation based on the idea of making the learned representations robust to partial corruption of the input pattern. This approach can be used to train autoencoders, and these denoising autoencoders can be stacked to initialize deep architectures. The algorithm can be motivated from a manifold learning and information theoretic perspective or from a generative model perspective. Comparative experiments clearly show the surprising advantage of corrupting the input of autoencoders on a pattern classification benchmark suite.

Abstract 1 Motivated in part by the hierarchical organization of the neocortex, a number of recently proposed algorithms have tried 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 thesis describes an unsupervised learning model that faithfully mimics certain properties of visual area V2. Specifically, we develop a sparse variant of the deep belief networks described by Hinton et al. (2006). We learn two layers of representation 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 simple cell receptive fields in area V1. Further, the second layer in our model encodes various combinations of the first layer responses in the data. Specifically, it picks up both collinear (“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 Ito & Komatsu’s study of neural responses to angular stimuli in area V2 of the macaque. This suggests that our sparse variant of deep belief networks holds promise for modeling more higher-order features that are encoded in visual cortex. Conversely, one may also interpret the results reported here as suggestive that visual area V2 is performing computations on its input similar to those performed in (sparse) deep belief networks. This plausible relationship generates some intriguing hypotheses about V2 computations. 1 This thesis is an extended version of an earlier paper by Honglak Lee, Chaitanya Ekanadham, and Andrew Ng titled “Sparse deep belief net model for visual area V2.” 1

Abstract—Gaussian mixture models are currently the dominant technique for modeling the emission distribution of hidden Markov models for speech recognition. We show that better phone recognition on the TIMIT dataset can be achieved by replacing Gaussian mixture models by deep neural networks that contain many layers of features and a very large number of parameters. These networks are first pre-trained as a multi-layer generative model of a window of spectral feature vectors without making use of any discriminative information. Once the generative pre-training has designed the features, we perform discriminative fine-tuning using backpropagation to adjust the features slightly to make them better at predicting a probability distribution over the states of monophone hidden Markov models. Index Terms—Acoustic modeling, deep belief networks (DBNs), neural networks, phone recognition. I.

Humans and animals learn much better when the examples are not randomly presented but organized in a meaningful order which illustrates gradually more concepts, and gradually more complex ones. Here, we formalize such training strategies in the context of machine learning, and call them “curriculum learning”. In the context of recent research studying the difficulty of training in the presence of non-convex training criteria (for deep deterministic and stochastic neural networks), we explore curriculum learning in various set-ups. The experiments show that significant improvements in generalization can be achieved. We hypothesize that curriculum learning has both an effect on the speed of convergence of the training process to a minimum and, in the case of non-convex criteria, on the quality of the local minima obtained: curriculum learning can be seen as a particular form of continuation method (a general strategy for global optimization of non-convex functions). 1.

Recently, many applications for Restricted Boltzmann Machines (RBMs) have been developed for a large variety of learning problems. However, RBMs are usually used as feature extractors for another learning algorithm or to provide a good initialization for deep feed-forward neural network classifiers, and are not considered as a standalone solution to classification problems. In this paper, we argue that RBMs provide a self-contained framework for deriving competitive non-linear classifiers. We present an evaluation of different learning algorithms for RBMs which aim at introducing a discriminative component to RBM training and improve their performance as classifiers. This approach is simple in that RBMs are used directly to build a classifier, rather than as a stepping stone. Finally, we demonstrate how discriminative RBMs can also be successfully employed in a semi-supervised setting.

We introduce a new type of top-level model for Deep Belief Nets and evaluate it on a 3D object recognition task. The top-level model is a third-order Boltzmann machine, trained using a hybrid algorithm that combines both generative and discriminative gradients. Performance is evaluated on the NORB database (normalized-uniform version), which contains stereo-pair images of objects under different lighting conditions and viewpoints. Our model achieves 6.5 % error on the test set, which is close to the best published result for NORB (5.9%) using a convolutional neural net that has built-in knowledge of translation invariance. It substantially outperforms shallow models such as SVMs (11.6%). DBNs are especially suited for semi-supervised learning, and to demonstrate this we consider a modified version of the NORB recognition task in which additional unlabeled images are created by applying small translations to the images in the database. With the extra unlabeled data (and the same amount of labeled data as before), our model achieves 5.2 % error. 1

Restricted Boltzmann machines were developed using binary stochastic hidden units. These can be generalized by replacing each binary unit by an infinite number of copies that all have the same weights but have progressively more negative biases. The learning and inference rules for these “Stepped Sigmoid Units ” are unchanged. They can be approximated efficiently by noisy, rectified linear units. Compared with binary units, these units learn features that are better for object recognition on the NORB dataset and face verification on the Labeled Faces in the Wild dataset. Unlike binary units, rectified linear units preserve information about relative intensities as information travels through multiple layers of feature detectors. 1.

Most current speech recognition systems use hidden Markov models (HMMs) to deal with the temporal variability of speech and Gaussian mixture models to determine how well each state of each HMM fits a frame or a short window of frames of coefficients that represents the acoustic input. An alternative way to evaluate the fit is to use a feedforward neural network that takes several frames of coefficients as input and produces posterior probabilities over HMM states as output. Deep neural networks with many hidden layers, that are trained using new methods have been shown to outperform Gaussian mixture models on a variety of speech recognition benchmarks, sometimes by a large margin. This paper provides an overview of this progress and represents the shared views of four research groups who have had recent successes in using deep neural networks for acoustic modeling in speech recognition. I.

For many pattern recognition tasks, the ideal input feature would be invariant to multiple confounding properties (such as illumination and viewing angle, in computer vision applications). Recently, deep architectures trained in an unsupervised manner have been proposed as an automatic method for extracting useful features. However, it is difficult to evaluate the learned features by any means other than using them in a classifier. In this paper, we propose a number of empirical tests that directly measure the degree to which these learned features are invariant to different input transformations. We find that stacked autoencoders learn modestly increasingly invariant features with depth when trained on natural images. We find that convolutional deep belief networks learn substantially more invariant features in each layer. These results further justify the use of “deep ” vs. “shallower ” representations, but suggest that mechanisms beyond merely stacking one autoencoder on top of another may be important for achieving invariance. Our evaluation metrics can also be used to evaluate future work in deep learning, and thus help the development of future algorithms. 1