There has been much interest in unsupervised learning of hierarchical generative models such as deep belief networks. Scaling such models to full-sized, high-dimensional images remains a difficult problem. To address this problem, we present the convolutional deep belief network, a hierarchical generative model which scales to realistic image sizes. This model is translation-invariant and supports efficient bottom-up and top-down probabilistic inference. Key to our approach is probabilistic max-pooling, a novel technique which shrinks the representations of higher layers in a probabilistically sound way. Our experiments show that the algorithm learns useful high-level visual features, such as object parts, from unlabeled images of objects and natural scenes. We demonstrate excellent performance on several visual recognition tasks and show that our model can perform hierarchical (bottom-up and top-down) inference over full-sized images. 1.

We present an unsupervised method for learning a hierarchy of sparse feature detectors that are invariant to small shifts and distortions. The resulting feature extractor consists of multiple convolution filters, followed by a pointwise sigmoid non-linearity, and a feature-pooling layer that computes the max of each filter output within adjacent windows. A second level of larger and more invariant features is obtained by training the same algorithm on patches of features from the first level. Training a supervised classifier on these features yields 0.64 % error on MNIST, and 54 % average recognition rate on Caltech 101

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.

In many recent object recognition systems, feature extraction stages are generally composed of a filter bank, a non-linear transformation, and some sort of feature pooling layer. Most systems use only one stage of feature extraction in which the filters are hard-wired, or two stages where the filters in one or both stages are learned in supervised or unsupervised mode. This paper addresses three questions: 1. How does the non-linearities that follow the filter banks influence the recognition accuracy? 2. does learning the filter banks in an unsupervised or supervised manner improve the performance over random filters or hardwired filters? 3. Is there any advantage to using an architecture with two stages of feature extraction, rather than one? We show that using non-linearities that include rectification and local contrast normalization is the single most important ingredient for good accuracy on object recognition benchmarks. We show that two stages of feature extraction yield better accuracy than one. Most surprisingly, we show that a two-stage system with random filters can yield almost 63 % recognition rate on Caltech-101, provided that the proper non-linearities and pooling layers are used. Finally, we show that with supervised refinement, the system achieves state-of-the-art performance on NORB dataset (5.6%) and unsupervised pre-training followed by supervised refinement produces good accuracy on Caltech-101 (> 65%), and the lowest known error rate on the undistorted, unprocessed MNIST dataset (0.53%). 1.

April 8, 2009Groups at MIT and NYU have collected a dataset of millions of tiny colour images from the web. It is, in principle, an excellent dataset for unsupervised training of deep generative models, but previous researchers who have tried this have found it di cult to learn a good set of lters from the images. We show how to train a multi-layer generative model that learns to extract meaningful features which resemble those found in the human visual cortex. Using a novel parallelization algorithm to distribute the work among multiple machines connected on a network, we show how training such a model can be done in reasonable time. A second problematic aspect of the tiny images dataset is that there are no reliable class labels which makes it hard to use for object recognition experiments. We created two sets of reliable labels. The CIFAR-10 set has 6000 examples of each of 10 classes and the CIFAR-100 set has 600 examples of each of 100 non-overlapping classes. Using these labels, we show that object recognition is signi cantly

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. 1

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

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.

Learning a generative model of natural images is a useful way of extracting features that capture interesting regularities. Previous work on learning such models has focused on methods in which the latent features are used to determine the mean and variance of each pixel independently, or on methods in which the hidden units determine the covariance matrix of a zero-mean Gaussian distribution. In this work, we propose a probabilistic model that combines these two approaches into a single framework. We represent each image using one set of binary latent features that model the image-specific covariance and a separate set that model the mean. We show that this approach provides a probabilistic framework for the widely used simple-cell complex-cell architecture, it produces very realistic samples of natural images and it extracts features that yield state-of-the-art recognition accuracy on the challenging CIFAR 10 dataset. 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.