Showing papers by "Geoffrey E. Hinton published in 2010"

Rectified Linear Units Improve Restricted Boltzmann Machines

Abstract: 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.

Learning to detect roads in high-resolution aerial images

Abstract: Reliably extracting information from aerial imagery is a difficult problem with many practical applications. One specific case of this problem is the task of automatically detecting roads. This task is a difficult vision problem because of occlusions, shadows, and a wide variety of non-road objects. Despite 30 years of work on automatic road detection, no automatic or semi-automatic road detection system is currently on the market and no published method has been shown to work reliably on large datasets of urban imagery. We propose detecting roads using a neural network with millions of trainable weights which looks at a much larger context than was used in previous attempts at learning the task. The network is trained on massive amounts of data using a consumer GPU. We demonstrate that predictive performance can be substantially improved by initializing the feature detectors using recently developed unsupervised learning methods as well as by taking advantage of the local spatial coherence of the output labels.We show that our method works reliably on two challenging urban datasets that are an order of magnitude larger than what was used to evaluate previous approaches.

Learning to combine foveal glimpses with a third-order Boltzmann machine

Abstract: We describe a model based on a Boltzmann machine with third-order connections that can learn how to accumulate information about a shape over several fixations. The model uses a retina that only has enough high resolution pixels to cover a small area of the image, so it must decide on a sequence of fixations and it must combine the "glimpse" at each fixation with the location of the fixation before integrating the information with information from other glimpses of the same object. We evaluate this model on a synthetic dataset and two image classification datasets, showing that it can perform at least as well as a model trained on whole images.

Binary Coding of Speech Spectrograms Using a Deep Auto-encoder

Abstract: This paper reports our recent exploration of the layer-by-layer learning strategy for training a multi-layer generative model of patches of speech spectrograms. The top layer of the generative model learns binary codes that can be used for efficient compression of speech and could also be used for scalable speech recognition or rapid speech content retrieval. Each layer of the generative model is fully connected to the layer below and the weights on these connections are pretrained efficiently by using the contrastive divergence approximation to the log likelihood gradient. After layer-bylayer pre-training we “unroll” the generative model to form a deep auto-encoder, whose parameters are then fine-tuned using back-propagation. To reconstruct the full-length speech spectrogram, individual spectrogram segments predicted by their respective binary codes are combined using an overlapand-add method. Experimental results on speech spectrogram coding demonstrate that the binary codes produce a logspectral distortion that is approximately 2 dB lower than a subband vector quantization technique over the entire frequency range of wide-band speech. Index Terms: deep learning, speech feature extraction, neural networks, auto-encoder, binary codes, Boltzmann machine

Phone Recognition with the Mean-Covariance Restricted Boltzmann Machine

Abstract: Straightforward application of Deep Belief Nets (DBNs) to acoustic modeling produces a rich distributed representation of speech data that is useful for recognition and yields impressive results on the speaker-independent TIMIT phone recognition task. However, the first-layer Gaussian-Bernoulli Restricted Boltzmann Machine (GRBM) has an important limitation, shared with mixtures of diagonal-covariance Gaussians: GRBMs treat different components of the acoustic input vector as conditionally independent given the hidden state. The mean-covariance restricted Boltzmann machine (mcRBM), first introduced for modeling natural images, is a much more representationally efficient and powerful way of modeling the covariance structure of speech data. Every configuration of the precision units of the mcRBM specifies a different precision matrix for the conditional distribution over the acoustic space. In this work, we use the mcRBM to learn features of speech data that serve as input into a standard DBN. The mcRBM features combined with DBNs allow us to achieve a phone error rate of 20.5%, which is superior to all published results on speaker-independent TIMIT to date.

Modeling pixel means and covariances using factorized third-order boltzmann machines

Abstract: 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.

Learning to represent spatial transformations with factored higher-order boltzmann machines

Abstract: To allow the hidden units of a restricted Boltzmann machine to model the transformation between two successive images, Memisevic and Hinton (2007) introduced three-way multiplicative interactions that use the intensity of a pixel in the first image as a multiplicative gain on a learned, symmetric weight between a pixel in the second image and a hidden unit This creates cubically many parameters, which form a three-dimensional interaction tensor We describe a low-rank approximation to this interaction tensor that uses a sum of factors, each of which is a three-way outer product This approximation allows efficient learning of transformations between larger image patches Since each factor can be viewed as an image filter, the model as a whole learns optimal filter pairs for efficiently representing transformations We demonstrate the learning of optimal filter pairs from various synthetic and real image sequences We also show how learning about image transformations allows the model to perform a simple visual analogy task, and we show how a completely unsupervised network trained on transformations perceives multiple motions of transparent dot patterns in the same way as humans

Factored 3-Way Restricted Boltzmann Machines For Modeling Natural Images

Abstract: Deep belief nets have been successful in modeling handwritten characters, but it has proved more difficult to apply them to real images. The problem lies in the restricted Boltzmann machine (RBM) which is used as a module for learning deep belief nets one layer at a time. The Gaussian-Binary RBMs that have been used to model real-valued data are not a good way to model the covariance structure of natural images. We propose a factored 3-way RBM that uses the states of its hidden units to represent abnormalities in the local covariance structure of an image. This provides a probabilistic framework for the widely used simple/complex cell architecture. Our model learns binary features that work very well for object recognition on the “tiny images” data set. Even better features are obtained by then using standard binary RBM’s to learn a deeper model.

Dynamical binary latent variable models for 3D human pose tracking

Abstract: We introduce a new class of probabilistic latent variable model called the Implicit Mixture of Conditional Restricted Boltzmann Machines (imCRBM) for use in human pose tracking. Key properties of the imCRBM are as follows: (1) learning is linear in the number of training exemplars so it can be learned from large datasets; (2) it learns coherent models of multiple activities; (3) it automatically discovers atomic “movemes” and (4) it can infer transitions between activities, even when such transitions are not present in the training set. We describe the model and how it is learned and we demonstrate its use in the context of Bayesian filtering for multi-view and monocular pose tracking. The model handles difficult scenarios including multiple activities and transitions among activities. We report state-of-the-art results on the HumanEva dataset.

Phone recognition using Restricted Boltzmann Machines

Abstract: For decades, Hidden Markov Models (HMMs) have been the state-of-the-art technique for acoustic modeling despite their unrealistic independence assumptions and the very limited representational capacity of their hidden states. Conditional Restricted Boltzmann Machines (CRBMs) have recently proved to be very effective for modeling motion capture sequences and this paper investigates the application of this more powerful type of generative model to acoustic modeling. On the standard TIMIT corpus, one type of CRBM outperforms HMMs and is comparable with the best other methods, achieving a phone error rate (PER) of 26.7% on the TIMIT core test set.

Gated Softmax Classification

Abstract: We describe a "log-bilinear" model that computes class probabilities by combining an input vector multiplicatively with a vector of binary latent variables. Even though the latent variables can take on exponentially many possible combinations of values, we can efficiently compute the exact probability of each class by marginalizing over the latent variables. This makes it possible to get the exact gradient of the log likelihood. The bilinear score-functions are defined using a three-dimensional weight tensor, and we show that factorizing this tensor allows the model to encode invariances inherent in a task by learning a dictionary of invariant basis functions. Experiments on a set of benchmark problems show that this fully probabilistic model can achieve classification performance that is competitive with (kernel) SVMs, backpropagation, and deep belief nets.

Learning to represent visual input

Abstract:  One of the central problems in computational neuroscience is to understand how the object-recognition pathway of the cortex learns a deep hierarchy of nonlinear feature detectors. Recent progress in machine learning shows that it is possible to learn deep hierarchies without requiring any labelled data. The feature detectors are learned one layer at a time and the goal of the learning procedure is to form a good generative model of images, not to predict the class of each image. The learning procedure only requires the pairwise correlations between the activations of neuron-like processing units in adjacent layers. The original version of the learning procedure is derived from a quadratic ‘energy’ function but it can be extended to allow third-order, multiplicative interactions in which neurons gate the pairwise interactions between other neurons. A technique for factoring the third-order interactions leads to a learning module that again has a simple learning rule based on pairwise correlations. This module looks remarkably like modules that have been proposed by both biologists trying to explain the responses of neurons and engineers trying to create systems that can recognize objects.

Generating more realistic images using gated MRF's

Abstract: Probabilistic models of natural images are usually evaluated by measuring performance on rather indirect tasks, such as denoising and inpainting. A more direct way to evaluate a generative model is to draw samples from it and to check whether statistical properties of the samples match the statistics of natural images. This method is seldom used with high-resolution images, because current models produce samples that are very different from natural images, as assessed by even simple visual inspection. We investigate the reasons for this failure and we show that by augmenting existing models so that there are two sets of latent variables, one set modelling pixel intensities and the other set modelling image-specific pixel covariances, we are able to generate high-resolution images that look much more realistic than before. The overall model can be interpreted as a gated MRF where both pair-wise dependencies and mean intensities of pixels are modulated by the states of latent variables. Finally, we confirm that if we disallow weight-sharing between receptive fields that overlap each other, the gated MRF learns more efficient internal representations, as demonstrated in several recognition tasks.

Comparing classification methods for longitudinal fmri studies

Abstract: We compare 10 methods of classifying fMRI volumes by applying them to data from a longitudinal study of stroke recovery: adaptive Fisher's linear and quadratic discriminant; gaussian naive Bayes; support vector machines with linear, quadratic, and radial basis function (RBF) kernels; logistic regression; two novel methods based on pairs of restricted Boltzmann machines (RBM); and K-nearest neighbors. All methods were tested on three binary classification tasks, and their out-of-sample classification accuracies are compared. The relative performance of the methods varies considerably across subjects and classification tasks. The best overall performers were adaptive quadratic discriminant, support vector machines with RBF kernels, and generatively trained pairs of RBMs.

Deep Belief Nets

Abstract: Deep belief nets are probabilistic generative models that are composed of multiple layers of stochastic latent variables (also called “feature detectors” or “hidden units”). The top two layers have undirected, symmetric connections between them and form an associative memory. The lower layers receive top-down, directed connections from the layer above. Deep belief nets have two important computational properties. First, there is an efficient procedure for learning the topdown, generative weights that specify how the variables in one layer determine the probabilities of variables in the layer below. This procedure learns one layer of latent variables at a time. Second, after learning multiple layers, the values of the latent variables in every layer can be inferred by a single, bottom-up pass that starts with an observed data vector in the bottom layer and uses the generative weights in the reverse direction.