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143
A fast learning algorithm for deep belief nets
 Neural Computation
, 2006
"... We show how to use “complementary priors ” to eliminate the explaining away effects that make inference difficult in denselyconnected belief nets that have many hidden layers. Using complementary priors, we derive a fast, greedy algorithm that can learn deep, directed belief networks one layer at a ..."
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Cited by 445 (48 self)
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We show how to use “complementary priors ” to eliminate the explaining away effects that make inference difficult in denselyconnected belief nets that have many hidden layers. Using complementary priors, we derive a fast, greedy algorithm that can learn deep, directed belief networks one layer at a time, provided the top two layers form an undirected associative memory. The fast, greedy algorithm is used to initialize a slower learning procedure that finetunes the weights using a contrastive version of the wakesleep algorithm. After finetuning, a network with three hidden layers forms a very good generative model of the joint distribution of handwritten digit images and their labels. This generative model gives better digit classification than the best discriminative learning algorithms. The lowdimensional manifolds on which the digits lie are modelled by long ravines in the freeenergy landscape of the toplevel associative memory and it is easy to explore these ravines by using the directed connections to display what the associative memory has in mind. 1
Robust object recognition with cortexlike mechanisms
 IEEE Trans. Pattern Analysis and Machine Intelligence
, 2007
"... Abstract—We introduce a new general framework for the recognition of complex visual scenes, which is motivated by biology: We describe a hierarchical system that closely follows the organization of visual cortex and builds an increasingly complex and invariant feature representation by alternating b ..."
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Cited by 202 (36 self)
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Abstract—We introduce a new general framework for the recognition of complex visual scenes, which is motivated by biology: We describe a hierarchical system that closely follows the organization of visual cortex and builds an increasingly complex and invariant feature representation by alternating between a template matching and a maximum pooling operation. We demonstrate the strength of the approach on a range of recognition tasks: From invariant single object recognition in clutter to multiclass categorization problems and complex scene understanding tasks that rely on the recognition of both shapebased as well as texturebased objects. Given the biological constraints that the system had to satisfy, the approach performs surprisingly well: It has the capability of learning from only a few training examples and competes with stateoftheart systems. We also discuss the existence of a universal, redundant dictionary of features that could handle the recognition of most object categories. In addition to its relevance for computer vision, the success of this approach suggests a plausibility proof for a class of feedforward models of object recognition in cortex.
Convolutional Deep Belief Networks for Scalable Unsupervised Learning of Hierarchical Representations
"... There has been much interest in unsupervised learning of hierarchical generative models such as deep belief networks. Scaling such models to fullsized, highdimensional images remains a difficult problem. To address this problem, we present the convolutional deep belief network, a hierarchical gene ..."
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Cited by 160 (15 self)
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There has been much interest in unsupervised learning of hierarchical generative models such as deep belief networks. Scaling such models to fullsized, highdimensional 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 translationinvariant and supports efficient bottomup and topdown probabilistic inference. Key to our approach is probabilistic maxpooling, a novel technique which shrinks the representations of higher layers in a probabilistically sound way. Our experiments show that the algorithm learns useful highlevel 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 (bottomup and topdown) inference over fullsized images. 1.
PAMPAS: RealValued Graphical Models for Computer Vision
, 2003
"... Probabilistic models have been adopted for many computer vision applications, however inference in highdimensional spaces remains problematic. As the statespace of a model grows, the dependencies between the dimensions lead to an exponential growth in computation when performing inference. Many comm ..."
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Cited by 91 (3 self)
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Probabilistic models have been adopted for many computer vision applications, however inference in highdimensional spaces remains problematic. As the statespace of a model grows, the dependencies between the dimensions lead to an exponential growth in computation when performing inference. Many common computer vision problems naturally map onto the graphical model framework; the representation is a graph where each node contains a portion of the statespace and there is an edge between two nodes only if they are not independent conditional on the other nodes in the graph. When this graph is sparsely connected, belief propagation algorithms can turn an exponential inference computation into one which is linear in the size of the graph. However belief propagation is only applicable when the variables in the nodes are discretevalued or jointly represented by a single multivariate Gaussian distribution, and this rules out many computer vision applications.
A hierarchical Bayesian model of invariant pattern recognition in the visual cortex
 In Proceedings of the International Joint Conference on Neural Networks. IEEE
, 2005
"... Abstract — We describe a hierarchical model of invariant visual pattern recognition in the visual cortex. In this model, the knowledge of how patterns change when objects move is learned and encapsulated in terms of high probability sequences at each level of the hierarchy. Configuration of object p ..."
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Cited by 43 (1 self)
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Abstract — We describe a hierarchical model of invariant visual pattern recognition in the visual cortex. In this model, the knowledge of how patterns change when objects move is learned and encapsulated in terms of high probability sequences at each level of the hierarchy. Configuration of object parts is captured by the patterns of coincident high probability sequences. This knowledge is then encoded in a highly efficient Bayesian Network structure.The learning algorithm uses a temporal stability criterion to discover object concepts and movement patterns. We show that the architecture and algorithms are biologically plausible. The large scale architecture of the system matches the large scale organization of the cortex and the microcircuits derived from the local computations match the anatomical data on cortical circuits. The system exhibits invariance across a wide variety of transformations and is robust in the presence of noise. Moreover, the model also offers alternative explanations for various known cortical phenomena. I.
A computational model of the cerebral cortex
 In Proceedings of AAAI05, 938–943
, 2005
"... Our current understanding of the primate cerebral cortex (neocortex) and in particular the posterior, sensory association cortex has matured to a point where it is possible to develop a family of graphical models that capture the structure, scale and power of the neocortex for purposes of associativ ..."
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Cited by 20 (4 self)
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Our current understanding of the primate cerebral cortex (neocortex) and in particular the posterior, sensory association cortex has matured to a point where it is possible to develop a family of graphical models that capture the structure, scale and power of the neocortex for purposes of associative recall, sequence prediction and pattern completion among other functions. Implementing such models using readily available computing clusters is now within the grasp of many labs and would provide scientists with the opportunity to experiment with both hardwired connection schemes and structurelearning algorithms inspired by animal learning and developmental studies. While neural circuits involving structures external to the neocortex such as the thalamic nuclei are less well understood, the availability of a computational model on which to test hypotheses would likely accelerate our understanding of these circuits. Furthermore, the existence of an agreedupon cortical substrate would not only facilitate our understanding of the brain but enable researchers to combine lessons learned from biology with stateoftheart graphicalmodel and machinelearning techniques to design hybrid systems that combine the best of biological and traditional computing approaches.
Hierarchical models in the brain
 PLoS Computational Biology
, 2008
"... This paper describes a general model that subsumes many parametric models for continuous data. The model comprises hidden layers of statespace or dynamic causal models, arranged so that the output of one provides input to another. The ensuing hierarchy furnishes a model for many types of data, of a ..."
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Cited by 20 (9 self)
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This paper describes a general model that subsumes many parametric models for continuous data. The model comprises hidden layers of statespace or dynamic causal models, arranged so that the output of one provides input to another. The ensuing hierarchy furnishes a model for many types of data, of arbitrary complexity. Special cases range from the general linear model for static data to generalised convolution models, with system noise, for nonlinear timeseries analysis. Crucially, all of these models can be inverted using exactly the same scheme, namely, dynamic expectation maximization. This means that a single model and optimisation scheme can be used to invert a wide range of models. We present the model and a brief review of its inversion to disclose the relationships among, apparently, diverse generative models of empirical data. We then show that this inversion can be formulated as a simple neural network and may provide a useful metaphor for inference and learning in the brain.
Principles of image representation in visual cortex,” in The Visual Neurosciences
, 2003
"... The visual cortex is responsible for most of our conscious perception of the visual world, yet we remain largely ignorant of the principles underlying its function despite progress on many fronts of neuroscience. ..."
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Cited by 19 (2 self)
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The visual cortex is responsible for most of our conscious perception of the visual world, yet we remain largely ignorant of the principles underlying its function despite progress on many fronts of neuroscience.
Hierarchical Bayesian inference in networks of spiking neurons
 Advances in Neural Information Processing Systems 17
, 2005
"... There is growing evidence from psychophysical and neurophysiological studies that the brain utilizes Bayesian principles for inference and decision making. An important open question is how Bayesian inference for arbitrary graphical models can be implemented in networks of spiking neurons. In this p ..."
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Cited by 18 (0 self)
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There is growing evidence from psychophysical and neurophysiological studies that the brain utilizes Bayesian principles for inference and decision making. An important open question is how Bayesian inference for arbitrary graphical models can be implemented in networks of spiking neurons. In this paper, we show that recurrent networks of noisy integrateandfire neurons can perform approximate Bayesian inference for dynamic and hierarchical graphical models. The membrane potential dynamics of neurons is used to implement belief propagation in the log domain. The spiking probability of a neuron is shown to approximate the posterior probability of the preferred state encoded by the neuron, given past inputs. We illustrate the model using two examples: (1) a motion detection network in which the spiking probability of a directionselective neuron becomes proportional to the posterior probability of motion in a preferred direction, and (2) a twolevel hierarchical network that produces attentional effects similar to those observed in visual cortical areas V2 and V4. The hierarchical model offers a new Bayesian interpretation of attentional modulation in V2 and V4. 1
What and where: A Bayesian inference theory of attention
, 2010
"... In the theoretical framework described in this thesis, attention is part of the inference process that solves the visual recognition problem of what is where. The theory proposes a computational role for attention and leads to a model that predicts some of its main properties at the level of psychop ..."
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Cited by 17 (5 self)
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In the theoretical framework described in this thesis, attention is part of the inference process that solves the visual recognition problem of what is where. The theory proposes a computational role for attention and leads to a model that predicts some of its main properties at the level of psychophysics and physiology. In our approach, the main goal of the visual system is to infer the identity and the position of objects in visual scenes: spatial attention emerges as a strategy to reduce the uncertainty in shape information while featurebased attention reduces the uncertainty in spatial information. Featural and spatial attention represent two distinct modes of a computational process solving the problem of recognizing and localizing objects, especially in difficult recognition tasks such as in cluttered natural scenes. We describe a specific computational model and relate it to the known functional anatomy of attention. We show that several wellknown attentional phenomena – including bottomup popout effects, multiplicative modulation of neuronal tuning