Modelling natural images with sparse coding (SC) has faced two main challenges: flexibly representing varying pixel intensities and realistically representing lowlevel image components. This paper proposes a novel multiple-cause generative model of low-level image statistics that generalizes the standard SC model in two crucial points: (1) it uses a spike-and-slab prior distribution for a more realistic representation of component absence/intensity, and (2) the model uses the highly nonlinear combination rule of maximal causes analysis (MCA) instead of a linear combination. The major challenge is parameter optimization because a model with either (1) or (2) results in strongly multimodal posteriors. We show for the first time that a model combining both improvements can be trained efficiently while retaining the rich structure of the posteriors. We design an exact piecewise Gibbs sampling method and combine this with a variational method based on preselection of latent dimensions. This combined training scheme tackles both analytical and computational intractability and enables application of the model to a large number of observed and hidden dimensions.

Recent work in unsupervised feature learning has focused on the goal of discovering high-level features from unlabeled images. Much progress has been made in this direction, but in most cases it is still standard to use a large amount of labeled data in order to construct detectors sensitive to object classes or other complex patterns in the data. In this paper, we aim to test the hypothesis that unsupervised feature learning methods, provided with only unlabeled data, can learn high-level, invariant features that are sensitive to commonly-occurring objects. Though a handful of prior results suggest that this is possible when each object class accounts for a large fraction of the data (as in many labeled datasets), it is unclear whether something similar can be accomplished when dealing with completely unlabeled data. A major obstacle to this test, however, is scale: we cannot expect to succeed with small datasets or with small numbers of learned features. Here, we propose a large-scale feature learning system that enables us to carry out this experiment, learning 150,000 features from tens of millions of unlabeled images. Based on two scalable clustering algorithms (K-means and agglomerative clustering), we find that our simple system can discover features sensitive to a commonly occurring object class (human faces) and can also combine these into detectors invariant to significant global distortions like large translations and scale.

Recent work in unsupervised feature learning has focused on the goal of discovering high-level features from unlabeled images. Much progress has been made in this direction, but in most cases it is still standard to use a large amount of labeled data in order to construct detectors sensitive to object classes or other complex patterns in the data. In this paper, we aim to test the hypothesis that unsupervised feature learning methods, provided with only unlabeled data, can learn high-level, invariant features that are sensitive to commonly-occurring objects. Though a handful of prior results suggest that this is possible when each object class accounts for a large fraction of the data (as in many labeled datasets), it is unclear whether something similar can be accomplished when dealing with completely unlabeled data. A major obstacle to this test, however, is scale: we cannot expect to succeed with small datasets or with small numbers of learned features. Here, we propose a large-scale feature learning system that enables us to carry out this experiment, learning 150,000 features from tens of millions of unlabeled images. Based on two scalable clustering algorithms (K-means and agglomerative clustering), we find that our simple system can discover features sensitive to a commonly occurring object class (human faces) and can also combine these into detectors invariant to significant global distortions like large translations and scale.

Using a recurrent neural network of excitatory spiking neurons with adapting synapses we show that both effects could be explained by a fast and a slow compo(cid:173) nent in the synaptic adaptation. This component-given by infomax learning rule-explains contrast adaptation of the averaged membrane potential (DC component) as well as the surprising experi(cid:173) mental result, that the stimulus modulated component (Fl component) of a cortical cell's membrane potential adapts only weakly. Based on our results, we propose a new experiment to estimate the strength of the ef(cid:173) fective excitatory feedback to a cortical neuron, and we also suggest a relatively simple experimental test to justify our hypothesized synaptic mechanism for contrast adaptation.

We describe a neuromorphic chip transistor heterogeneity, introduced by the fabrication process, to generate orientation maps similar to those imaged in vivo. Our model consists of a recurrent network of excitatory and inhibitory cells in parallel with a push-pull stage. Similar to a previous model the recurrent network displays hotspots of activity that give rise to visual feature maps. Unlike previous work, however, the map for orientation does not depend on the sign of contrast. Instead, sign- independent cells driven by both ON and OFF channels anchor the map, while push-pull interactions give rise to sign-preserving cells.

Modelling natural images with sparse coding (SC) has faced two main challenges: flexibly representing varying pixel intensities and realistically representing low- level image components. This paper proposes a novel multiple-cause generative model of low-level image statistics that generalizes the standard SC model in two crucial points: (1) it uses a spike-and-slab prior distribution for a more realistic representation of component absence/intensity, and (2) the model uses the highly nonlinear combination rule of maximal causes analysis (MCA) instead of a lin- ear combination. The major challenge is parameter optimization because a model with either (1) or (2) results in strongly multimodal posteriors. We show for the first time that a model combining both improvements can be trained efficiently while retaining the rich structure of the posteriors. We design an exact piece- wise Gibbs sampling method and combine this with a variational method based on preselection of latent dimensions. This combined training scheme tackles both analytical and computational intractability and enables application of the model to a large number of observed and hidden dimensions.

The receptive fields of simple cells in the visual cortex can be understood as linear filters. These filters can be modelled by Gabor functions, or by Gaussian derivatives. Gabor functions can also be combined in an `energy model' of the complex cell response. This paper proposes an alternative model of the complex cell, based on Gaussian derivatives. It is most important to account for the insensitivity of the complex response to small shifts of the image. The new model uses a linear combination of the first few derivative filters, at a single position, to approximate the first derivative filter, at a series of adjacent positions. The maximum response, over all positions, gives a signal that is insensitive to small shifts of the image. This model, unlike previous approaches, is based on the scale space theory of visual processing. In particular, the complex cell is built from filters that respond to the \twod\ differential structure of the image. The computational aspects of the new model are studied in one and two dimensions, using the steerability of the Gaussian derivatives. The response of the model to basic images, such as edges and gratings, is derived formally. The response to natural images is also evaluated, using statistical measures of shift insensitivity. The relevance of the new model to the cortical image representation is discussed.

The receptive field (RF) of a sensory neuron describes how the neuron integrates sensory stimuli over time and space. In typical experiments with naturalistic or flickering spatiotemporal stimuli, RFs are very high-dimensional, due to the large number of coefficients needed to specify an integration profile across time and space. Estimating these coefficients from small amounts of data poses a variety of challenging statistical and computational problems. Here we address these challenges by developing Bayesian reduced rank regression methods for RF estimation. This corresponds to modeling the RF as a sum of several space-time separable (i.e., rank-1) filters, which proves accurate even for neurons with strongly oriented space-time RFs. This approach substantially reduces the number of parameters needed to specify the RF, from 1K-100K down to mere 100s in the examples we consider, and confers substantial benefits in statistical power and computational efficiency. In particular, we introduce a novel prior over low-rank RFs using the restriction of a matrix normal prior to the manifold of low-rank matrices. We then use a localized'' prior over row and column covariances to obtain sparse, smooth, localized estimates of the spatial and temporal RF components. We develop two methods for inference in the resulting hierarchical model: (1) a fully Bayesian method using blocked-Gibbs sampling; and (2) a fast, approximate method that employs alternating coordinate ascent of the conditional marginal likelihood. We develop these methods under Gaussian and Poisson noise models, and show that low-rank estimates substantially outperform full rank estimates in accuracy and speed using neural data from retina and V1."

Modelling natural images with sparse coding (SC) has faced two main challenges: flexibly representing varying pixel intensities and realistically representing lowlevel image components. This paper proposes a novel multiple-cause generative model of low-level image statistics that generalizes the standard SC model in two crucial points: (1) it uses a spike-and-slab prior distribution for a more realistic representation of component absence/intensity, and (2) the model uses the highly nonlinear combination rule of maximal causes analysis (MCA) instead of a linear combination. The major challenge is parameter optimization because a model with either (1) or (2) results in strongly multimodal posteriors. We show for the first time that a model combining both improvements can be trained efficiently while retaining the rich structure of the posteriors. We design an exact piecewise Gibbs sampling method and combine this with a variational method based on preselection of latent dimensions. This combined training scheme tackles both analytical and computational intractability and enables application of the model to a large number of observed and hidden dimensions.

Modelling natural images with sparse coding (SC) has faced two main challenges: flexibly representing varying pixel intensities and realistically representing lowlevel image components. This paper proposes a novel multiple-cause generative model of low-level image statistics that generalizes the standard SC model in two crucial points: (1) it uses a spike-and-slab prior distribution for a more realistic representation of component absence/intensity, and (2) the model uses the highly nonlinear combination rule of maximal causes analysis (MCA) instead of a linear combination. The major challenge is parameter optimization because a model with either (1) or (2) results in strongly multimodal posteriors. We show for the first time that a model combining both improvements can be trained efficiently while retaining the rich structure of the posteriors. We design an exact piecewise Gibbs sampling method and combine this with a variational method based on preselection of latent dimensions. This combined training scheme tackles both analytical and computational intractability and enables application of the model to a large number of observed and hidden dimensions.