In recent years, artificial neural networks have achieved state-of-the-art performance for predicting the responses of neurons in the visual cortex to natural stimuli. However, they require a time consuming parameter optimization process for accurately modeling the tuning function of newly observed neurons, which prohibits many applications including real-time, closed-loop experiments.

We introduce a new type of neural network activation function based on recent physiological rate models for complex cells in visual area V1. A single-hidden-layer neural network of this kind of model achieves 1.5% error on MNIST. We also introduce an existing criterion for learning slow, decorrelated features as a pretraining strategy for image models.

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.

Many visual and auditory neurons have response properties that are well explained by pooling the rectified responses of a set of spatially shifted linear filters. These filters cannot be estimated using spike-triggered averaging (STA). Subspace methods such as spike-triggered covariance (STC) can recover multiple filters, but require substantial amounts of data, and recover an orthogonal basis for the subspace in which the filters reside rather than the filters themselves.

The computational modelling of the primary auditory cortex (A1) has been less fruitful than that of the primary visual cortex (V1) due to the less organized properties of A1. Greater disorder has recently been demonstrated for the tonotopy of A1 that has traditionally been considered to be as ordered as the retinotopy of V1. This disorder appears to be incongruous, given the uniformity of the neocortex; however, we hypothesized that both A1 and V1 would adopt an efficient coding strategy and that the disorder in A1 reflects natural sound statistics. To provide a computational model of the tonotopic disorder in A1, we used a model that was originally proposed for the smooth V1 map. In contrast to natural images, natural sounds exhibit distant correlations, which were learned and reflected in the disordered map. The auditory model predicted harmonic relationships among neighbouring A1 cells; furthermore, the same mechanism used to model V1 complex cells reproduced nonlinear responses similar to the pitch selectivity. These results contribute to the understanding of the sensory cortices of different modalities in a novel and integrated manner.

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.

For something so effortless and automatic, vision is a tough job for the brain. It's remarkable that we can transform electromagnetic radiation--light--into a meaningful world of objects and scenes. After all, light focused into an eye is merely a stream of photons with different wave properties, projecting continuously on our retinas, a layer of cells on the backside of our eyes. Before it's transduced by our eyes, light has no brightness or color, which are properties of animal perception. Our retinas transform this energy into electrical impulses that propagate within our nervous system. Somehow this comes out as a world: skies, children, art, auroras, and occasionally ghosts and UFOs.

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.

This article presents a theory for constructing hierarchical networks in such a way that the networks are guaranteed to be provably scale covariant. We first present a general sufficiency argument for obtaining scale covariance, which holds for a wide class of networks defined from linear and non-linear differential expressions expressed in terms of scale-normalized scale-space derivatives. Then, we present a more detailed development of one example of such a network constructed from a combination of mathematically derived models of receptive fields and biologically inspired computations. Based on a functional model of complex cells in terms of an oriented quasi quadrature combination of first- and second-order directional Gaussian derivatives, we couple such primitive computations in cascade over combinatorial expansions over image orientations. Scale-space properties of the computational primitives are analysed and we give explicit proofs of how the resulting representation allows for scale and rotation covariance. A prototype application to texture analysis is developed and it is demonstrated that a simplified mean-reduced representation of the resulting QuasiQuadNet leads to promising experimental results on three texture datasets.