https://www2.econ.iastate.edu/tesfatsi/DeepLearningInNeuralNetworksOverview.JSchmidhuber2015.pdf

Deep learning in neural networks

In recent years, many new cortical areas have been identified in the macaque monkey. The number of identified connections between areas has increased even more dramatically. We report here on (1) a summary of the layout of cortical areas associated with vision and with other modalities, (2) a computerized database for storing and representing large amounts of information on connectivity patterns, and (3) the application of these data to the analysis of hierarchical organization of the cerebral cortex. Our analysis concentrates on the visual system, which includes 25 neocortical areas that are predominantly or exclusively visual in function, plus an additional 7 areas that we regard as visual-association areas on the basis of their extensive visual inputs. A total of 305 connections among these 32 visual and visual-association areas have been reported. This represents 31% of the possible number of pathways if each area were connected with all others. The actual degree of connectivity is likely to be closer to 40%. The great majority of pathways involve reciprocal connections between areas. There are also extensive connections with cortical areas outside the visual system proper, including the somatosensory cortex, as well as neocortical, transitional, and archicortical regions in the temporal and frontal lobes. In the somatosensory/motor system, there are 62 identified pathways linking 13 cortical areas, suggesting an overall connectivity of about 40%. Based on the laminar patterns of connections between areas, we propose a hierarchy of visual areas and of somatosensory/motor areas that is more comprehensive than those suggested in other recent studies. The current version of the visual hierarchy includes 10 levels of cortical processing. Altogether, it contains 14 levels if one includes the retina and lateral geniculate nucleus at the bottom as well as the entorhinal cortex and hippocampus at the top. Within this hierarchy, there are multiple, intertwined processing streams, which, at a low level, are related to the compartmental organization of areas V1 and V2 and, at a high level, are related to the distinction between processing centers in the temporal and parietal lobes. However, there are some pathways and relationships (about 10% of the total) whose descriptions do not fit cleanly into this hierarchical scheme for one reason or another. In most instances, though, it is unclear whether these represent genuine exceptions to a strict hierarchy rather than inaccuracies or uncertainities in the reported assignment.

/pdf/distributed-hierarchical-processing-in-the-primate-cerebral-1dvblm6d82.pdf

Distributed Hierarchical Processing in the Primate Cerebral Cortex

The receptive fields of simple cells in mammalian primary visual cortex can be characterized as being spatially localized, oriented and bandpass (selective to structure at different spatial scales), comparable to the basis functions of wavelet transforms. One approach to understanding such response properties of visual neurons has been to consider their relationship to the statistical structure of natural images in terms of efficient coding. Along these lines, a number of studies have attempted to train unsupervised learning algorithms on natural images in the hope of developing receptive fields with similar properties, but none has succeeded in producing a full set that spans the image space and contains all three of the above properties. Here we investigate the proposal that a coding strategy that maximizes sparseness is sufficient to account for these properties. We show that a learning algorithm that attempts to find sparse linear codes for natural scenes will develop a complete family of localized, oriented, bandpass receptive fields, similar to those found in the primary visual cortex. The resulting sparse image code provides a more efficient representation for later stages of processing because it possesses a higher degree of statistical independence among its outputs.

/pdf/emergence-of-simple-cell-receptive-field-properties-by-bulmogedmu.pdf

Emergence of simple-cell receptive field properties by learning a sparse code for natural images

Sparse Coding with an Overcomplete Basis Set: A Strategy Employed by V1 ?

Two-dimensional spatial linear filters are constrained by general uncertainty relations that limit their attainable information resolution for orientation, spatial frequency, and two-dimensional (2D) spatial position. The theoretical lower limit for the joint entropy, or uncertainty, of these variables is achieved by an optimal 2D filter family whose spatial weighting functions are generated by exponentiated bivariate second-order polynomials with complex coefficients, the elliptic generalization of the one-dimensional elementary functions proposed in Gabor’s famous theory of communication [ J. Inst. Electr. Eng.93, 429 ( 1946)]. The set includes filters with various orientation bandwidths, spatial-frequency bandwidths, and spatial dimensions, favoring the extraction of various kinds of information from an image. Each such filter occupies an irreducible quantal volume (corresponding to an independent datum) in a four-dimensional information hyperspace whose axes are interpretable as 2D visual space, orientation, and spatial frequency, and thus such a filter set could subserve an optimally efficient sampling of these variables. Evidence is presented that the 2D receptive-field profiles of simple cells in mammalian visual cortex are well described by members of this optimal 2D filter family, and thus such visual neurons could be said to optimize the general uncertainty relations for joint 2D-spatial–2D-spectral information resolution. The variety of their receptive-field dimensions and orientation and spatial-frequency bandwidths, and the correlations among these, reveal several underlying constraints, particularly in width/length aspect ratio and principal axis organization, suggesting a polar division of labor in occupying the quantal volumes of information hyperspace. Such an ensemble of 2D neural receptive fields in visual cortex could locally embed coarse polar mappings of the orientation–frequency plane piecewise within the global retinotopic mapping of visual space, thus efficiently representing 2D spatial visual information by localized 2D spectral signatures.

Uncertainty relation for resolution in space, spatial frequency, and orientation optimized by two-dimensional visual cortical filters.

http://hopf.cns.nyu.edu/~tony/vns/readings/devalois-albrecht-thorell-1982.pdf

Spatial frequency selectivity of cells in macaque visual cortex

Spatial mapping of monkey V1 cells with pure color and luminance stimuli.

Neurons in the visual cortex of monkeys and cats have been characterized as either (i) bar and edge detectors or (ii) cells selective for certain spatial frequencies. To assess which of these functional descriptions is more accurate, we measured (i) the selectivity and (ii) the responsivity-sensitivity of these neurons to bars of various widths and gratings of various spatial frequencies. All of the cells recorded from were considerably more selective along the dimension of spatial frequency than along the dimension of bar width. Further, most were more responsive and sensitive to the grating of optimal frequency than to the bar of optimal width.

https://science.sciencemag.org/content/sci/207/4426/88.full.pdf

Visual cortical neurons: are bars or gratings the optimal stimuli?

Until the pioneering work of HUBEL and WIESEL (1, 2, 3), visual scientists could do little more than guess about the functions of cells in visual cortex and the manner in which complex patterns were analyzed. Their initial reports, however, established that cells in Area 17 of cat (and also monkey) were quite unresponsive to full-field illumination, requiring more specific patterns to elicit a response. Their receptive field (RF) maps of simple cells showed an elongated excitatory center and inhibitory flanks, or vice versa; or two adjacent excitatory and inhibitory areas. Initially HUBEL and WIESEL (2) reported that there was summation within the excitatory and inhibitory regions and an antagonism between them. As we shall see, such summation, if true, would have implications not at all foreseen at the time, and would lead one, in fact, to a quite different model of what such cells do from the one which they actually proposed.

Cortical cells ; Bar and edge detectors, or spatial frequency filters

If striate cells had the simple bipartite or tripartite receptive fields (RF’s) classically attributed to them, they should be quite broadly tuned for spatial frequency. Most striate-cortex cells, however, are fairly narrowly tuned and would be expected to have more-periodic RF’s. We have examined this question in recordings of the responses of cat and monkey striate-cortex cells to gratings of increasingly large number of cycles, all centered on the cells’ RF’s. Simple cells narrowly tuned for spatial frequency were found to increase their responses with increasing numbers of stimulus cycles beyond the 1½ cycles expected from the classical RF shape. Broadly tuned simple cells were found to have less-periodic RF’s. Whereas narrowly tuned complex cells were also found to respond maximally to many stimulus cycles, other more broadly tuned complex cells did as well (possibly reflecting summation across many broadly tuned simple cells without regard to phase). A suppressive region was often seen just outside the excitatory two-dimensional spatial-frequency region, at off orientations and/or off spatial frequencies and around the whole RF in space. Most striate cells can thus be described as having periodic RF’s in the space domain such that they fire just to patterns whose local spatial-frequency spectra fall within a compact, restricted, roughly circular two-dimensional spatial-frequency region, with an encircling suppressive region in both the space and the frequency domains.

Lisa G. Thorell

Papers

Spatial frequency selectivity of cells in macaque visual cortex

Spatial mapping of monkey V1 cells with pure color and luminance stimuli.

Visual cortical neurons: are bars or gratings the optimal stimuli?

Cortical cells ; Bar and edge detectors, or spatial frequency filters

Periodicity of striate-cortex-cell receptive fields.