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K Obermayer

Publications and source records attributed to K Obermayer.

29 records · Page 2Linked to original sources
PubMed1993

Geometry of orientation and ocular dominance columns in monkey striate cortex.

In addition to showing that ocular dominance is organized in slabs and that orientation preferences are organized in linear sequences likely to reflect slabs, Hubel and Wiesel (1974a) discussed the intriguing possibility that slabs of orientation might intersect slabs of ocular dominance at some consistent angle. Advances in optical imaging now make it possible to test this possibility directly. When maps of orientation are analyzed quantitatively, they appear to arise from a combination of at least two competing themes: one where orientation preferences change linearly along straight axes, remaining constant along perpendicular axes and forming iso-orientation slabs along the way, and one where orientation preferences change continuously along circular axes, remaining constant along radial axes and forming singularities at the centers of the spaces enclosed. When orientation patterns are compared with ocular dominance patterns from the same cortical regions, quantitative measures reveal (1) that singularities tend to lie at the centers of ocular dominance columns, (2) that linear zones (arising where orientation preferences change along straight axes) tend to lie at the edges of ocular dominance columns, and (3) that the short iso-orientation bands within each linear zone tend to intersect the borders of ocular dominance slabs at angles of approximately 90 degrees.

Animals↗
PubMed1992

Self-organizing maps: stationary states, metastability and convergence rate.

We investigate the effect of various types of neighborhood function on the convergence rates and the presence or absence of metastable stationary states of Kohonen's self-organizing feature map algorithm in one dimension. We demonstrate that the time necessary to form a topographic representation of the unit interval [0, 1] may vary over several orders of magnitude depending on the range and also the shape of the neighborhood function, by which the weight changes of the neurons in the neighborhood of the winning neuron are scaled. We will prove that for neighborhood functions which are convex on an interval given by the length of the Kohonen chain there exist no metastable states. For all other neighborhood functions, metastable states are present and may trap the algorithm during the learning process. For the widely-used Gaussian function there exists a threshold for the width above which metastable states cannot exist. Due to the presence or absence of metastable states, convergence time is very sensitive to slight changes in the shape of the neighborhood function. Fastest convergence is achieved using neighborhood functions which are "convex" over a large range around the winner neuron and yet have large differences in value at neighboring neurons.

Algorithms↗
PubMed1992

Self-organizing maps: ordering, convergence properties and energy functions.

We investigate the convergence properties of the self-organizing feature map algorithm for a simple, but very instructive case: the formation of a topographic representation of the unit interval [0, 1] by a linear chain of neurons. We extend the proofs of convergence of Kohonen and of Cottrell and Fort to hold in any case where the neighborhood function, which is used to scale the change in the weight values at each neuron, is a monotonically decreasing function of distance from the winner neuron. We prove that the learning dynamics cannot be described by a gradient descent on a single energy function, but may be described using a set of potential functions, one for each neuron, which are independently minimized following a stochastic gradient descent. We derive the correct potential functions for the one- and multi-dimensional case, and show that the energy functions given by Tolat (1990) are an approximation which is no longer valid in the case of highly disordered maps or steep neighborhood functions.

Algorithms↗
PubMed1990

A principle for the formation of the spatial structure of cortical feature maps.

Orientation-selective cells in the striate cortex of higher animals are organized as a hierarchical topographic map of two stimulus features: (i) position in visual space and (ii) orientation. We show that the observed structure of the topographic map can arise from a principle of continuous mapping. For the realization of this principle we use a mathematical model that can be interpreted as an adaptive process changing a set of synaptic weights, or synaptic connection strengths, between two layers of cells. The patterns of orientation preference and selectivity generated by the model are similar to the patterns seen in the visual cortex of macaque monkey and cat and correspond to a neural projection that maps a more than two-dimensional feature space onto a two-dimensional cortical surface under the constraint that shape and position of the receptive fields of the neurons very smoothly over the cortical surface.

Animals↗
PubMedDate not supplied

Organization of ocular dominance and orientation columns in the striate cortex of neonatal macaque monkeys.

Previous work has shown that small, stimulus-dependent changes in light absorption can be used to monitor cortical activity, and to provide detailed maps of ocular dominance and optimal stimulus orientation in the striate cortex of adult macaque monkeys (Blasdel & Salama, 1986; Ts'o et al., 1990). We now extend this approach to infant animals, in which we find many of the organizational features described previously in adults, including patch-like linear zones, singularities, and fractures (Blasdel, 1992b), in animals as young as 3 1/2 weeks of age. Indeed, the similarities between infant and adult patterns are more compelling than expected. Patterns of ocular dominance and orientation, for example, show many of the correlations described previously in adults, including a tendency for orientation specificity to decrease in the centers of ocular dominance columns, and for iso-orientation contours to cross the borders of ocular dominance columns at angles of 90 deg. In spite of these similarities, there are differences, one of which entails the strength of ocular dominance signals, which appear weaker in the younger animals and which increase steadily with age. Another, more striking, difference concerns the widths of ocular dominance columns, which increase by 20% during the first 3 months of life. Since the cortical surface area increases by a comparable amount, during the same time, this 20% expansion implies that growth occurs anisotropically, perpendicular to the ocular dominance columns, as the cortical surface expands. Since the observed patterns of orientation preference expand more slowly, at approximately half this rate, these results also imply that ocular dominance and orientation patterns change their relationship, and may even drift past one another, as young animals mature.

Aging↗
PubMedDate not supplied

A model for the intracortical origin of orientation preference and tuning in macaque striate cortex.

We report results of numerical simulations for a model of generation of orientation selectivity in macaque striate cortex. In contrast to previous models, where the initial orientation bias is generated by convergent geniculate input to simple cells and subsequently sharpened by lateral circuits, our approach is based on anisotropic intracortical excitatory connections which provide both the initial orientation bias and its subsequent amplification. Our study shows that the emerging response properties are similar to the response properties that are observed experimentally, hence the hypothesis of an intracortical generation of orientation bias is a sensible alternative to the notion of an afferent bias by convergent geniculocortical projection patterns. In contrast to models based on an afferent orientation bias, however, the "intracortical hypothesis" predicts that orientation tuning gradually evolves from an initially nonoriented response and a complete loss of orientation tuning when the recurrent excitation is blocked, but new experiments must be designed to unambiguously decide between both hypotheses.

Animals↗