Can Hebbian Volume Learning Explain Discontinuities in Cortical Maps?

  title={Can Hebbian Volume Learning Explain Discontinuities in Cortical Maps?},
  author={Graeme J. Mitchison and Nicholas V. Swindale},
  journal={Neural Computation},
It has recently been shown that orientation and retinotopic position, both of which are mapped in primary visual cortex, can show correlated jumps (Das & Gilbert, 1997). This is not consistent with maps generated by Kohonen's algorithm (Kohonen, 1982), where changes in mapped variables tend to be anticorrelated. We show that it is possible to obtain correlated jumps by introducing a Hebbian component (Hebb, 1949) into Kohonen's algorithm. This corresponds to a volume learning mechanism where… 

Link between orientation and retinotopic maps in primary visual cortex

It is shown that a mechanism predicts a link between the layout of orientation preferences around singularities of different signs and the cardinal axes of the retinotopic map, and this findings provide additional support for the notion that spatially structured input from the retina may provide a blueprint for the early development of cortical maps and receptive fields.

Multimap formation in visual cortex.

The results support the hypothesis that cortical maps containing a fine mixture of different response types, whether in monkey extrastriate cortex, mouse V1 or elsewhere in the cortex, are a product of a generic cortical developmental scheme designed to map cells with a diversity of response properties across a shared topographic space.

Symmetry Breaking and Pattern Selection in Models of Visual Development

Response properties of neurons in the visual cortex form spatial representations called maps of several stimulus features such as orientation preference (OP) or ocular dominance (OD). This thesis

Influence of lateral connections on the structure of cortical maps.

It is demonstrated that functions that oscillate more than once do not produce maps closely resembling those seen biologically, which strongly suggests that local lateral connections in visual cortex oscillate only once and have the form of a Mexican hat.

Microcircuits in visual cortex

  • K. Martin
  • Biology
    Current Opinion in Neurobiology
  • 2002

Consistent mapping of orientation preference across irregular functional domains in ferret visual cortex

Opt optical imaging of intrinsic signals and electrophysiological techniques are used to investigate the organization of the maps of orientation preference, ocular dominance, and visual space in ferret and show that orientation preference is mapped consistently within both V1 and V2, and across the interareal boundary.

A computational model for the development of multiple maps in primary visual cortex.

It is shown that this model robustly produces combined maps of these four variables that bear a close resemblance to experimental maps, providing strong support for the hypothesis that cortical representations attempt to optimize a trade-off between coverage and continuity.

Coordinated Optimization of Visual Cortical Maps (I) Symmetry-based Analysis

A general dynamical systems approach to the combined optimization of visual cortical maps of OP and another scalar feature such as OD or spatial frequency preference is developed and it is shown that each individual coupling energy leads to a different class of OP solutions with different correlations among the maps.

Analysis of the elastic net model applied to the formation of ocular dominance and orientation columns.

Analysis of the development and structure of orientation (OR) and ocular dominance maps in the primary visual cortex of cats and monkeys using the elastic net algorithm suggests that developmental order can be predicted from the final OR and OD periodicities.

Analysis of the elastic net model applied to the formation of ocular dominance and orientation columns

Analysis of the development and structure of orientation (OR) and ocular dominance maps in the primary visual cortex of cats and monkeys using the elastic net algorithm suggests that developmental order can be predicted from the final OR and OD periodicities.



A dimension reduction framework for understanding cortical maps

It is found that, in a simple case, certain self-organizing models generate maps that are near-optimally local, in the sense that they come close to minimizing the neuronal wiring required for local operations.

Distortions of visuotopic map match orientation singularities in primary visual cortex

It is found that the map of visual space on cat V1 shows strong and systematic local distortions in register with inhomogeneities in the orientation map, with the rate of receptive field movement across cortex being largely proportional to the local rate of change of orientation.

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

It is shown that the observed structure of the topographic map can arise from a principle of continuous mapping, and a mathematical model is used that can be interpreted as an adaptive process changing a set of synaptic weights, or synaptic connection strengths, between two layers of cells.

Synaptic plasticity in rat hippocampal slice cultures: local "Hebbian" conjunction of pre- and postsynaptic stimulation leads to distributed synaptic enhancement.

It is reported here that two recording techniques--optical recording, using voltage-sensitive dyes, and double intracellular recordings--reveal that synaptic enhancement is not restricted to the stimulated cell, and that the synapses of many neighboring postsynaptic cells are enhanced.

Relation Between Retinotopical and Orientation Maps in Visual Cortex

Using a simple cortical model, it is shown that this covariation of discontinuities in maps of orientation preference and local distortions in Maps of visual space reflects collective effects of the lateral cortical feedback.

Spatial Relationships among Three Columnar Systems in Cat Area 17

The spatial relationships between the orientation, ocular dominance, and spatial frequency domains in cat area 17 are investigated using optical imaging of intrinsic signals to obtain high resolution maps for each of these stimulus features from the same cortical regions.

A Type of Duality between Self-Organizing Maps and Minimal Wiring

It is shown here that two interpretations of neural maps are closely related, which sees these maps as forming by an adaptive process in response to stimuli and the minimal wiring or dimension-reduction perspective, which interprets the maps as the solution of a minimization problem.

Application of Kohonen's self–organizing feature map algorithm to cortical maps of orientation and direction preference

  • N. SwindaleH. Bauer
  • Geology
    Proceedings of the Royal Society of London. Series B: Biological Sciences
  • 1998
Cortical maps of orientation preference in cats, ferrets and monkeys contain numerous half–rotation point singularities. Experimental data have shown that direction preference also has a smooth

Orientation selectivity, preference, and continuity in monkey striate cortex

  • Gg Blasdel
  • Biology
    The Journal of neuroscience : the official journal of the Society for Neuroscience
  • 1992
Maps of orientation preference and selectivity, inferred from differential images of orientation (Blasdel, 1992), reveal linear organizations in patches, 0.5-1.0 mm across, where orientation