Computational Differences between Asymmetrical and Symmetrical Networks

Symmetrically connected recurrent networks have recently been used as models of a host of neural computations. However, biological neural networks have asymmetrical connections, at the very least because of the separation between excitatory and inhibitory neurons in the brain. We study characteristic differences between asymmetrical networks and their symmetrical counterparts in cases for which they act as selective amplifiers for particular classes of input patterns. We show that the dramatically different dynamical behaviours to which they have access, often make the asymmetrical networks computationally superior. We illustrate our results in networks that selectively amplify oriented bars and smooth contours in visual inputs.

[1]  Vision Research , 1961, Nature.

[2]  J. Cowan,et al.  Excitatory and inhibitory interactions in localized populations of model neurons. , 1972, Biophysical journal.

[3]  H. Kalmus.  Biological Cybernetics , 1972, Nature.

[4]  J. Cowan,et al.  Temporal oscillations in neuronal nets , 1979, Journal of mathematical biology.

[5]  J. Cowan.  Spontaneous symmetry breaking in large scale nervous activity , 1982 .

[6]  J J Hopfield,et al.  Neural networks and physical systems with emergent collective computational abilities. , 1982, Proceedings of the National Academy of Sciences of the United States of America.

[7]  Stephen Grossberg,et al.  Absolute stability of global pattern formation and parallel memory storage by competitive neural networks , 1983, IEEE Transactions on Systems, Man, and Cybernetics.

[8]  J J Hopfield,et al.  Neurons with graded response have collective computational properties like those of two-state neurons. , 1984, Proceedings of the National Academy of Sciences of the United States of America.

[9]  Ennio Mingolla,et al.  Neural dynamics of perceptual grouping: Textures, boundaries, and emergent segmentations , 1985 .

[10]  Stephen Grossberg,et al.  Nonlinear neural networks: Principles, mechanisms, and architectures , 1988, Neural Networks.

[11]  Christoph von der Malsburg,et al.  Pattern recognition by labeled graph matching , 1988, Neural Networks.

[12]  Toshiaki Sakaguchi,et al.  Redundant coding for fault tolerant computing on Hopfield network , 1988, Neural Networks.

[13]  M. V. Rossum,et al.  In Neural Computation , 2022 .

[14]  Steven W. Zucker,et al.  Two Stages of Curve Detection Suggest Two Styles of Visual Computation , 1989, Neural Computation.

[15]  W. Singer,et al.  Oscillatory responses in cat visual cortex exhibit inter-columnar synchronization which reflects global stimulus properties , 1989, Nature.

[16]  H Sompolinsky,et al.  Global processing of visual stimuli in a neural network of coupled oscillators. , 1990, Proceedings of the National Academy of Sciences of the United States of America.

[17]  Peter König,et al.  Stimulus-Dependent Assembly Formation of Oscillatory Responses: I. Synchronization , 1991, Neural Computation.

[18]  G Tononi,et al.  Modeling perceptual grouping and figure-ground segregation by means of active reentrant connections. , 1991, Proceedings of the National Academy of Sciences of the United States of America.

[19]  Peter König,et al.  Stimulus-Dependent Assembly Formation of Oscillatory Responses: II. Desynchronization , 1991, Neural Computation.

[20]  D. V. van Essen,et al.  Neuronal responses to static texture patterns in area V1 of the alert macaque monkey. , 1992, Journal of neurophysiology.

[21]  Peter König,et al.  Stimulus-Dependent Assembly Formation of Oscillatory Responses: III. Learning , 1992, Neural Computation.

[22]  T. Sejnowski,et al.  A model for 8-10 Hz spindling in interconnected thalamic relay and reticularis neurons. , 1993, Biophysical journal.

[23]  T. Sejnowski,et al.  Thalamocortical oscillations in the sleeping and aroused brain. , 1993, Science.

[24]  Zhaoping Li,et al.  Modeling the Sensory Computations of the Olfactory Bulb , 1994 .

[25]  Christof Koch,et al.  Perceptual contour completion A model based on local, anisotropic, fast-adapting interactions between oriented filters , 1994 .

[26]  Christoph von der Malsburg,et al.  The Correlation Theory of Brain Function , 1994 .

[27]  D. Signorini,et al.  Neural networks , 1995, The Lancet.

[28]  H. Sompolinsky,et al.  Theory of orientation tuning in visual cortex. , 1995, Proceedings of the National Academy of Sciences of the United States of America.

[29]  C. Koch,et al.  Modeling direction selectivity of simple cells in striate visual cortex within the framework of the canonical microcircuit , 1995, The Journal of neuroscience : the official journal of the Society for Neuroscience.

[30]  C. Gilbert,et al.  Improvement in visual sensitivity by changes in local context: Parallel studies in human observers and in V1 of alert monkeys , 1995, Neuron.

[31]  L. Abbott,et al.  A model of multiplicative neural responses in parietal cortex. , 1996, Proceedings of the National Academy of Sciences of the United States of America.

[32]  J. Rinzel,et al.  Propagation of spindle waves in a thalamic slice model. , 1996, Journal of neurophysiology.

[33]  P. Katz.  Neurons, Networks, and Motor Behavior , 1996, Neuron.

[34]  Alexander Dimitrov,et al.  Visual Cortex Circuitry and Orientation Tuning , 1996, NIPS.

[35]  K. Zhang,et al.  Representation of spatial orientation by the intrinsic dynamics of the head-direction cell ensemble: a theory , 1996, The Journal of neuroscience : the official journal of the Society for Neuroscience.

[36]  H S Seung,et al.  How the brain keeps the eyes still. , 1996, Proceedings of the National Academy of Sciences of the United States of America.

[37]  M. Carandini,et al.  Predictions of a recurrent model of orientation selectivity , 1997, Vision Research.

[38]  Jeffrey C. Lagarias,et al.  Minimax and Hamiltonian Dynamics of Excitatory-Inhibitory Networks , 1997, NIPS.

[39]  E. Bullmore,et al.  Society for Neuroscience Abstracts , 1997 .

[40]  B L McNaughton,et al.  Path Integration and Cognitive Mapping in a Continuous Attractor Neural Network Model , 1997, The Journal of Neuroscience.

[41]  Peter E. Latham,et al.  Statistically Efficient Estimation Using Population Coding , 1998, Neural Computation.

[42]  Zhaoping Li.  Primary cortical dynamics for visual grouping , 1998 .

[43]  K. M. Wong.  Primary Cortical Dynamics for Visual Grouping , 1998 .

[44]  Zhaoping Li,et al.  A Neural Model of Contour Integration in the Primary Visual Cortex , 1998, Neural Computation.

[45]  A. Rosenfeld,et al.  IEEE TRANSACTIONS ON SYSTEMS , MAN , AND CYBERNETICS , 2022 .