Population Computation of Vectorial Transformations

Many neurons of the central nervous system are broadly tuned to some sensory or motor variables. This property allows one to assign to each neuron a preferred attribute (PA). The width of tuning curves and the distribution of PAs in a population of neurons tuned to a given variable define the collective behavior of the population. In this article, we study the relationship of the nature of the tuning curves, the distribution of PAs, and computational properties of linear neuronal populations. We show that noise-resistant distributed linear algebraic processing and learning can be implemented by a population of cosine tuned neurons assuming a nonuniform but regular distribution of PAs. We extend these results analytically to the noncosine tuning and uniform distribution case and show with a numerical simulation that the results remain valid for a nonuniform regular distribution of PAs for broad noncosine tuning curves. These observations provide a theoretical basis for modeling general nonlinear sensorimotor transformations as sets of local linearized representations.

[1]  L. M. Schmid,et al.  Magnification factors, receptive field images and point-image size in the superior colliculus of flying foxes: comparison with the primary visual cortex , 2004, Experimental Brain Research.

[2]  Stephen Grossberg,et al.  Neural dynamics of adaptive sensory-motor control , 1986 .

[3]  Gordon M. Redding,et al.  Adaptive Spatial Alignment , 1997 .

[4]  Paul B. Johnson,et al.  Visuomotor transformations underlying arm movements toward visual targets: a neural network model of cerebral cortical operations , 1992, The Journal of neuroscience : the official journal of the Society for Neuroscience.

[5]  Herman P. Snippe,et al.  Parameter Extraction from Population Codes: A Critical Assessment , 1996, Neural Computation.

[6]  Kanti V. Mardia,et al.  Statistics of Directional Data , 1972 .

[7]  H B Barlow,et al.  Direction-Selective Units in Rabbit Retina: Distribution of Preferred Directions , 1967, Science.

[8]  Terence D Sanger,et al.  Neural population codes , 2003, Current Opinion in Neurobiology.

[9]  J. V. Gisbergen,et al.  Collicular ensemble coding of saccades based on vector summation , 1987, Neuroscience.

[10]  Kurt Hornik,et al.  Learning in linear neural networks: a survey , 1995, IEEE Trans. Neural Networks.

[11]  TJ Gawne,et al.  How independent are the messages carried by adjacent inferior temporal cortical neurons? , 1993, The Journal of neuroscience : the official journal of the Society for Neuroscience.

[12]  B L McNaughton,et al.  Interpreting neuronal population activity by reconstruction: unified framework with application to hippocampal place cells. , 1998, Journal of neurophysiology.

[13]  B. Frost,et al.  Common reference frame for neural coding of translational and rotational optic flow , 1998, Nature.

[14]  Peter Dayan,et al.  The Effect of Correlated Variability on the Accuracy of a Population Code , 1999, Neural Computation.

[15]  Emmanuel Guigon,et al.  Computing with Populations of Monotonically Tuned Neurons , 2003, Neural Computation.

[16]  Terence D. Sanger,et al.  Theoretical Considerations for the Analysis of Population Coding in Motor Cortex , 1994, Neural Computation.

[17]  J. Kalaska,et al.  Proprioceptive activity in primate primary somatosensory cortex during active arm reaching movements. , 1994, Journal of neurophysiology.

[18]  W T Newsome,et al.  How Is a Sensory Map Read Out? Effects of Microstimulation in Visual Area MT on Saccades and Smooth Pursuit Eye Movements , 1997, The Journal of Neuroscience.

[19]  R. Wurtz,et al.  Responses of MT and MST neurons to one and two moving objects in the receptive field. , 1997, Journal of neurophysiology.

[20]  C. Koch,et al.  Recurrent excitation in neocortical circuits , 1995, Science.

[21]  A. P. Georgopoulos,et al.  Primate motor cortex and free arm movements to visual targets in three- dimensional space. III. Positional gradients and population coding of movement direction from various movement origins , 1988, The Journal of neuroscience : the official journal of the Society for Neuroscience.

[22]  C D Salzman,et al.  Neural mechanisms for forming a perceptual decision. , 1994, Science.

[23]  D. Hubel,et al.  Receptive fields, binocular interaction and functional architecture in the cat's visual cortex , 1962, The Journal of physiology.

[24]  S. Grossberg,et al.  A Self-Organizing Neural Model of Motor Equivalent Reaching and Tool Use by a Multijoint Arm , 1993, Journal of Cognitive Neuroscience.

[25]  Audra E. Kosh,et al.  Linear Algebra and its Applications , 1992 .

[26]  O. Braddick,et al.  Integration across Directions in Dynamic Random Dot Displays: Vector Summation or Winner Take All? , 1996, Vision Research.

[27]  A. P. Georgopoulos,et al.  Primate motor cortex and free arm movements to visual targets in three- dimensional space. I. Relations between single cell discharge and direction of movement , 1988, The Journal of neuroscience : the official journal of the Society for Neuroscience.

[28]  Geoffrey E. Hinton,et al.  Parallel computations for controlling an arm. , 1984, Journal of motor behavior.

[29]  Geoffrey E. Hinton,et al.  Learning Population Codes by Minimizing Description Length , 1993, Neural Computation.

[30]  Hank S. Wan,et al.  The Sinusoidal Array: A Theory of Representation for Spatial Vectors , 1994 .

[31]  F. Lacquaniti,et al.  Representing spatial information for limb movement: role of area 5 in the monkey. , 1995, Cerebral cortex.

[32]  P. Morasso,et al.  Kinematic networks , 1988, Biological Cybernetics.

[33]  J Porrill,et al.  Kinematic coordination of reach and balance. , 1998, Journal of motor behavior.

[34]  Ehud Zohary,et al.  Correlated neuronal discharge rate and its implications for psychophysical performance , 1994, Nature.

[35]  F. Lacquaniti,et al.  Early coding of reaching in the parietooccipital cortex. , 2000, Journal of neurophysiology.

[36]  Stan C. A. M. Gielen,et al.  The Population Vector, an unbiased estimator for non-uniformly distributed neural maps , 1997, Neural Networks.

[37]  A. P. Georgopoulos,et al.  Neuronal population coding of movement direction. , 1986, Science.

[38]  J F Soechting,et al.  Moving in three-dimensional space: frames of reference, vectors, and coordinate systems. , 1992, Annual review of neuroscience.

[39]  R Caminiti,et al.  Making arm movements within different parts of space: the premotor and motor cortical representation of a coordinate system for reaching to visual targets , 1991, The Journal of neuroscience : the official journal of the Society for Neuroscience.

[40]  M Kuperstein,et al.  Neural model of adaptive hand-eye coordination for single postures. , 1988, Science.

[41]  Geoffrey E. Hinton,et al.  How neural networks learn from experience. , 1992, Scientific American.

[42]  F. Mussa-Ivaldi,et al.  Do neurons in the motor cortex encode movement direction? An alternative hypothesis , 1988, Neuroscience Letters.

[43]  H Sompolinsky,et al.  Simple models for reading neuronal population codes. , 1993, Proceedings of the National Academy of Sciences of the United States of America.

[44]  L F Abbott,et al.  Transfer of coded information from sensory to motor networks , 1995, The Journal of neuroscience : the official journal of the Society for Neuroscience.

[45]  Emilio Salinas,et al.  Vector reconstruction from firing rates , 1994, Journal of Computational Neuroscience.

[46]  M. Paradiso,et al.  A theory for the use of visual orientation information which exploits the columnar structure of striate cortex , 2004, Biological Cybernetics.

[47]  J. Kalaska,et al.  Tactile activity in primate primary somatosensory cortex during active arm movements: correlation with receptive field properties. , 1994, Journal of neurophysiology.

[48]  David S. Touretzky,et al.  Neural Representation of Space Using Sinusoidal Arrays , 1993, Neural Computation.

[49]  Tharam S. Dillon,et al.  Exponential stability and oscillation of Hopfield graded response neural network , 1994, IEEE Trans. Neural Networks.

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

[51]  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.

[52]  David S. Touretzky,et al.  The reaching task: evidence for vector arithmetic in the motor system? , 1994, Biological Cybernetics.

[53]  S G Lisberger,et al.  Vector Averaging for Smooth Pursuit Eye Movements Initiated by Two Moving Targets in Monkeys , 1997, The Journal of Neuroscience.

[54]  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.

[55]  A. Georgopoulos.  On the translation of directional motor cortical commands to activation of muscles via spinal interneuronal systems. , 1996, Brain research. Cognitive brain research.

[56]  P. Germain,et al.  Computational properties and auto-organization of a population of cortical neurons , 1996, Proceedings of International Conference on Neural Networks (ICNN'96).

[57]  Emmanuel Guigon,et al.  Where Does the Population Vector of Motor Cortical Cells Point during Reaching Movements? , 1998, NIPS.