A learned neural network that simulates properties of the neuronal population vector

This paper considers steady-state and timedependent characteristics of the response of the hidden-layer neurons in a dynamic model for the neural network trained through supervised learning to perform transformation of input signals into output signals. This transformation is set up so as to correspond to variation in the directions of two-dimensional vectors and is treated as creation by the network of a “movement” direction in response to a “stimulus” direction. The input vector is encoded in the state of the input layer at the initial instant of time, and the output vector in the state of the output layer at great values of time. After the network has been trained on examples of the input-output relation, the hidden neurons turn out to be broadly tuned to direction. The corresponding dependence for their activity is approximated with a smooth function, whose maximum allows some preferred direction to be attributed to each neuron. If each hidden neuron is assigned a vector pointing in its preferred direction, then any arbitrarily chosen direction can be characterized by an imaginary neuronal population vector (Georgopoulos et al. 1986) defined as the sum of the vectors of preferred direction for the neurons, with the weights equal to their activities for the chosen direction. It is demonstrated that, although hidden neurons are broadly tuned to direction, the population vector points in a direction congruent with that of the input vector at the initial moment of time and accurately predicts the direction of the output vector at great values of time. In between, the population vector turns continuously from the one direction towards the other. The dynamic and stationary properties of the population vector of the hidden-layer neurons, as obtained within the framework of the model in question, show a close similarity to the experimentally observed (Georgopoulos et al. 1986; Georgopoulos et al. 1989) behaviour of the population vector constructed in the same manner on the ensemble of motor cortex neurons sensitive to a certain type of movement.

[1]  E. Bizzi,et al.  A neural network model for limb trajectory formation , 1989, Biological Cybernetics.

[2]  J A Kelso,et al.  Dynamic pattern generation in behavioral and neural systems. , 1988, Science.

[3]  B. Amirikian,et al.  On the ability of neural networks to perform generalization by induction , 1989, Biological Cybernetics.

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

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

[6]  T. Sejnowski,et al.  Perspectives on cognitive neuroscience. , 1988, Science.

[7]  C. D. Gelatt,et al.  Optimization by Simulated Annealing , 1983, Science.

[8]  James L. McClelland,et al.  Parallel distributed processing: explorations in the microstructure of cognition, vol. 1: foundations , 1986 .

[9]  J. T. Massey,et al.  Mental rotation of the neuronal population vector. , 1989, Science.

[10]  Terrence J. Sejnowski,et al.  Network model of shape-from-shading: neural function arises from both receptive and projective fields , 1988, Nature.

[11]  Arthur Prochazka,et al.  Methods for neuronal recording in conscious animals , 1984 .

[12]  P. Carnevali,et al.  Exhaustive Thermodynamical Analysis of Boolean Learning Networks , 1987 .

[13]  S G Lisberger,et al.  The neural basis for learning of simple motor skills. , 1988, Science.

[14]  J. Hopfield,et al.  Computing with neural circuits: a model. , 1986, Science.

[15]  G. Josin.  Neural-space generalization of a topological transformation , 2004, Biological Cybernetics.

[16]  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.

[17]  S Dehaene,et al.  Neural networks that learn temporal sequences by selection. , 1987, Proceedings of the National Academy of Sciences of the United States of America.

[18]  M. Virasoro,et al.  Perceptron beyond the limit of capacity , 1989 .

[19]  R. Desimone,et al.  Behavioral neurophysiology: insights into seeing and grasping. , 1988, Science.

[20]  Klaus Schulten,et al.  Topology-conserving maps for learning visuo-motor-coordination , 1989, Neural Networks.

[21]  W. Kristan,et al.  Function of identified interneurons in the leech elucidated using neural networks trained by back-propagation , 1989, Nature.

[22]  Richard A. Andersen,et al.  A back-propagation programmed network that simulates response properties of a subset of posterior parietal neurons , 1988, Nature.