Learning State Space Trajectories in Recurrent Neural Networks

  title={Learning State Space Trajectories in Recurrent Neural Networks},
  author={Barak A. Pearlmutter},
  journal={Neural Computation},
Many neural network learning procedures compute gradients of the errors on the output layer of units after they have settled to their final values. We describe a procedure for finding E/wij, where E is an error functional of the temporal trajectory of the states of a continuous recurrent network and wij are the weights of that network. Computing these quantities allows one to perform gradient descent in the weights to minimize E. Simulations in which networks are taught to move through limit… 
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  • Richard Hans Robert Hahnloser
  • Computer Science
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  • 1998
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  • Y. C. Wong, M. Sundareshan
  • Computer Science
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  • 1999
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Recurrent Backpropagation and the Dynamical Approach to Adaptive Neural Computation
  • F. Pineda
  • Computer Science
    Neural Computation
  • 1989
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Learning scheme for recurrent neural network by genetic algorithm
  • T. Fukuda, T. Kohno, T. Shibata
  • Computer Science
    Proceedings of 1993 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS '93)
  • 1993
A new learning scheme for recurrent neural networks using a genetic algorithm is presented and used to determine the interconnection weights and the GA approach is compared with backpropagation through time.
Learning temporal patterns in recurrent neural networks
  • K. Doya
  • Computer Science
    1990 IEEE International Conference on Systems, Man, and Cybernetics Conference Proceedings
  • 1990
General learning algorithms for recurrent neural networks that can be used for both discrete-time and continuous-time models are described. They are based on the notion of the derivatives of mappings


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  • Pineda
  • Computer Science
    Physical review letters
  • 1987
An adaptive neural network with asymmetric connections is introduced that bears a resemblance to the master/slave network of Lapedes and Farber but it is architecturally simpler.
Learning state space trajectories in recurrent neural networks : a preliminary report.
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Analysis of Recurrent Backpropagation
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A Learning Algorithm for Boltzmann Machines
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