Analog Computation via Neural Networks

@article{Siegelmann1994AnalogCV,
  title={Analog Computation via Neural Networks},
  author={H. Siegelmann and Eduardo Sontag},
  journal={Theor. Comput. Sci.},
  year={1994},
  volume={131},
  pages={331-360}
}
  • H. Siegelmann, Eduardo Sontag
  • Published 1994
  • Computer Science
  • Theor. Comput. Sci.
  • Abstract We pursue a particular approach to analog computation, based on dynamical systems of the type used in neural networks research. Our systems have a fixed structure, invariant in time, corresponding to an unchanging number of “neurons”. If allowed exponential time for computation, they turn out to have unbounded power. However, under polynomial-time constraints there are limits on their capabilities, though being more powerful than Turing machines. (A similar but more restricted model… CONTINUE READING
    365 Citations
    Stochastic Analog Networks and Computational Complexity
    • 14
    • PDF
    The Simple Dynamics of Super Turing Theories
    • 36
    • PDF
    On the Computational Power of Neural Nets
    • 769
    Neural and Super-Turing Computing
    • 51
    • PDF
    Discontinuities in Recurrent Neural Networks
    • 17
    • PDF
    Computational capabilities of recurrent neural networks based on their attractor dynamics
    • 9
    Analog neuron hierarchy
    • J. Síma
    • Computer Science, Medicine
    • Neural Networks
    • 2020
    • 6
    • PDF
    Subrecursive neural networks
    • J. Síma
    • Mathematics, Medicine
    • Neural Networks
    • 2019
    • 5
    • PDF
    Three Analog Neurons Are Turing Universal
    • 3
    • PDF

    References

    SHOWING 1-10 OF 37 REFERENCES
    On the computational power of neural nets
    • 53
    • PDF
    On the Computational Power of Neural Nets
    • 769
    On the power of sigmoid neural networks
    • 26
    • PDF
    A Computationally Universal Field Computer That is Purely Linear
    • 17
    The complexity of analog computation
    • 150
    • PDF
    Competitive neural architecture for hardware solution to the assignment problem
    • 71
    On connectionist models
    • 50
    Complexity in Electronic Switching Circuits
    • D. Muller
    • Mathematics, Computer Science
    • IRE Trans. Electron. Comput.
    • 1956
    • 91