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Related Experiment Videos

Discontinuities in recurrent neural networks.

R Gavaldá1, H T Siegelmann

  • 1Department of Software, Universitat Politècnica de Catalunya, Barcelona, SPAIN.

Neural Computation
|March 23, 1999
PubMed
Summary

Arithmetic networks, enhanced analog recurrent neural networks (ARNNs), can compute complex recursive functions. Adding discontinuous functions allows them to solve PSPACE-complete problems in polynomial time.

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Area of Science:

  • Computational theory
  • Artificial intelligence
  • Neural networks

Background:

  • Classical analog recurrent neural networks (ARNNs) use polynomial net functions and continuous activation functions.
  • The computational power of ARNNs is limited by precision requirements linear to computation time.

Purpose of the Study:

  • To investigate the computational power of discontinuous real computational models based on ARNNs.
  • To introduce and analyze arithmetic networks, an extension of ARNNs.
  • To compare the capabilities of arithmetic networks with existing computational models.

Main Methods:

  • Augmenting ARNNs with discontinuous neurons (e.g., threshold, zero test) to create arithmetic networks.
  • Analyzing computational complexity with polynomial time computable real weights.
  • Comparing arithmetic networks to the Blum-Shub-Smale model.
  • Investigating the impact of adding periodic functions.

Main Results:

  • Arithmetic networks with polynomial time computable real weights can compute arbitrarily complex recursive functions.
  • These networks are equivalent to the Blum-Shub-Smale model with bounded registers.
  • Arithmetic networks with rational weights require exponential precision for simulation.
  • Arithmetic networks with real weights do not have fixed precision bounds, unlike ARNNs.
  • Incorporating periodic functions makes these networks computationally equivalent to massively parallel machines.

Conclusions:

  • Arithmetic networks possess significantly greater computational power than classical ARNNs.
  • Discontinuous networks can solve PSPACE-complete problems efficiently.
  • These findings have implications for understanding the limits of computation in neural networks.

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