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Symmetry in reservoir computers (RCs) hinders learning. Introducing a square readout matrix can break symmetry, but specific data symmetries prevent its formation, impacting RC multifunctionality and performance near the edge of chaos.

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Area of Science:

  • Computational neuroscience
  • Nonlinear dynamics
  • Machine learning

Background:

  • Reservoir computers (RCs) are powerful tools for time-series analysis.
  • Symmetry in RC design can limit their learning capabilities.
  • Mirror-attractors, inverted copies of solutions, can arise and interfere with RC performance.

Purpose of the Study:

  • To investigate the impact of data symmetries on the formation of square readout matrices in RCs.
  • To explore the concept of multifunctionality in RCs trained to handle symmetric attractors.
  • To understand the relationship between RC internal connection spectral radius and square readout matrix emergence.

Main Methods:

  • Analytical proof of symmetry constraints on square readout matrix existence.
  • Numerical simulations training RCs to reconstruct coexisting Lorenz attractors and their mirror-attractors.
  • Analysis of RC performance under varying attractor positions and spectral radius values.

Main Results:

  • Certain training data symmetries analytically forbid the existence of the square readout matrix.
  • The square readout matrix emerges numerically when attractor positions are slightly altered, even with overlapping regions.
  • The square readout matrix reappears at large spectral radius values before the edge of chaos is reached.

Conclusions:

  • Data symmetry is a critical factor limiting the effectiveness of square readout matrices in RCs.
  • RC multifunctionality, particularly in handling symmetric attractors, is sensitive to subtle changes in initial conditions.
  • The spectral radius of internal connections plays a significant role in the emergence of the square readout matrix and RC stability.