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A tighter generalization bound for reservoir computing.

Xinyu Han1, Yi Zhao1, Michael Small2

  • 1Harbin Institute of Technology, Shenzhen, 518055 Guangdong, China.

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Summary
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This study introduces a new generalization bound for reservoir computing (RC) using Rademacher complexity. The proposed bound is tighter and explores hyperparameter dependencies, outperforming existing methods.

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Area of Science:

  • Machine Learning
  • Computational Neuroscience
  • Complex Systems

Background:

  • Reservoir computing (RC) shows high performance but its generalization ability on unseen data is not well understood.
  • Existing generalization bounds for RC lack specificity regarding model hyperparameters.

Purpose of the Study:

  • To develop a novel generalization bound for reservoir computing (RC).
  • To analyze the impact of model hyperparameters on RC generalization.
  • To compare generalization bounds for different reservoir graph structures.

Main Methods:

  • Utilizing the probably approximately correct (PAC) learning framework.
  • Deriving a generalization bound based on empirical Rademacher complexity.
  • Analyzing reservoir graphs including directed acyclic graphs (DAGs) and Erdős-Rényi (ER) random graphs.

Main Results:

  • A novel, tighter generalization bound for RC is proposed, dependent on model hyperparameters.
  • The generalization bound for DAG-based RC can be refined using the longest path length.
  • DAG-based RC exhibits a lower and less hyperparameter-sensitive generalization bound compared to ER graph-based RC.

Conclusions:

  • The developed generalization bound provides deeper insights into RC performance.
  • Structural properties of reservoir graphs significantly influence generalization capabilities.
  • DAGs offer superior generalization properties in reservoir computing compared to ER graphs.