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Physical effects of learning.

Menachem Stern1, Andrea J Liu1,2, Vijay Balasubramanian1,3,4

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Learning in physical systems, like neural networks, leaves imprints on their structure. These imprints, observable in the system

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Area of Science:

  • Complex systems
  • Physical networks
  • Machine learning

Background:

  • Interacting many-body physical systems exhibit learning capabilities.
  • Learning occurs via evolutionary selection or active learning from experience.

Purpose of the Study:

  • Investigate the structural imprints of learning in linear physical networks.
  • Analyze the effects of weak input signals on system architecture.

Main Methods:

  • Analysis of the Hessian matrix in physical systems.
  • Characterization of system response to weak input signals.

Main Results:

  • Learning decreases the effective physical dimension of input response.
  • Learning increases the susceptibility of physical degrees of freedom.
  • Low-eigenvalue eigenvectors of the Hessian align with learned tasks.

Conclusions:

  • Observed effects characterize learning in physical systems under weak input conditions.
  • These findings suggest methods for identifying trained physical networks.