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Equilibrium propagation for learning in Lagrangian dynamical systems.

Serge Massar1

  • 1Université Libre de Bruxelles, Laboratoire d'Information Quantique CP224, (ULB), Av. F. D. Roosevelt 50, 1050 Bruxelles, Belgium.

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Summary

We introduce a novel training method for dynamical systems using equilibrium propagation and action extremization. This approach efficiently updates parameters for systems with fixed or periodic boundary conditions, avoiding complex backpropagation.

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Area of Science:

  • Computational physics
  • Machine learning
  • Dynamical systems

Background:

  • Equilibrium propagation (EP) is effective for training energy-based models.
  • Training dynamical systems often requires computationally intensive backpropagation through time.
  • Lagrangian mechanics provides a framework for describing system dynamics.

Purpose of the Study:

  • To develop a novel training method for dynamical systems governed by Lagrangian mechanics.
  • To extend equilibrium propagation to dynamical trajectories.
  • To enable efficient parameter updates without explicit backpropagation.

Main Methods:

  • Leveraging the principle of action extremization to adapt equilibrium propagation.
  • Nudging trajectories towards targets and measuring conjugate variable responses.
  • Applying the method to systems with periodic boundary conditions and fixed initial/final states.

Main Results:

  • The proposed method facilitates efficient parameter updates for Lagrangian dynamical systems.
  • For periodic boundary conditions, it recovers the semiclassical limit of quantum equilibrium propagation.
  • The approach is suitable for systems with dissipation.

Conclusions:

  • This work presents an efficient and broadly applicable training method for dynamical systems.
  • The technique offers an alternative to traditional backpropagation for specific system types.
  • It bridges concepts from Lagrangian mechanics, equilibrium propagation, and quantum mechanics.