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Area of Science:

  • Quantum Many-Body Physics
  • Machine Learning
  • Computational Science

Background:

  • Tensor networks offer efficient high-dimensional tensor representation.
  • Their application in machine learning is a rapidly growing research area.
  • Matrix product states (tensor trains) are a key architecture.

Purpose of the Study:

  • Investigate the trainability of tensor network machine learning models.
  • Analyze the impact of loss functions on training landscapes.
  • Focus on the matrix product states architecture.

Main Methods:

  • Exploration of loss function landscapes.
  • Rigorous mathematical analysis of gradient behavior.
  • Focus on matrix product states (tensor trains).

Main Results:

  • Barren plateaus (vanishing gradients) are proven for global loss functions.
  • Gradients for local loss functions do not vanish with increasing system size.
  • Tensor network models with local loss functions are efficiently trainable.

Conclusions:

  • Loss function choice critically impacts tensor network model trainability.
  • Local loss functions mitigate barren plateau issues.
  • Findings guide future tensor network machine learning research and applications.