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Taming hyperparameter tuning in continuous normalizing flows using the JKO scheme.

Alexander Vidal1, Samy Wu Fung2, Luis Tenorio3

  • 1Department of Applied Mathematics and Statistics, Colorado School of Mines, Golden, USA. vidal@mines.edu.

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|March 19, 2023
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Summary
This summary is machine-generated.

JKO-Flow introduces a novel algorithm for continuous normalizing flows (CNFs) that eliminates the need to tune hyperparameters in optimal transport (OT) based methods. This approach simplifies density estimation and data generation in machine learning.

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Area of Science:

  • Machine Learning
  • Data Science
  • Probability Theory

Background:

  • Normalizing flows (NF) are crucial for data generation and density estimation.
  • Continuous normalizing flows (CNFs) use neural ODEs for tractable Jacobian determinant computation.
  • Optimal transport (OT) aids CNFs but requires hyperparameter tuning.

Purpose of the Study:

  • To present JKO-Flow, an algorithm for OT-based CNFs that removes the need for hyperparameter tuning.
  • To integrate OT CNF with the JKO scheme for a more efficient solution.
  • To offer a "divide and conquer" approach for solving complex optimization problems.

Main Methods:

  • Developed JKO-Flow by integrating OT CNF with the Wasserstein gradient flow (JKO scheme).
  • Replaced hyperparameter tuning with repeated optimization problem solutions for fixed time-steps.
  • Employed a "divide and conquer" strategy by solving simpler, sequential problems.

Main Results:

  • Successfully eliminated the need for tuning the OT penalty hyperparameter ([Formula: see text]).
  • Demonstrated an effective "divide and conquer" approach for solving OT-based CNFs.
  • Provided a more tractable method for density estimation and data generation using CNFs.

Conclusions:

  • JKO-Flow offers a significant advancement in OT-based CNF methods by removing critical hyperparameter tuning.
  • The algorithm simplifies the application of CNFs in machine learning and data science.
  • This work paves the way for more accessible and efficient density estimation techniques.