Symplectic Bregman Divergences

publication Evidence: moderate

Author Information

Author(s): Frank Nielsen

Primary Institution: Sony Computer Science Laboratories Inc.

Hypothesis

This paper introduces a generalization of Bregman divergences in finite-dimensional symplectic vector spaces.

Conclusion

The study presents symplectic Bregman divergences and discusses their potential applications in various fields including geometric mechanics and machine learning.

Supporting Evidence

Symplectic Bregman divergences are derived from a symplectic generalization of the Fenchel–Young inequality.
The study shows that symplectic Bregman divergences can recover ordinary Bregman divergences under certain conditions.
Potential applications of symplectic divergences in geometric mechanics and machine learning are discussed.

Takeaway

This paper talks about a new way to measure differences between things using a special math tool called symplectic Bregman divergences, which can help in areas like physics and computer learning.

Methodology

The paper defines symplectic Bregman divergences and explores their properties and applications.

Digital Object Identifier (DOI)

10.3390/e26121101

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