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Beyond holography: the entropic quantum gravity foundations of image processing

Created by
  • Haebom

Author

Ginestra Bianconi

Outline

This paper explores the connection between artificial intelligence (AI) and theoretical physics. Specifically, we focus on the Gravity-from-Entropy (GfE) approach, where gravity is derived from the geometric quantum relative entropy (GQRE) of two Lorentzian spacetimes. We show that the well-known Perona-Malik algorithm, used in image processing, is simply a gradient-flow GfE action. Specifically, this algorithm is the result of minimizing GQRE between the image's support and two Euclidean metrics induced by the image. The Perona-Malik algorithm is known to preserve sharp contours, which means that the GfE action does not lead to a uniform image, as would be expected when repeating gradient-flow dynamics. Rather, the result of GQRE minimization is compatible with the preservation of complex structure. These results provide geometric and information-theoretic foundations for the Perona-Malik algorithm and may contribute to building deeper connections between GfE, machine learning, and brain research.

Takeaways, Limitations

Takeaways:
Provides geometric and information-theoretic foundations of the Perona-Malik algorithm.
GfE presents a new link between machine learning and brain research.
It provides a new perspective on the concept of entropy by showing that entropic actions do not always lead to uniform images.
We show that GQRE minimization is compatible with preserving complex structures.
Limitations:
Currently, the GfE approach has only been applied to simple scenarios. Generalization to more complex scenarios is needed.
Further research is needed on the connections between GfE, machine learning, and brain research.
Because it focuses only on specific properties of the Perona-Malik algorithm, its extensibility to other image processing algorithms may be limited.
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