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Beyond holography: The entropic quantum gravity foundations of anisotropic diffusion
1Queen Mary University of London, School of Mathematical Sciences, London E1 4NS, United Kingdom.
Physical Review. E
|November 18, 2025
Summary
The Gravity from Entropy (GfE) approach reveals the Perona-Malik algorithm as a gradient flow. This connection offers new insights into quantum gravity, image processing, and machine learning foundations.
Area of Science:
- Theoretical Physics
- Artificial Intelligence
- Quantum Gravity
- Information Theory
Background:
- Increasing scientific interest connects theoretical physics and artificial intelligence (AI).
- Traditional focus includes string theory, holography, and image processing.
- The Gravity from Entropy (GfE) approach derives gravity from geometric quantum relative entropy (GQRE).
Purpose of the Study:
- To demonstrate the Perona-Malik algorithm as the gradient flow of the GfE action.
- To explore the implications of GfE action maximization for image processing.
- To establish geometrical and information theory foundations for the Perona-Malik algorithm.
Main Methods:
- Formulation of the Gravity from Entropy (GfE) approach by G. Bianconi.
- Analysis of the Perona-Malik algorithm as a gradient flow of the GfE action.
- Investigation of GfE action maximization between Euclidean metrics associated with images.
Main Results:
- The Perona-Malik algorithm is shown to be the gradient flow of the GfE action in a simplified scenario.
- Maximizing the GfE action preserves complex structures in images, unlike classical entropy maximization.
- This finding provides geometrical and information theory underpinnings for the Perona-Malik algorithm.
Conclusions:
- The GfE approach offers a novel link between quantum gravity and image processing.
- The Perona-Malik algorithm's structure is explained through GfE principles.
- These results may foster deeper connections between GfE, machine learning, and brain research.
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