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Energy Manifold Natural Gradient Descent: From Riemannian Optimization to Modern Neuroscience, NeuroAI and Quantum Physics

Dr. Rishabh Pathak
When Geometry, Energy, Artificial Intelligence and Neuroscience Converge Modern Artificial Intelligence is rapidly moving beyond the idea that learning simply means minimizing an error function. Increasingly, researchers are asking a deeper question: what is the structure of the space in which learning takes place? This question becomes particularly important when the system being modelled is constrained, nonlinear, dynamic, or governed by physical principles. A recent work titled “Energy Manifold Natural Gradient Descent: Riemannian Optimization for Neural PDE Solvers” , by Zhangyong Liang and Huanhuan Gao, introduces Energy Manifold Natural Gradient Descent (EMNGD) , a mathematical framework that extends energy-based natural-gradient optimization from unconstrained Euclidean parameter spaces to constrained Riemannian parameter manifolds . At its core, the framework proposes a simple but powerful principle: An optimization algorithm should not only determine how to reduce error; it sh...
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Mittens compared to K Complexes

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Dr. Rishabh Pathak

When comparing mittens to K complexes in EEG recordings, several distinguishing features can be highlighted as:

1. Waveform Composition

    • Polarity:
      • Mittens: Both components (the sharp wave and the slow wave) have the same polarity.
      • K Complexes: Composed of two sharp waves of opposite polarity.

2. Shape and Duration

    • Duration:
      • Mittens: The sharp wave in a mitten typically has a longer duration (about 400 to 500 milliseconds) and a less sharp contour compared to the sharp wave in K complexes.
      • K Complexes: The sharp waves in K complexes are usually shorter and have a more defined, sharper contour.

3. Temporal Relationship

    • Inconsistency:
      • Mittens: The temporal relationship between the sharp wave and the slow wave is inconsistent, meaning that the timing can vary from one occurrence to another.
      • K Complexes: The two components of K complexes have a relatively fixed temporal relationship, with the sharp waves occurring at a consistent distance from the peak of the slow wave.

4. Location

    • Positioning:
      • Mittens: Typically centered in the frontal-central midline regions, with possible extension into the parasagittal regions.
      • K Complexes: Generally found at the vertex of the scalp.

5. Associated Features

    • Accompanying EEG Patterns:
      • Mittens: Often occur alongside other features of NREM sleep, such as sleep spindles and positive occipital sharp transients of sleep (POSTS).
      • K Complexes: Also associated with NREM sleep but are distinct in their morphology and the nature of their accompanying features.

Summary

Mittens and K complexes can be differentiated based on their waveform composition, duration, temporal relationships, localization, and associated EEG features. Understanding these differences is crucial for accurate EEG interpretation and for distinguishing between normal variants and potential pathological findings.

 

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