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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 in Different Neurological Conditions

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Dr. Rishabh Pathak

Mittens, as a specific EEG pattern, have been studied in the context of various neurological conditions, although they are primarily considered normal variants in adults. Here are some insights into their presence and significance in different neurological conditions:

1. Epilepsy

    • Historical Context: In earlier studies, mittens were sometimes misinterpreted as indicators of epileptic activity due to their sharp wave components. However, current understanding emphasizes that mittens are generally benign and should not be confused with interictal epileptiform discharges (IEDs) associated with epilepsy.

2. Thalamic Tumors

    • Previous Associations: Mittens were once thought to be associated with thalamic tumors, reflecting the belief that certain EEG patterns could indicate specific structural brain abnormalities. However, this association has not been consistently supported by modern research.

3. Parkinsonism

    • Historical Beliefs: Similar to thalamic tumors, mittens were previously considered potential markers for parkinsonism. This belief stemmed from early EEG studies that linked specific patterns to movement disorders. However, contemporary research has not substantiated these claims, and mittens are now viewed as normal variants rather than indicators of parkinsonism.

4. Mood Disorders and Psychosis

    • Misinterpretation Risks: Mittens were historically associated with mood disorders and psychosis, leading to concerns about their clinical significance in psychiatric evaluations. However, modern interpretations suggest that these associations may have been due to methodological limitations in earlier studies, and mittens are not currently recognized as markers for these conditions.

5. General Neurological Conditions

    • Recognition of Benign Nature: While mittens may appear in patients with various neurological conditions, their presence is now understood to be more reflective of normal sleep architecture rather than indicative of specific pathologies. This shift in understanding emphasizes the importance of recognizing mittens as benign patterns that do not necessarily correlate with neurological disorders.

Summary

Mittens have been historically linked to several neurological conditions, including epilepsy, thalamic tumors, parkinsonism, mood disorders, and psychosis. However, contemporary research has largely discredited these associations, recognizing mittens as normal EEG variants. Their significance lies in accurate identification to prevent misdiagnosis rather than serving as indicators of specific neurological conditions.

 

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