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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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Lambda Waves Compared to the Posterior Slow Waves of Youth

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Dr. Rishabh Pathak

Lambda waves and Posterior Slow Waves of Youth (PSWY) are both EEG patterns observed in the occipital region, particularly in children. However, they have distinct characteristics and contexts of occurrence. Here are the key differences between the two:

1. State of Occurrence

    • Lambda Waves: These waves occur exclusively during wakefulness, particularly when the eyes are open and the individual is engaged in visual exploration. They are associated with visual attention and processing.
    • Posterior Slow Waves of Youth: In contrast, PSWY occur primarily when the eyes are closed. They are typically present during wakefulness but are blocked when the eyes are open, making their occurrence dependent on eye closure.

2. Waveform Characteristics

    • Lambda Waves: Lambda waves are characterized by a triangular or sawtooth waveform, with a sharp contour at the apex. They are generally diphasic or sometimes triphasic.
    • Posterior Slow Waves of Youth: PSWY have a different morphology, appearing as slower, more diffuse waves that are not triangular in shape. They are typically broader and less sharply defined than lambda waves.

3. Temporal Patterns

    • Lambda Waves: These waves are often isolated transients that may recur at intervals of 200 to 500 milliseconds. They are not typically seen in trains.
    • Posterior Slow Waves of Youth: PSWY can occur in trains and are more likely to be seen as repetitive patterns, especially when the eyes are closed.

4. Response to Eye Closure

    • Lambda Waves: The presence of lambda waves is blocked when the eyes are closed, as they are dependent on visual stimuli and eye movements. They are absent during sustained eye closure.
    • Posterior Slow Waves of Youth: PSWY are present during eye closure and are specifically associated with this state. They disappear when the eyes are opened, indicating their dependence on the eyes being closed.

5. Clinical Implications

    • Lambda Waves: While generally considered a normal finding in awake individuals, abnormal patterns or asymmetry in lambda waves may indicate underlying neurological issues related to visual processing.
    • Posterior Slow Waves of Youth: PSWY are also considered a normal finding in children, but their presence can vary with age and developmental stages. They are typically seen in younger populations and may decrease in prevalence as children grow older.

Conclusion

In summary, lambda waves and Posterior Slow Waves of Youth are distinct EEG patterns that differ in their state of occurrence, waveform characteristics, temporal patterns, and response to eye closure. Understanding these differences is crucial for accurate interpretation of EEG recordings and for distinguishing between normal and abnormal brain activity in children.

 

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