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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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Types of Phantom Spike and Wave

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Dr. Rishabh Pathak

Phantom Spike and Wave (PhSW) can be categorized into different types based on specific features such as amplitude, location, gender of the patient, and the state of wakefulness. The two primary forms of PhSW are often referred to by the acronyms WHAM and FOLD. 

1. WHAM (Waking, High amplitude, Anterior, usually Male)

    • Characteristics:
      • Waking State: This form typically occurs during wakefulness.
      • High Amplitude: The spikes in this pattern are defined as having a high amplitude, generally greater than 45 μV.
      • Anterior Location: The discharges are predominantly recorded from the frontal regions of the scalp.
      • Demographics: More commonly observed in male patients.
    • Clinical Context:
      • WHAM patterns may be associated with various neurological conditions and can indicate significant underlying pathology, particularly in males during awake states.

2. FOLD (Female, Occipital, Low amplitude, Drowsy)

    • Characteristics:
      • Drowsy State: This form is typically observed during drowsiness or light sleep.
      • Low Amplitude: The spikes are of lower amplitude compared to WHAM, often less than 40 μV, making them sometimes difficult to discern.
      • Occipital Location: The discharges are predominantly recorded from the occipital regions of the scalp.
      • Demographics: More commonly seen in female patients.
    • Clinical Context:
      • FOLD patterns are often associated with benign conditions and may be seen in patients with a history of migraines or other non-epileptic phenomena. They are generally considered to have a better prognosis compared to WHAM patterns.

Summary of Differences

Feature

WHAM

FOLD

State

Waking

Drowsy

Amplitude

High amplitude (≥ 45 μV)

Low amplitude (< 40 μV)

Location

Anterior (frontal regions)

Occipital (occipital regions)

Demographics

Usually Male

Usually Female

 

Additional Notes

    • Prevalence: PhSW is relatively uncommon, occurring in about 0.5% to 1% of EEGs, but its occurrence is slightly more likely in females overall.
    • Age Range: The pattern is most likely to occur during adolescence and young adulthood, with a higher occurrence rate in this demographic.

Understanding these types of Phantom Spike and Wave patterns is crucial for clinicians in diagnosing and managing patients with neurological symptoms, as they can provide insights into the underlying conditions and their potential implications.

 

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