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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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Vertex Sharp Transients compared to IED

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Dr. Rishabh Pathak

Vertex Sharp Transients (VSTs) and Interictal Epileptiform Discharges (IEDs) are both EEG patterns, but they have distinct characteristics that help differentiate them. 

1.      Morphology:

§  VSTs: Typically exhibit a triphasic waveform, consisting of two small positive waves surrounding a larger negative sharp wave. They may also appear as diphasic or monophasic but are most commonly recognized in their triphasic form.

§  IEDs: Generally have a sharper contour and lower amplitude compared to VSTs. IEDs can take various forms, including spikes and spike-and-wave complexes, and they do not typically exhibit the triphasic morphology seen in VSTs.

2.     Localization:

§  VSTs: Primarily recorded from midline electrodes, especially at the vertex (Cz), and show phase reversal at this location. Their distribution is usually confined to the parasagittal regions.

§  IEDs: More commonly found in central or lateral regions of the scalp and can be parasagittal but are not restricted to the midline. They may also show different localization patterns depending on the type of epilepsy.

3.     Clinical Context:

§  VSTs: Generally considered a normal finding during drowsiness and non-REM sleep. They can occur spontaneously or be evoked by sensory stimuli, particularly auditory stimuli.

§  IEDs: Indicative of underlying epileptic activity and are associated with epilepsy. They are typically observed in awake individuals or during sleep but are not considered normal findings in the same way as VSTs.

4.    Amplitude and Background Activity:

§  VSTs: Can vary in amplitude but typically do not exceed the amplitude of the background activity. They maintain a consistent morphology during a train of transients.

§  IEDs: Often stand out against the background activity due to their sharper contour and can exceed the amplitude of the background. They may also show significant evolution in amplitude and frequency during a run of discharges.

5.     Response to Stimulation:

§  VSTs: May be evoked by sensory stimuli, particularly auditory stimuli, and can reflect a mechanism to maintain sleep after stimulation.

§  IEDs: Do not typically respond to sensory stimuli in the same way and are more indicative of a pathological process rather than a normal physiological response.

In summary, Vertex Sharp Transients are generally benign EEG patterns associated with normal sleep, characterized by their triphasic morphology and midline localization. In contrast, Interictal Epileptiform Discharges are indicative of epilepsy, with sharper contours, different localization, and a clinical context that suggests underlying neurological issues. These differences are crucial for accurate EEG interpretation and diagnosis.

 

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