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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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Cooccurring waves in Breach effects

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Dr. Rishabh Pathak


In the context of breach effects in EEG recordings, several co-occurring waves and patterns may be observed.


1.      Focal Slowing:

o Focal slowing may co-localize with breach effect rhythms, especially when the underlying tissue near the skull defect is abnormal.

o Trauma-induced or surgically produced skull defects may exhibit higher amplitude slowing with a sharp contour within the breach effect region, indicating potential cerebral injury or dysfunction.

2.     Paroxysmal Fast Activity (PFA):

o Paroxysmal fast activity (PFA) may be present alongside breach effects, characterized by bursts of fast activity interspersed with normal rhythms.

o PFA can co-localize with independent focal slowing, suggesting underlying abnormalities or dysfunction in the cerebral tissue near the skull defect.

3.     Epileptiform Discharges:

o  Epileptiform discharges (IEDs) may occur within a region affected by breach effects, potentially related to the cause of the skull defect.

o  Normal brain activity may exhibit spike-like, epileptiform appearances within breach effect regions, requiring careful analysis to differentiate between epileptic spikes and normal rhythms.

4.    Eye Movement Artifact Reduction:

o  In cases where the skull defect is within the frontal bone, the breach effect may reduce ipsilateral eye movement artifact by shunting the eye's electrical field through the defect, affecting the distribution of the artifact across the frontal aspect of the head.

5.     Clinical Significance:

o  While breach effects are not indicative of brain abnormalities and are related to bone abnormalities, the presence of abnormal slowing or low amplitude within breach effect regions may signal cerebral pathology.

o Recognizing and documenting breach effects is crucial for accurate EEG interpretation, as they can prevent misidentification of activity as abnormal by future readers of the EEG.

By understanding the co-occurring waves and patterns associated with breach effects in EEG recordings, clinicians can better interpret and differentiate between postoperative changes near skull defects, abnormal brain activity, and artifacts. Identifying these co-occurring features is essential for accurate diagnosis and management of patients undergoing EEG evaluations in the presence of skull defects or surgical interventions.

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