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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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Breach Effect with Abnormal Slowing

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Dr. Rishabh Pathak


In the context of breach effects in EEG recordings accompanied by abnormal slowing, several key observations and implications can be noted.

Description:

o Breach effects with abnormal slowing may manifest as localized changes in brain activity near a skull defect or craniotomy site, characterized by increased amplitude and altered frequencies.

o  Abnormal slowing refers to a pattern of reduced frequency activity that may indicate underlying cerebral dysfunction or injury in the vicinity of the breach effect.

2.     Spatial Distribution:

o Broad left-sided slowing may be present in EEG recordings with breach effects, particularly in regions adjacent to the skull defect or surgical site.

o  The asymmetry of slowing and the distribution of abnormal activity can provide insights into the specific brain regions affected by the breach effect and potential underlying pathologies.

3.     Frequency Characteristics:

o Predominantly anterior left-sided increase in beta activity may co-occur with abnormal slowing in breach effect regions, reflecting alterations in cortical excitability or functional changes near the breach site.

o  The presence of abnormal slowing alongside breach effects suggests a complex interplay between postoperative changes, cerebral injuries, and cortical dysfunction in the affected brain regions.

4.    Clinical Correlation:

o  Breach effects with abnormal slowing may be associated with prior neurosurgical procedures, such as craniotomies performed to address vascular abnormalities like aneurysms.

o  MRI findings demonstrating regions of ischemic injury across the left hemisphere in patients with breach effects and abnormal slowing further support the clinical relevance of these EEG patterns.

5.     Interpretation Challenges:

o Identifying breach effects with abnormal slowing requires careful analysis of EEG waveforms, frequency distributions, and spatial patterns to differentiate postoperative changes from pathological abnormalities.

o Clinicians interpreting EEG recordings with breach effects and abnormal slowing should consider the clinical history, imaging findings, and the specific characteristics of the EEG patterns to make accurate diagnostic assessments.

By recognizing breach effects in EEG recordings accompanied by abnormal slowing, healthcare providers can better understand the complex interplay between postoperative changes, cerebral injuries, and cortical dysfunction in patients with skull defects or prior neurosurgical interventions. This understanding is essential for accurate interpretation, diagnosis, and management of patients undergoing EEG evaluations in the presence of breach effects and associated abnormalities.

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