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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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Environmental Artifacts Compared to Periodic Epileptiform Discharges

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Dr. Rishabh Pathak

Environmental artifacts and Periodic Epileptiform Discharges (PEDs) in EEG recordings can share some similarities but also have distinguishing features that help differentiate between them. Here are the key points of comparison between environmental artifacts and PEDs based on the provided document:

1.     Environmental Artifacts:

o Description: Environmental artifacts are typically caused by external factors such as electrical devices or mechanical sources.

o    Characteristics:

§Recurrence: Often have a regular interval and may appear rhythmic in nature.

§Waveform: Rarely exhibit the diphasic or triphasic morphology seen in PEDs.

§Distribution: Electrodes involved in environmental artifacts may not be adjacent to each other.

§Generalized Occurrence: Environmental artifacts may have a fully generalized distribution, which is uncommon for PEDs.

2.   Periodic Epileptiform Discharges (PEDs):

oDescription: PEDs are characterized by recurrent epileptiform discharges seen in patients with epilepsy or other neurological conditions.

o    Characteristics:

§Waveform: Typically exhibit diphasic or triphasic morphology.

§Regularity: The intervals between PEDs may vary but are usually not as regular as environmental artifacts.

§Bilateral Synchrony: PEDs are often bilaterally synchronous, but not necessarily in all cases.

§Field Distribution: PEDs may have large, bifrontal fields compared to the more localized distribution of environmental artifacts.

3.   Differentiation:

o Waveform Morphology: The presence of diphasic or triphasic waveforms is more indicative of PEDs than environmental artifacts.

o Interval Regularity: PEDs may have fewer regular intervals between discharges compared to the fixed intervals often seen in environmental artifacts.

o Electrode Distribution: The distribution of electrodes involved in the artifact can provide clues, with PEDs typically showing a different pattern than environmental artifacts.

o Generalization: Fully generalized occurrence is more common in environmental artifacts, while PEDs may have specific field distributions.

Understanding these differences between environmental artifacts and PEDs is essential for accurate EEG interpretation. Proper identification and differentiation of these patterns contribute to the correct diagnosis and management of patients with epilepsy or other neurological conditions.

 

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