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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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Benign Epileptiform Transients of Sleep Compared to Cardiac Artifact, Electrocardiogram

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Dr. Rishabh Pathak

Benign Epileptiform Transients of Sleep (BETS) and Cardiac Artifact, specifically Electrocardiogram (ECG) artifacts, can sometimes present similar patterns in EEG recordings.

Similarities:

o  Both BETS and ECG artifacts are individual transients that can be low in amplitude and sharply contoured, making them morphologically similar in EEG recordings.

o  Both patterns can be present within mid-temporal regions, adding to the challenge of distinguishing between them based on morphology alone.

2.     Key Differentiating Features:

o  Co-occurrence with ECG: The presence of simultaneously recorded ECG signals is crucial in differentiating ECG artifacts from BETS. The synchronous occurrence with ECG signals is a reliable indicator of ECG artifacts.

o Waveform Analysis: Analyzing the waveform characteristics can help differentiate between BETS and ECG artifacts. BETS typically have specific waveform features, such as monophasic or diphasic patterns with abrupt rises and falls.

o  Bilateral vs. Unilateral Occurrence: ECG artifacts tend to occur bilaterally and synchronously, while BETS are bilateral in only a small minority of occurrences, aiding in their differentiation.

o Amplitude Distribution: ECG artifacts typically have maximal amplitudes with ear electrodes, which is not expected with BETS. This difference in amplitude distribution can be helpful in distinguishing between the two patterns.

3.     Additional Considerations:

o Wakefulness vs. Sleep: BETS are specific to sleep stages, particularly stages 1 and 2 of NREM sleep, while ECG artifacts can occur in wakefulness as well. This difference in occurrence can provide additional context for differentiation.

o Regular Interval Analysis: In the absence of ECG signals, analyzing the regularity of intervals between transients can help differentiate ECG artifacts from BETS. Regular intervals that align with heartbeats support the presence of ECG artifacts.

Understanding these distinguishing features and considerations is essential for accurately differentiating between BETS and ECG artifacts in EEG recordings, ensuring proper interpretation and diagnosis.

 

 

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