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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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Cardiac Artifacts

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Dr. Rishabh Pathak

Cardiac artifacts in EEG recordings refer to unwanted signals that originate from the electrical or mechanical activity of the heart. These artifacts can interfere with the accurate interpretation of brain activity captured by the EEG.


1.     Electrical Cardiac Artifacts:

o Description: Electrical cardiac artifacts result from the electrical signals generated by the heart's activity.

o  Characteristics: These artifacts are time-locked to cardiac events and can appear similar to ECG signals. However, due to the distance from the heart and suboptimal visualization axis, they may not always resemble typical ECG waveforms.

o    Types:

§  Pacemaker Artifact: This type of artifact has high-frequency polyphasic potentials with a shorter duration compared to ECG artifacts. It often shows a broader distribution across the EEG channels.

§ ECG Artifact: Represents the actual ECG signal recorded from head electrodes but may not always be easily recognizable as ECG due to recording conditions.

2.   Mechanical Cardiac Artifacts:

o  Description: Mechanical cardiac artifacts arise from the physical movements associated with cardiac contractions.

o  Characteristics: These artifacts may manifest as periodic slow waves following the ECG peak or exhibit saw-tooth patterns or sharply contoured waveforms.

o    Types:

§Pulse Artifact: Typically seen as a slow wave following the ECG peak, commonly observed over frontal and temporal regions. Pressure on the electrode can alter the appearance of this artifact.

§Ballistocardiographic Artifact: Results from slight head or body movements during cardiac contractions, with a waveform similar to pulse artifact but more widespread.

3.   Identification and Differentiation:

oDistinguishing Features: Pacemaker artifacts have distinct high-frequency polyphasic potentials, while pulse artifacts exhibit slow waves following the ECG peak.

o  Location: Pulse artifacts are often observed over frontal and temporal regions, while ballistocardiographic artifacts may involve multiple electrodes due to head or body movements.

Proper recognition and differentiation of cardiac artifacts from genuine brain activity are crucial for accurate EEG interpretation and diagnosis. Techniques to minimize or eliminate these artifacts during EEG recording can help improve the quality and reliability of EEG data for clinical analysis.

 

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