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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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Review Settings of EEG

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Dr. Rishabh Pathak

The review settings of an EEG recording refer to the parameters that can be adjusted to optimize the visualization and interpretation of electrical brain activity. Here is an overview of the key review settings in EEG analysis:

1.      Amplification (Gain/Sensitivity):

oDefinition: Amplification, also known as gain or sensitivity, determines how much the electrical signals from the brain are amplified before being displayed on the EEG recording.

oMeasurement: Typically measured in microvolts per millimeter (μV/mm).

oImpact: Adjusting the amplification setting can affect the visibility of high-amplitude and low-amplitude activity. High-amplitude activity may require vertical compression to fit within the display range, while low-amplitude activity may require lower sensitivity settings for better visualization.

2.     Frequency Filtering:

oBandpass: The frequency range within which EEG signals are analyzed. Common settings include a low-frequency filter (LFF) and a high-frequency filter (HFF).

oStandard Range: Typically, EEG devices accurately record activity within a frequency range of 0.1 to 125 Hz. Standard review settings often use a bandpass of 1 to 70 Hz to capture clinically relevant EEG activity.

oNotch Filter: A filter set to the frequency of the power supply's AC current to reduce noise from electrical interference.

3.     Time Scale:

oDefinition: The duration of time represented on each page of the EEG recording.

o Recommended Setting: The recommended time scale is 10 seconds per page, but adjustments can be made based on the specific needs of the analysis.

oHorizontal Compression/Expansion: Modifying the time scale can enhance the visualization of subtle changes, evolution of activity, or spread during seizures. Compression or expansion of the time scale can aid in observing different aspects of brain activity.

4.    Filter Adjustments:

oHigh-Frequency Filter (HFF): Reducing the HFF setting can help reduce high-frequency noise, such as muscle activity. However, it is essential to be cautious as filtering can distort the intended EEG activity.

o Low-Frequency Filter (LFF): Adjusting the LFF setting can impact the visibility of slow roving eye movements and baseline stability. Increasing the LFF setting may flatten the baseline and improve readability of high-frequency activity.

By understanding and appropriately adjusting these review settings, EEG analysts can optimize the visualization and interpretation of electrical brain activity, ensuring accurate and meaningful analysis of EEG recordings.

 

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