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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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Near Infrared Spectroscopy

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Dr. Rishabh Pathak

Near Infrared Spectroscopy (NIRS) is a non-invasive optical imaging technique that measures changes in blood oxygenation levels in the brain by detecting near-infrared light absorption. 

1.     Principle:

    • Near Infrared Spectroscopy (NIRS) is based on the principle that near-infrared light can penetrate biological tissues, including the human skull, allowing for the measurement of changes in blood oxygen levels in the brain.
    • NIRS utilizes near-infrared light sources and detectors placed on the scalp to monitor changes in light absorption, which are indicative of variations in oxygenated and deoxygenated hemoglobin concentrations in the brain.

2.     Applications:

    • NIRS is commonly used in neuroscience research to study brain activity, cognitive functions, and hemodynamic responses during various tasks and stimuli.
    • NIRS has applications in studying cognitive processes, language processing, motor functions, emotional responses, and developmental changes in the brain, particularly in infants and young children.

3.     Advantages:

    • Non-Invasive: NIRS is a non-invasive imaging technique that does not require exposure to ionizing radiation, making it safe for use in various populations, including infants, children, and clinical populations.
    • Portable and Flexible: NIRS systems are portable and adaptable for use in different settings, such as laboratories, hospitals, and research facilities, allowing for flexible data collection and monitoring.

4.     Limitations:

    • Depth of Penetration: NIRS has limited depth penetration compared to other neuroimaging techniques like fMRI, restricting its ability to measure brain activity in deeper brain regions.
    • Signal Contamination: NIRS signals can be affected by scalp blood flow, motion artifacts, and signal contamination from superficial tissues, requiring careful data processing and artifact correction.

5.     Research and Clinical Use:

    • NIRS is used in cognitive neuroscience research to investigate brain function, neural correlates of behavior, and developmental changes in brain activity.
    • In clinical settings, NIRS is employed to study neurological disorders, brain injuries, stroke rehabilitation, and cognitive impairments, providing valuable insights into brain function and hemodynamic responses in patient populations.

In summary, Near Infrared Spectroscopy (NIRS) is a valuable non-invasive optical imaging technique used in neuroscience research and clinical settings to study brain activity, cognitive functions, and hemodynamic responses. NIRS offers advantages such as portability, safety, and flexibility, making it a versatile tool for investigating brain function and neural processes in various populations and experimental conditions.

 

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