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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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What is fMRI ?

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Dr. Rishabh Pathak

 


Functional Magnetic Resonance Imaging (fMRI) is a non-invasive neuroimaging technique that measures brain activity by detecting changes in blood flow and oxygen levels in response to neural activity. fMRI is widely used in neuroscience and cognitive psychology to study brain function and connectivity during various tasks, behaviors, and resting states.

Key features of fMRI include:


1.     Principle of fMRI:

o    fMRI is based on the principle that changes in neural activity are accompanied by changes in blood flow and oxygenation levels in the brain.

o    When a specific brain region becomes active, it requires more oxygenated blood to support the increased metabolic demands of neural activity.

o    The fMRI scanner detects these changes in blood oxygen level-dependent (BOLD) signals, providing a measure of brain activity in different regions.

2.     Task-Based fMRI:

o    In task-based fMRI studies, participants perform specific cognitive tasks or stimuli while inside the MRI scanner.

o    By comparing brain activity during task performance to baseline activity, researchers can identify brain regions involved in task processing and cognitive functions.

3.     Resting-State fMRI:

o    Resting-state fMRI involves measuring spontaneous brain activity while the participant is at rest and not engaged in any specific task.

o    Resting-state fMRI is used to study functional connectivity between different brain regions and identify intrinsic brain networks that are synchronized in their activity.

4.     Spatial and Temporal Resolution:

o    fMRI provides high spatial resolution, allowing researchers to localize brain activity to specific regions or structures.

o    The temporal resolution of fMRI is relatively slow compared to other neuroimaging techniques like EEG, with changes in brain activity measured over seconds to minutes.

5.     Data Analysis:

o    fMRI data is processed and analyzed using specialized software to identify regions of brain activation, create statistical maps, and study functional connectivity.

o    Common analysis methods include general linear modeling, region of interest analysis, independent component analysis, and seed-based correlation analysis.

6.     Applications:

o    fMRI is used in a wide range of research areas, including cognitive neuroscience, psychology, neurology, and psychiatry.

o    Applications of fMRI include studying language processing, memory, emotion regulation, sensory perception, motor function, and clinical conditions such as Alzheimer's disease, schizophrenia, and depression.

Overall, fMRI is a powerful tool for studying brain function and connectivity in both healthy and clinical populations, providing valuable insights into the neural mechanisms underlying cognition, behavior, and brain disorders.


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