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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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Brain Computer Interface

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Dr. Rishabh Pathak

A Brain-Computer Interface (BCI) is a direct communication pathway between the brain and an external device or computer that allows for control of the device using brain activity. BCIs translate brain signals into commands that can be understood by computers or other devices, enabling interaction without the use of physical movement or traditional input methods.

Components of BCIs:

1.      Signal Acquisition: BCIs acquire brain signals using methods such as:

  • Electroencephalography (EEG): Non-invasive method that measures electrical activity in the brain via electrodes placed on the scalp.
  • Invasive Techniques: Such as implanting electrodes directly into the brain, which can provide higher quality signals but come with greater risks.
  • Other methods can include fMRI (functional Magnetic Resonance Imaging) and fNIRS (functional Near-Infrared Spectroscopy).

2.     Signal Processing: Once brain signals are acquired, they need to be processed to filter out noise and extract useful information. This involves various algorithms and machine learning approaches to interpret the signals effectively.

3.     Device Control: The processed signals are translated into commands that can control various applications—ranging from simple tasks (like moving a cursor on a screen) to more complex interactions (like controlling prosthetic limbs or enabling communication for individuals with disabilities).

Applications of BCIs:

  • Medical Rehabilitation: Helping patients with severe mobility impairments to regain control and independence (e.g., wheelchair or robotic arm control).
  • Communication Aids: Assisting individuals with conditions like ALS or stroke to communicate through thought-based systems.
  • Gaming and Entertainment: Enhancing user experiences in gaming by allowing players to control game elements through brain activity.
  • Research: Studying brain activity and cognitive functions for scientific advancements in psychology and neuroscience.

Overall, BCIs represent a significant intersection of neurology, engineering, and computer science, with the potential to profoundly influence healthcare, technology, and communication methods in the future. 

 


Kawala-Sterniuk, A., Browarska, N., Al-Bakri, A., Pelc, M., Zygarlicki, J., Sidikova, M., Martinek, R., & Gorzelanczyk, E. J. (2021). Summary of over fifty years with brain-computer interfaces—A review. Brain Sciences, 11(43). https://doi.org/10.3390/brainsci11010043

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