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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 are the direct connection and indirect connection performance of BCI systems over 50 years?

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Dr. Rishabh Pathak

The performance of Brain-Computer Interface (BCI) systems has significantly evolved over the past 50 years, distinguishing between direct and indirect connection methods.

Direct Connection Performance:

1.      Definition: Direct connection BCIs involve the real-time measurement of electrical activity directly from the brain, typically using techniques such as:

  • Electroencephalography (EEG): Non-invasive, measuring electrical activity through electrodes on the scalp.
  • Invasive Techniques: Such as implanted electrodes, which provide higher signal fidelity and resolution.

2.     Historical Development:

  • Early Research: The journey began in the 1970s with initial experiments at UCLA aimed at establishing direct communication pathways between the brain and devices. Research in this period focused primarily on animal subjects and theoretical frameworks.
  • Technological Advancements: As technology advanced, particularly in the areas of signal processing and machine learning, the direct connection methods began to yield more accurate and reliable interpretations of brain signals for practical applications like controlling devices.

3.     Current Performance:

  • Complex Command Recognition: Improved algorithms now allow for high accuracy in interpreting user intentions, enabling the control of complex devices (e.g., robotic prosthetics) .
  • Calibration: While intrusive methods such as implanted electrodes offer better signals, they require more extensive calibration and carry risks.

Indirect Connection Performance:

1.      Definition: Indirect connection BCIs acquire brain-related metrics that do not directly measure the electrical activity of neurons. Methods include:

  • Functional Magnetic Resonance Imaging (fMRI): Measures brain activity by detecting changes associated with blood flow.
  • Functional Near-Infrared Spectroscopy (fNIRS): Involves measuring hemodynamic responses associated with neural activity.

2.     Historical Development:

  • Emergence of Non-invasive Techniques: The non-invasive BCI systems became more prevalent in the 1990s, leveraging indirect methods to allow users to interact with computers without the need for invasive procedures 
  • Application Expansion: This evolution led to applications beyond medical, including gaming and consumer products 

3.     Current Performance:

  • User Comfort and Accessibility: Indirect BCIs, such as fNIRS and fMRI, offer a user-friendly environment without the risks associated with invasive methods, making them more widely acceptable for use in various applications.
  • Real-time Analysis: Although providing less temporal resolution than direct methods, advances in imaging technologies have enhanced the real-time analysis capabilities of indirect BCIs for practical tasks.

Summary of Performance:

In summary, the direct connection BCIs have made strides in accuracy and capability through improved electrode technology and sophisticated algorithms, particularly beneficial in medical applications. Indirect connection BCIs, while generally less invasive, have developed to become user-friendly alternatives, particularly suited for research, entertainment, and rehabilitation. Overall, both approaches have expanded significantly over the last fifty years, leading to a diverse array of applications that enhance human-computer interaction, especially for individuals with disabilities.

 


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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