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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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Gradual evolution of BCIs and their growing significance in scientific research.

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Dr. Rishabh Pathak

Brain-Computer Interfaces (BCIs) have undergone a significant transformation over the past fifty years, moving from theoretical concepts to practical applications. Initially, BCIs were primarily experimental and based on invasive techniques, but advancements in technology, especially in non-invasive methods, have expanded their potential.

The gradual evolution of BCIs include:

1.      Technological Advancements: The development of more sophisticated tools and methods for brain signal acquisition and processing has enabled researchers to gather data more effectively, enhancing the reliability and accuracy of BCIs.

2.     Non-invasive Techniques: The emergence of non-invasive BCI systems in the 1990s made the technology more accessible. These systems, such as EEG-based BCIs, opened up numerous applications, particularly in rehabilitation for individuals with disabilities.

3.     Diverse Applications: The review highlights various applications of BCIs, including communication tools for disabled individuals, control systems for assistive devices, and even entertainment, illustrating their versatility and growing importance across different sectors.

4.    Research and Development: As BCIs become more integrated into scientific research, there has been a focus on developing intelligent algorithms for data analysis, improving calibration times, and enhancing classification accuracy, indicating an ongoing commitment to refining these technologies.

5.     Future Trends: The paper points out that the future of BCIs is linked to the advancement of passive systems that require less user engagement and are more autonomous, showing a shift toward user-friendly and efficient technologies.

Overall, the significance of BCIs in scientific research is underscored by their transformative potential for communication, rehabilitation, and various technological innovations, marking a critical milestone in the interface between human cognition and machines. 

 


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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