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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 typical frequency ranges for low and high stimulation frequencies that may produce photomyogenic artifacts?

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Dr. Rishabh Pathak


Photomyogenic artifacts in EEG recordings can be influenced by the frequency of photic stimulation. The typical frequency ranges for low and high stimulation frequencies that may produce these artifacts are as follows:


1.      Low Stimulation Frequencies:

o Low stimulation frequencies are generally considered to be below 6 Hz. At these frequencies, photomyogenic artifacts tend to resemble other EMG potentials more closely. The artifacts produced may not exhibit a well-formed photic driving response, and the waveforms can appear more irregular and less synchronized with the stimulus. The muscle contractions may be less pronounced, leading to lower amplitude artifacts.

2.     High Stimulation Frequencies:

o High stimulation frequencies are typically above 6 Hz, with common ranges extending up to 30 Hz or higher. At these higher frequencies, photomyogenic artifacts can appear less like typical EMG and more similar to the photic driving response. The waveforms at high frequencies tend to have sharper contours and can show a more rhythmic pattern that aligns more closely with the frequency of the photic stimulus. However, they still differ from the photic driving response in terms of their waveform characteristics and may not always be time-locked to the strobe stimulation.

In summary, low stimulation frequencies (below 6 Hz) are associated with more irregular and less synchronized photomyogenic artifacts, while high stimulation frequencies (above 6 Hz) can produce artifacts that are sharper and more rhythmic, but still distinct from true photic driving responses.

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