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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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Short Intracortical Inhibitions (SICI)

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Dr. Rishabh Pathak

Short Intracortical Inhibition (SICI) is a neurophysiological phenomenon observed in the context of transcranial magnetic stimulation (TMS) studies, particularly in investigations of cortical excitability and neural circuits. Here is an overview of Short Intracortical Inhibition (SICI):


1.      Definition:

oShort Intracortical Inhibition (SICI) is a specific neurophysiological mechanism characterized by a decrease in cortical excitability in response to a conditioning TMS pulse followed by a test TMS pulse with a short interstimulus interval (ISI) typically ranging from 1 to 5 milliseconds.

2.     Experimental Setup:

oIn TMS studies investigating SICI, two TMS pulses are delivered to the motor cortex: a conditioning pulse followed by a test pulse. The conditioning pulse, usually subthreshold, is applied first, followed by the test pulse, which is supra-threshold. The short ISI between the two pulses is critical for observing the inhibitory effect.

3.     Neuronal Mechanisms:

o SICI is believed to reflect the activity of inhibitory interneurons within the motor cortex. The subthreshold conditioning pulse activates inhibitory circuits, leading to a temporary reduction in cortical excitability that results in a decrease in the amplitude of the motor evoked potential (MEP) elicited by the subsequent test pulse.

4.    Physiological Significance:

oSICI plays a crucial role in modulating motor cortex excitability and fine-tuning motor output. It is involved in the regulation of motor control, movement precision, and the suppression of unwanted muscle activity.

5.     Clinical Applications:

oStudies of SICI have clinical implications in various neurological and neuropsychiatric conditions. Alterations in SICI have been reported in conditions such as stroke, Parkinson's disease, epilepsy, and schizophrenia, providing insights into the underlying pathophysiology of these disorders.

6.    Measurement:

oSICI is typically quantified by comparing the amplitude of MEPs elicited by the test pulse alone versus the test pulse preceded by the conditioning pulse. A reduction in MEP amplitude following the conditioning pulse indicates the presence of SICI.

7.     Research Tools:

oSICI is commonly studied using paired-pulse TMS paradigms, where the interplay between inhibitory and excitatory circuits in the motor cortex can be investigated. Researchers use SICI measurements to assess cortical inhibitory processes and their role in motor function.

In summary, Short Intracortical Inhibition (SICI) is a neurophysiological phenomenon observed in TMS studies, reflecting the inhibitory modulation of cortical excitability through the activation of inhibitory interneurons in the motor cortex. Understanding SICI provides valuable insights into motor control mechanisms, neural circuitry, and the pathophysiology of various neurological conditions.

 

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