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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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Theta Burst Stimulation (TBS)

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Dr. Rishabh Pathak

Theta Burst Stimulation (TBS) is a form of repetitive transcranial magnetic stimulation (rTMS) that has gained attention in neuroscience and clinical research for its ability to modulate cortical excitability and induce lasting effects on brain function. Here is an overview of Theta Burst Stimulation (TBS):


1.      Definition:

oTheta Burst Stimulation (TBS) is a patterned form of repetitive transcranial magnetic stimulation (rTMS) that involves delivering bursts of magnetic pulses at a specific frequency (typically theta frequency, around 5 Hz) to targeted regions of the brain.

2.     Types of TBS:

o    There are two main types of Theta Burst Stimulation:

§ Continuous Theta Burst Stimulation (cTBS): Involves continuous bursts of stimulation over a period of time, typically leading to inhibitory effects on cortical excitability.

§Intermittent Theta Burst Stimulation (iTBS): Involves intermittent bursts of stimulation with short breaks in between, often resulting in facilitatory effects on cortical excitability.

3.     Effects on Cortical Excitability:

oTBS protocols have been shown to induce changes in cortical excitability that outlast the stimulation period. Inhibitory TBS can lead to long-term depression (LTD) of synaptic activity, while facilitatory TBS can induce long-term potentiation (LTP), resembling mechanisms of synaptic plasticity.

4.    Research and Therapeutic Applications:

oTBS has been widely used in research settings to investigate neural plasticity, motor learning, and cognitive functions. It is also being explored as a potential therapeutic tool for various neurological and psychiatric conditions.

5.     Clinical Applications:

oTBS has shown promise in the treatment of neurological and psychiatric disorders, including depression, schizophrenia, chronic pain, stroke rehabilitation, and movement disorders like Parkinson's disease. It is being studied as a non-invasive neuromodulation technique with potential therapeutic benefits.

6.    Targeted Brain Regions:

oTBS can be applied to specific brain regions based on the research or clinical objectives. Common targets include the primary motor cortex (M1), dorsolateral prefrontal cortex (DLPFC), cerebellum, and other areas implicated in motor control, mood regulation, and cognitive functions.

7.     Safety and Efficacy:

oTBS is generally considered safe when administered by trained professionals following established protocols. It is non-invasive and well-tolerated by most individuals. However, individual responses to TBS may vary, and its long-term effects are still being studied.

In summary, Theta Burst Stimulation (TBS) is a specialized form of repetitive transcranial magnetic stimulation that can modulate cortical excitability and induce lasting changes in brain function. Its potential applications in research and clinical settings make it a valuable tool for studying neural plasticity and exploring therapeutic interventions for various neurological and psychiatric conditions.

 

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