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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 is TMS?

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Dr. Rishabh Pathak


 

Transcranial Magnetic Stimulation (TMS) is a non-invasive neuromodulation technique that involves the use of magnetic fields to stimulate specific regions of the brain. Here are some key points about TMS:

 1. Mechanism of Action:

   - TMS works by generating a magnetic field that induces electrical currents in targeted areas of the brain, leading to the depolarization of neurons and the modulation of neural activity.

   - The stimulation can either increase or decrease the excitability of neurons, depending on the frequency and intensity of the magnetic pulses applied.

 2. Therapeutic Application:

   - TMS is commonly used in the treatment of various neuropsychiatric conditions, including depression, anxiety disorders, and certain neurological disorders.

   - In the context of depression, repetitive TMS (rTMS) is often used to target specific brain regions implicated in mood regulation, such as the left dorsolateral prefrontal cortex (dlPFC) and the subgenual anterior cingulate cortex (sgACC).

 3. Treatment for Depression:

   - TMS has been approved by regulatory agencies, such as the FDA in the United States, as a treatment for medication-resistant depression.

   - The therapeutic effects of TMS in depression are thought to involve both short-term changes in neural excitability and long-term neuroplastic changes that may contribute to symptom improvement.

 4. Administration:

   - TMS is typically administered in multiple sessions over a period of weeks, with each session lasting around 20-30 minutes.

   - The treatment schedule and parameters (e.g., frequency, intensity) of TMS sessions are tailored to individual patient needs and treatment protocols.

 5. Efficacy:

   - Clinical studies have shown that TMS can be effective in reducing depressive symptoms in a subset of patients who do not respond to traditional antidepressant medications.

   - Response rates to TMS treatment for depression typically range from 29% to 46%, with remission rates in the range of 18% to 31%.

 6. Safety:

   - TMS is considered a safe and well-tolerated treatment option for depression, with minimal side effects compared to other interventions like electroconvulsive therapy (ECT).

   - Common side effects of TMS may include mild headache, scalp discomfort, or muscle twitching during stimulation.

 

In summary, TMS is a non-invasive neuromodulation technique that has shown promise as a treatment option for depression, particularly in cases where traditional therapies have been ineffective. By targeting specific brain regions involved in mood regulation, TMS can help alleviate depressive symptoms and improve overall well-being in some individuals.

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