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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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Supplementary Motor Area (SMA)

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Dr. Rishabh Pathak

The Supplementary Motor Area (SMA) is a region of the cerebral cortex that plays a crucial role in the planning, initiation, and coordination of voluntary movements. Here is an overview of the Supplementary Motor Area (SMA):


1.      Location:

oThe Supplementary Motor Area is located in the medial surface of the frontal lobe, anterior to the primary motor cortex (M1), and is part of the premotor cortex. It is situated bilaterally in the superior frontal gyrus.

2.     Function:

oThe SMA is involved in the planning and coordination of complex movements, especially sequences of movements and bilateral movements. It plays a role in the preparation and organization of motor actions before their execution.

3.     Motor Planning:

oThe SMA is particularly important for the internal generation of movements, such as those involved in tasks that require motor planning without external cues. It is involved in the coordination of movements based on internal representations of actions.

4.    Bilateral Movements:

oThe SMA is known to be involved in the coordination of bilateral movements, where both sides of the body need to work together in a synchronized manner. It helps in synchronizing movements between the two sides of the body.

5.     Role in Motor Learning:

oThe SMA is also implicated in motor learning processes. It is involved in the acquisition of new motor skills and the consolidation of motor memory. Damage to the SMA can lead to difficulties in learning new motor tasks.

6.    Connections:

oThe SMA has extensive connections with other motor areas of the brain, including the primary motor cortex, premotor cortex, basal ganglia, and cerebellum. These connections allow for the integration of motor planning and execution processes.

7.     Clinical Implications:

o Dysfunction of the SMA has been associated with movement disorders such as apraxia, where individuals have difficulty planning and executing purposeful movements. It is also implicated in conditions like Parkinson's disease and epilepsy.

8.    Research and Stimulation:

oThe SMA is a target for research using techniques like transcranial magnetic stimulation (TMS) to study its role in motor control and movement preparation. Stimulation of the SMA has been explored as a potential therapeutic approach in movement disorders.

In summary, the Supplementary Motor Area (SMA) is a critical region of the brain involved in motor planning, coordination of complex movements, and the internal generation of actions. Its functions extend to bilateral movements, motor learning, and the integration of motor processes. Understanding the role of the SMA provides insights into motor control mechanisms and neurological conditions affecting movement coordination.

 

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