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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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Gliding Joints

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Dr. Rishabh Pathak

Gliding joints, also known as plane joints, are a type of synovial joint that allows for limited gliding or sliding movements in various directions. Here is an overview of gliding joints:

Gliding Joints:

1.    Structure:

o    Gliding joints consist of flat or slightly curved articulating surfaces that glide over each other.

o    The joint surfaces are relatively flat, allowing for simple back-and-forth or side-to-side movements.

2.    Function:

o Gliding joints permit limited sliding movements in multiple directions, such as back-and-forth and side-to-side.

o These joints provide flexibility and smooth motion between adjacent bones.

3.    Examples:

o    Intercarpal Joints:

§  The joints between the carpal bones of the wrist are classic examples of gliding joints.

§  These joints allow for small gliding movements during wrist flexion, extension, abduction, and adduction.

o    Intertarsal Joints:

§  The joints between the tarsal bones of the foot are also gliding joints.

§  They facilitate subtle gliding motions during foot movements and weight-bearing activities.

4.    Movements:

o  Gliding: Sliding or gliding of one bone over another without significant angular or rotational movement.

o    Side-to-Side: Movement in a lateral direction.

o    Back-and-Forth: Movement in an anterior-posterior direction.

5.    Stability:

o    Gliding joints provide stability and support for fine movements and weight distribution.

o Ligaments, joint capsules, and surrounding soft tissues help maintain joint alignment and prevent excessive movement.

6.    Clinical Significance:

o    Gliding joints are prone to overuse injuries, such as repetitive strain injuries in the wrist or foot.

o    Proper ergonomics, strengthening exercises, and rest are essential for maintaining the health and function of gliding joints.

Understanding the structure and function of gliding joints is important for healthcare professionals, athletes, and individuals seeking to prevent joint injuries and maintain optimal movement patterns. Proper care, ergonomic practices, and targeted exercises can help preserve the function and longevity of gliding joints in the body.

 

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