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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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How does the fourfold increase in the volume of the human brain from birth to teenage years impact motor, cognitive, and perceptual abilities?

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Dr. Rishabh Pathak

The fourfold increase in the volume of the human brain from birth to teenage years has significant impacts on motor, cognitive, and perceptual abilities. Here is an explanation based on the some information: 

1.     Motor Abilities:

  • The increase in brain volume during this period is associated with the development of motor skills. As the brain grows and matures, it establishes and refines neural connections that are crucial for controlling movement and coordination.
  • This growth allows for the enhancement of motor abilities, leading to improvements in physical skills such as walking, running, grasping objects, and other complex movements.
  • The maturation of motor areas in the brain enables individuals to perform more intricate and coordinated movements as they progress from infancy to adolescence.

2.     Cognitive Abilities:

  • The expansion of the brain volume also plays a vital role in the development of cognitive functions. Cognitive abilities such as memory, attention, problem-solving, and language skills undergo significant advancements during this period.
  • The growth of brain structures involved in cognition, such as the prefrontal cortex responsible for decision-making and executive functions, contributes to the enhancement of cognitive abilities.
  • The increase in brain volume allows for the establishment of more complex neural networks, facilitating higher-order thinking processes and intellectual development throughout childhood and adolescence.

3.     Perceptual Abilities:

  • The growth of the brain from birth to teenage years influences perceptual abilities, including sensory processing, visual perception, and auditory processing.
  • The maturation of sensory areas in the brain leads to improved perceptual skills, allowing individuals to better interpret and respond to sensory information from the environment.
  • The expansion of brain regions involved in perception contributes to the refinement of sensory abilities, enhancing the individual's capacity to perceive and make sense of the world around them.

In summary, the substantial increase in brain volume during the developmental period from birth to teenage years has a profound impact on motor, cognitive, and perceptual abilities by supporting the maturation of neural circuits and structures essential for these functions.

 

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