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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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The Maturational perspective theory

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Dr. Rishabh Pathak

The maturational perspective is a theory in developmental neuroscience that focuses on the relationship between neural maturation and the emergence of sensory, motor, and cognitive functions during human development. 

1.     Theory Overview:

  • The maturational perspective posits that the development of specific regions of the brain, particularly the cerebral cortex, is closely linked to the acquisition of new sensory, motor, and cognitive abilities.
  • According to this theory, the maturation of distinct brain regions at different stages of development is responsible for the emergence of age-appropriate behaviors and functions.

2.     Neural Maturation and Behavior:

  • The theory suggests that the anatomical maturation of cortical regions is a key determinant of when specific functions will become functional.
  • Success in new behavioral tasks at certain ages is attributed to the maturation of corresponding brain regions, leading to the development of age-appropriate skills and abilities.

3.     Example: Visual Orienting and Attention:

  • One example provided in the articles relates to the neurodevelopment of visual orienting and attention.
  • Researchers argue that control over visually guided behavior initially involves subcortical structures but shifts to posterior cortical regions and eventually to anterior regions with age and development.
  • The characteristics of visually guided behavior in human infants during the first month of life resemble those observed in adult primates with cortical damage, supporting the maturational perspective.

4.     Comparison with Adult Lesions:

  • The maturational perspective often involves comparing the behavioral performance of adults with acquired brain lesions to behaviors observed during infancy.
  • By examining how specific brain regions mature and contribute to functional abilities, researchers can gain insights into the neural basis of cognitive development.

5.     Limitations and Considerations:

  • While the maturational perspective provides valuable insights into the relationship between neural maturation and behavior, it may not fully account for the dynamic changes in patterns of cortical activation observed during postnatal development.
  • Factors such as environmental influences, experience, and interactions between brain regions are also important considerations in understanding human functional brain development.

In summary, the maturational perspective theory in developmental neuroscience emphasizes the role of neural maturation in shaping the emergence of sensory, motor, and cognitive functions during human development. By examining the maturation of specific brain regions and their contributions to behavior, researchers can gain a better understanding of the neural mechanisms underlying cognitive development in infants and children.

 

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