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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 are the different perspectives on how functional specialization of regions of the cerebral cortex arises in the human brain?

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Dr. Rishabh Pathak

The different perspectives on how functional specialization of regions of the cerebral cortex arises in the human brain are: 

1.     Intrinsic Genetic and Molecular Mechanisms Perspective:

  • One perspective posits that the functional specialization of regions of the cerebral cortex arises primarily through intrinsic genetic and molecular mechanisms.
  • According to this view, genetic factors play a significant role in determining the initial organization and specialization of different brain regions.
  • Experience is considered to have a role in fine-tuning the functional properties of these specialized regions rather than being the primary driver of their development.

2.     Experience-Dependent Specialization Perspective:

  • An alternative perspective suggests that some aspects of human functional brain development involve a prolonged process of specialization that is shaped by postnatal experience.
  • This view emphasizes the influence of environmental stimuli and experiences in sculpting the functional organization of the cerebral cortex.
  • It proposes that the interactions between the developing brain and the external environment play a crucial role in determining how specific regions of the cortex become specialized for different functions.

3.     Interaction Between Genetic Factors and Postnatal Experience Perspective:

  • A more integrated perspective acknowledges the interplay between intrinsic genetic factors and postnatal experiences in shaping the functional specialization of cortical regions.
  • This viewpoint suggests that while genetic predispositions establish a foundation for brain development, experiences during infancy and childhood contribute to the refinement and adaptation of neural circuits.
  • It highlights the dynamic and interactive nature of brain development, where genetic predispositions and environmental influences work together to shape the functional organization of the cerebral cortex.

Overall,  a nuanced understanding of how the functional specialization of regions of the cerebral cortex arises in the human brain, considering the complex interplay between genetic factors, postnatal experiences, and environmental influences. These perspectives underscore the intricate processes involved in the development of specialized brain functions and highlight the importance of both intrinsic and extrinsic factors in shaping the functional organization of the human cortex.

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