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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 Interactive specialization approaches

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Dr. Rishabh Pathak

The interactive specialization approach is an alternative theory in developmental neuroscience that emphasizes the importance of organizing inter-regional interactions within the brain, particularly within the cerebral cortex, to understand functional brain development. Here is an explanation of the interactive specialization approach: 

1.     Theory Overview:

  • The interactive specialization approach proposes that postnatal functional brain development, especially within the cerebral cortex, involves a process of organizing interactions between different brain regions.
  • Unlike the maturational perspective that focuses on the maturation of specific brain regions, the interactive specialization approach highlights the importance of coordinated interactions among regions for the development of cognitive functions.

2.     Inter-Regional Interactions:

  • According to this theory, the specialization of brain functions does not solely rely on the maturation of individual regions but also on the refinement of connectivity and interactions between different brain areas.
  • Regions of the brain adjust their functionality together to enable new computations and support the emergence of complex cognitive abilities.

3.     Dynamic Changes in Brain Activation:

  • The interactive specialization approach suggests that understanding the emerging interactions between brain regions is as crucial as the development of connectivity within a single region.
  • This perspective accounts for the dynamic changes in patterns of cortical activation observed during postnatal development, indicating that functional brain development involves a complex interplay between different regions.

4.     Comparison with Maturational Perspective:

  • In contrast to the maturational perspective, which attributes behavioral developments to the maturation of specific brain regions, the interactive specialization approach emphasizes the importance of inter-regional interactions in shaping cognitive functions.
  • Rather than focusing on the sequential maturation of individual regions, this theory highlights the coordinated development of connectivity and interactions between brain areas.

5.     Importance of Connectivity:

  • The interactive specialization approach underscores the significance of connectivity and communication between brain regions in supporting the specialization of cognitive functions.
  • By considering how different regions of the brain interact and coordinate their activities, researchers can gain a more comprehensive understanding of how cognitive abilities develop during infancy and childhood.

In summary, the interactive specialization approach in developmental neuroscience emphasizes the role of organizing inter-regional interactions within the brain, particularly in the cerebral cortex, to explain functional brain development. This theory highlights the importance of connectivity and coordinated activity between brain regions in shaping cognitive functions and the emergence of specialized neural processes during development.

 

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