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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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Three accounts of the neural basis of an advance in behavioral abilities in Infant

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Dr. Rishabh Pathak

The three accounts of the neural basis of an advance in behavioral abilities in infants. Here is an explanation of each of the three accounts based on the information provided:

1.     Maturational View:

  • The maturational view proposes that the neuroanatomical maturation of specific brain regions, such as the dorsolateral prefrontal cortex (DLPC), plays a crucial role in the emergence of new behavioral abilities in infants.
  • According to this view, successful performance in tasks such as object retrieval is attributed to the maturation of a particular brain region, rather than changes in interactions between multiple regions.
  • The maturational perspective suggests that the development of specific brain regions at certain stages allows for the acquisition of new skills and behaviors in infants.

2.     Interactive Specialization View:

  • The interactive specialization view emphasizes the importance of changes in interactions between multiple brain regions that are already partially active in supporting the advancement of behavioral abilities in infants.
  • This perspective suggests that the refinement of connectivity between regions, rather than within a single region, is critical for the emergence of new cognitive functions.
  • According to this view, regions of the brain adjust their functionality together to enable new computations and support the development of complex behavioral abilities in infants.

3.     Skill-Learning Model:

  • The skill-learning model posits that the pattern of activation of cortical regions changes during the acquisition of new skills throughout the lifespan, including in infants.
  • This model suggests that during skill acquisition, there is greater activation of frontal regions initially, followed by a shift towards greater activation of posterior regions as the skill is mastered.
  • The skill-learning model highlights the dynamic changes in cortical activation patterns that occur during the acquisition of new skills, indicating a reorganization of brain activity as infants develop and refine their behavioral abilities.

In summary, the three accounts of the neural basis of an advance in behavioral abilities in infants - the maturational view, interactive specialization view, and skill-learning model - provide different perspectives on how neural maturation, inter-regional interactions, and skill acquisition processes contribute to the development of cognitive functions and behavioral abilities in infants. These accounts offer valuable insights into the complex mechanisms underlying infant cognitive development and the neural basis of emerging skills during early life.

 

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