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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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Development of Prefrontal Cortex: Changes in PFC Functions

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Dr. Rishabh Pathak

The development of the prefrontal cortex (PFC) is characterized by significant changes in its functions across the lifespan, reflecting the maturation of cognitive control, executive function, and emotional regulation. Here are key aspects of changes in PFC functions during development:


1.     Early Childhood:

o    Emergence of Executive Functions: In early childhood, there is a gradual development of executive functions mediated by the PFC, including working memory, inhibitory control, cognitive flexibility, and goal setting. These functions support the regulation of attention, behavior, and emotions in young children.

o    Prefrontal Activation: Studies have shown increased activation in the PFC during tasks requiring cognitive control and decision-making in children, indicating the early maturation of PFC functions related to executive control.

2.     Adolescence:

o  Refinement of Executive Functions: During adolescence, there is continued refinement of executive functions and cognitive control processes mediated by the PFC. Adolescents show improvements in planning, problem-solving, impulse control, and decision-making abilities as the PFC undergoes structural and functional changes.

o    Increased Risk-taking Behavior: Adolescents often exhibit heightened risk-taking behavior and sensation-seeking tendencies, which are influenced by the development of the PFC and its role in evaluating rewards, inhibiting impulses, and considering long-term consequences.

3.     Adulthood:

o    Peak Cognitive Control: In adulthood, the PFC reaches peak efficiency in supporting cognitive control, working memory, and goal-directed behavior. Adults demonstrate enhanced abilities in complex decision-making, strategic planning, and emotional regulation, reflecting the mature functioning of the PFC.

o Integration of Information: The adult PFC is adept at integrating information from multiple sources, maintaining task sets, and coordinating cognitive processes across different regions of the brain. This integration supports higher-order cognitive functions and adaptive behavior.

4.     Aging:

o   Changes in PFC Activation: With aging, there may be changes in PFC activation patterns during cognitive tasks, reflecting alterations in neural efficiency and cognitive processing. Older adults may show differences in PFC functions related to working memory, attentional control, and response inhibition.

o Compensatory Mechanisms: Older adults may engage compensatory mechanisms involving recruitment of additional brain regions to support PFC functions, allowing for the maintenance of cognitive performance despite age-related changes in brain structure and function.

Understanding the developmental changes in PFC functions provides insights into the maturation of cognitive control, executive function, and emotional regulation across the lifespan. These changes reflect the dynamic interplay between brain development, experience, and environmental influences on higher cognitive processes mediated by the prefrontal cortex.

 

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