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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 some key findings regarding the maturation of the prefrontal cortex in the developing human brain?

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Dr. Rishabh Pathak

The maturation of the prefrontal cortex in the developing human brain is a complex process that involves structural and functional changes over time. Some key findings regarding the maturation of the prefrontal cortex include:


1.     Prolonged Development: The prefrontal cortex is one of the last brain regions to mature, with a prolonged physiological development and organization during childhood. This region undergoes significant changes throughout childhood and adolescence, suggesting ongoing maturation well into early adulthood.


2.  Synaptic Pruning: During late childhood and adolescence, there is a gradual decrease in synaptic density in the prefrontal cortex, coinciding with the continued development of cognitive capacities. This pruning process involves the strengthening of remaining synaptic connections and the suppression of competing, irrelevant behaviors.


3.     Neural Plasticity: The prefrontal cortex shows a prolonged maturation relative to other cortical regions, such as the visual cortex. This region is associated with cognitive functions like working memory, attention, and decision-making, and its development is crucial for higher-order cognitive processes.


4.   Behavioral Changes: Changes in the prefrontal cortex are linked to behavioral changes, including improvements in cognitive abilities and executive functions. The development of attention, memory, and decision-making skills during childhood and adolescence is supported by the maturation of the prefrontal cortex.


5.     Functional MRI Studies: Normative pediatric fMRI studies have shown greater and more diffuse prefrontal cortical activity in children compared to adults during memory and attention tasks. These findings support the idea of ongoing development of attention and memory functions in children, both behaviorally and physiologically.


In summary, the maturation of the prefrontal cortex in the developing human brain involves a complex interplay of structural changes, synaptic pruning, neural plasticity, and functional development. Understanding these processes is essential for unraveling the neural bases of cognitive development during childhood and adolescence.

 

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