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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 differences in brain development between males and females?

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Dr. Rishabh Pathak

Brain development between males and females exhibits several key differences, including structural, functional, and cognitive aspects. Here are some notable variations:


1.     Brain Size and Neuronal Density: On average, males tend to have larger brains than females, with studies suggesting a size difference of about 10%. Additionally, some reports indicate a greater number of neurons across the cortex in the male brain, although this may vary by region or cortical layer.


2.     Cortical Volume: Research has shown that females may have greater cortical volume relative to the cerebrum, particularly in the frontal and medial paralimbic cortices, while males may have greater volume in the frontomedial cortex, amygdala, and hypothalamus.


3.     Hippocampus Size: The hippocampus, crucial for learning and memory, has been found to be larger in females relative to total brain size. This difference may have implications for cognitive functions related to memory and emotional processing.


4.  Corpus Callosum: The corpus callosum, which connects the left and right hemispheres, has been a focus of research on sex differences in cognitive function and lateralization. Studies have shown variations in the size and structure of the corpus callosum between males and females, potentially influencing cognitive abilities like language and visuospatial skills.


5.     Amygdala and Hypothalamus: Sex differences have been observed in the size and functional aspects of the amygdala and hypothalamus. For example, the amygdala has been found to be larger in females, and different patterns of lateralization in amygdala involvement in memory have been reported.


6.     Rate of Development: Variations in the rate of development of brain regions have been noted between males and females. For instance, the orbitofrontal cortex may develop more rapidly in males, and patterns of white and gray matter volume changes differ between the sexes during development.


These differences in brain development between males and females highlight the complex interplay of genetic, hormonal, and environmental factors that shape the structural and functional organization of the brain throughout development.

 

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