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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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Patterns of Change in sex differences in brain development

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Dr. Rishabh Pathak

Sex differences in brain development refer to the structural and functional variations between male and female brains that emerge during development. Here are some patterns of change in sex differences in brain development:


1.     Brain Size and Structure:

o    Early Differences: Male brains tend to be larger than female brains, with these differences appearing as early as 5 years of age. These size variations are attributed to differences in overall brain volume and specific regional volumes.

o    Regional Variations: Studies have reported regional differences in brain structure between males and females. For example, 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.

2.     Neuronal Numbers and Connectivity:

o    Neuronal Density: Some studies suggest that males have a greater number of neurons across the cortex compared to females. However, these differences may vary by region or cortical layer, indicating complex variations in neuronal density.

o    Connectivity Patterns: Sex differences in brain connectivity patterns have been observed, with variations in the strength and organization of neural networks between males and females. These differences may influence cognitive functions and information processing.

3.     Hormonal Influence:

o    Sex Hormones: The influence of sex hormones on brain development is a key factor contributing to sex differences. Research suggests that sex hormones play a role in shaping the structural and functional characteristics of the brain, particularly during critical developmental periods.

o    Gonadal Hormones: Studies in nonhuman animals have shown that regions with significant sex differences in humans correspond to areas with high levels of sex steroid receptors during development. This indirect evidence suggests that gonadal hormones may contribute to sexual dimorphisms in the human brain.

4.     Functional Variability:

o    Cognitive Functions: Sex differences in brain development can influence cognitive functions and behaviors. Variations in brain structure and connectivity may contribute to differences in cognitive abilities, emotional processing, and social behaviors between males and females.

o    Emotional Processing: Functional differences in brain regions involved in emotional processing, such as the amygdala, have been reported between males and females. These differences may impact emotional regulation, memory for emotional stimuli, and social cognition.

Understanding the patterns of change in sex differences in brain development provides insights into the complex interplay between biological factors, neural architecture, and cognitive functions. These variations contribute to the diversity of cognitive abilities and behaviors observed between males and females.

 

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