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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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Role of Gonadal Hormones in Brain Development

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Dr. Rishabh Pathak

Gonadal hormones, such as estrogen and testosterone, play a crucial role in brain development, influencing neural differentiation, synaptic connectivity, and behavioral outcomes. Here is an overview of the role of gonadal hormones in brain development:


1.     Prenatal Differentiation:

o    Gonadal hormones are involved in the prenatal differentiation of the genitals and also impact brain development during fetal development.

o    Exposure to gonadal hormones in utero influences the organization of neural circuits, neuronal morphology, and neurotransmitter systems in the developing brain, contributing to sexual differentiation and brain sexual dimorphism.

2.     Sex Differences:

o    Gonadal hormone receptors are present in the brain, and gonadal hormones contribute to sex differences in brain structure, function, and behavior.

o    Studies have shown that male and female brains exhibit differences in neuronal morphology, synaptic connectivity, and neurotransmitter activity, which are influenced by the effects of gonadal hormones during critical periods of brain development.

3.     Neural Plasticity:

o    Gonadal hormones modulate neural plasticity, synaptic transmission, and neurogenesis in brain regions implicated in social behavior, cognition, and emotional regulation.

o    Estrogen and testosterone can influence dendritic arborization, spine density, and synaptic pruning, shaping the connectivity and functional organization of neural networks involved in learning, memory, and social interactions.

4.     Brain Maturation:

o    Gonadal hormones contribute to the maturation of the brain, affecting the timing of brain development, myelination processes, and neuronal maturation during different stages of life.

o    Studies in animal models and humans have demonstrated that gonadal hormones influence the rate of brain development, cortical thickness, and gray matter volume, with implications for cognitive abilities, emotional regulation, and social behavior.

5.     Behavioral Effects:

o    Gonadal hormones influence behavioral outcomes, including social behaviors, aggression, mating behaviors, and cognitive performance, by modulating brain function and neural circuits.

o    Changes in gonadal hormone levels during puberty, menstrual cycles, and aging can impact mood regulation, stress responses, and social interactions, highlighting the role of hormonal fluctuations in shaping behavior and brain function.

6.     Hormone Receptors:

o    Gonadal hormone receptors are distributed throughout the brain, including regions involved in emotion processing, social cognition, and reward pathways.

o    Estrogen receptors and androgen receptors mediate the effects of gonadal hormones on neuronal activity, synaptic plasticity, and gene expression, influencing brain development and behavioral responses.

By understanding the influence of gonadal hormones on brain development and behavior, researchers and clinicians can explore the mechanisms underlying sex differences in brain function, cognitive abilities, and mental health outcomes, leading to insights into the interplay between hormones, brain development, and behavior across the lifespan.

 

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