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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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How do different environmental events such as sensory stimuli, psychoactive drugs, and parental-child relationships influence brain development and function?

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Dr. Rishabh Pathak

Different environmental events play a significant role in influencing brain development and function. Here is how various factors such as sensory stimuli, psychoactive drugs, and parental-child relationships impact the brain:


1.     Sensory Stimuli: Exposure to sensory stimuli can lead to changes in the brain's structure and function. For example, placing lab animals in enriched environments with diverse sensory and motor experiences can result in widespread changes throughout the sensory and motor cortex. These changes may not be permanent and can vary over time. Different types of sensory experiences can trigger transient or persistent alterations in neuronal networks, affecting behavior.


2.     Psychoactive Drugs: Exposure to psychoactive drugs, including substances like amphetamines, cocaine, and nicotine, can have profound effects on brain development. Research has shown that these drugs can induce structural changes in specific brain regions, such as the prefrontal cortex and nucleus accumbens. The effects of psychoactive drugs on brain structure differ based on the type of drug and the brain region, highlighting the complex relationship between drug exposure and brain plasticity.


3.     Parental-Child Relationships: The quality of parental-child relationships can significantly impact brain development. Positive interactions, emotional support, and secure attachments with caregivers can promote healthy brain development in children. Conversely, adverse experiences such as neglect, abuse, or chronic stress can have detrimental effects on the developing brain. Studies have shown that early adverse experiences can alter gene expression in the brain, leading to long-lasting changes that affect cognitive and emotional functions.


Overall, environmental factors such as sensory stimuli, psychoactive drugs, and parental-child relationships can shape brain development and function through their influence on neural plasticity, gene expression, and synaptic connectivity. Understanding how these environmental events interact with the developing brain provides valuable insights into the mechanisms underlying both normal and abnormal brain development.

 

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