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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 genetic, environmental, biochemical, and physical events interact to influence neurodevelopment?

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Dr. Rishabh Pathak

Genetic, environmental, biochemical, and physical events interact in a complex manner to influence neurodevelopment. Here is an explanation of how each of these factors plays a role:


1.     Genetic Factors: Genetic factors provide the blueprint for neurodevelopment by determining the initial structure and function of the brain. Genes regulate processes such as neuronal differentiation, migration, and connectivity, which are essential for the formation of neural circuits. Variations in genes can impact the development of the brain and contribute to neurodevelopmental disorders.


2.     Environmental Factors: Environmental factors, including prenatal and postnatal experiences, exposure to toxins, nutrition, and social interactions, can significantly influence neurodevelopment. Environmental stimuli can shape neuronal connections, synaptic plasticity, and brain structure. Adverse environmental conditions, such as stress or malnutrition, can disrupt normal neurodevelopment and lead to cognitive and behavioral impairments.


3.     Biochemical Factors: Biochemical processes, such as neurotransmitter signaling, neurotrophic factors, and gene expression, play a crucial role in neurodevelopment. These factors regulate neuronal growth, survival, and synaptic plasticity. Imbalances in biochemical signaling pathways can disrupt normal brain development and contribute to neurological disorders.


4. Physical Factors: Physical forces, such as mechanical stress, tension, and differential growth, also impact neurodevelopment. These forces influence the folding of the cerebral cortex, a critical process in brain development. Mechanical forces generated by neuronal migration, axon guidance, and synaptogenesis contribute to the formation of neural circuits and the overall structure of the brain.


Overall, the interaction of genetic, environmental, biochemical, and physical factors is essential for the intricate process of neurodevelopment. Understanding how these factors influence brain development can provide insights into normal brain function and the pathogenesis of neurological disorders.

 

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