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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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Synaptogenesis and Synaptic pruning shape the cerebral cortex

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Dr. Rishabh Pathak

Synaptogenesis and synaptic pruning are essential processes that shape the cerebral cortex during brain development. Here is an explanation of how these processes influence the structural and functional organization of the cortex:


1. Synaptogenesis: Synaptogenesis refers to the formation of synapses, the connections between neurons that enable communication in the brain. During early brain development, neurons extend axons and dendrites to establish synaptic connections with target cells. Synaptogenesis is a dynamic process that involves the formation of new synapses and the strengthening of existing connections. This process is crucial for building the neural circuitry that underlies sensory processing, motor control, cognition, and behavior.


2. Synaptic Pruning: Synaptic pruning, also known as synaptic elimination or refinement, is the process by which unnecessary or weak synapses are eliminated while stronger connections are preserved. This pruning process is essential for sculpting the neural network, refining synaptic connectivity, and optimizing the efficiency of information processing in the brain. Synaptic pruning occurs throughout development, with peaks at different stages, and is influenced by neural activity and experience.


3.   Cortical Plasticity: The balance between synaptogenesis and synaptic pruning contributes to cortical plasticity, the brain's ability to reorganize its structure and function in response to experience. During critical periods of development, synaptic connections are refined through pruning, allowing for the selective strengthening of important connections and the elimination of redundant or less functional synapses. This process shapes the functional architecture of the cerebral cortex and underlies learning, memory, and adaptation to the environment.


4.     Neuronal Connectivity: Synaptogenesis and synaptic pruning play a key role in establishing precise neuronal connectivity patterns within the cerebral cortex. By forming and eliminating synapses, these processes contribute to the development of specialized neural circuits that support sensory perception, motor coordination, language processing, and higher cognitive functions. Disruptions in synaptogenesis and pruning can lead to altered connectivity patterns and functional deficits in the cortex.


5.   Neurodevelopmental Disorders: Dysregulation of synaptogenesis and synaptic pruning has been implicated in various neurodevelopmental disorders, such as autism spectrum disorders, schizophrenia, and intellectual disabilities. Abnormalities in synaptic connectivity and pruning mechanisms can disrupt the proper maturation of neural circuits, leading to cognitive impairments, social deficits, and behavioral abnormalities.


In summary, synaptogenesis and synaptic pruning are fundamental processes that shape the cerebral cortex by establishing and refining synaptic connections between neurons. These processes are essential for building functional neural circuits, promoting cortical plasticity, and ensuring the proper development of cognitive and behavioral functions. Understanding the mechanisms underlying synaptogenesis and synaptic pruning is crucial for unraveling the complexities of brain development and for elucidating the pathophysiology of neurodevelopmental disorders.

 

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