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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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Regressive Events in the Postnatal Period

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Dr. Rishabh Pathak

Regressive events in the postnatal period refer to processes in brain development that involve the elimination or reduction of certain neural elements, such as neurons and glial cells, to refine and optimize neural circuits. These regressive events are essential for sculpting the developing brain and ensuring its proper functioning. Here are key points regarding regressive events in the postnatal period:


1.     Cell Death in Glial Populations:

o    While neural apoptosis peaks during prenatal development, apoptosis in glial cell populations occurs postnatally and is essential for the refinement of neural circuits.

o    Glial cells, particularly oligodendrocytes, undergo apoptosis after differentiating, with signals from nearby axons influencing the survival of oligodendrocytes to match the local axonal surface area, a process crucial for myelination and neural connectivity.

2.     Synaptic Pruning:

o    Synaptic pruning is a process in which excess synapses formed during early brain development are selectively eliminated to enhance the efficiency and specificity of neural communication.

o    During postnatal development, synaptic pruning occurs extensively, with up to 50% of synapses being eliminated to streamline neural circuits, eliminate redundant connections, and optimize synaptic transmission.

3.     Reduction in Synaptic Density:

o    Studies have shown a reduction in synaptic density in the cortex during childhood, indicating a refinement of synaptic connections through the elimination of unnecessary synapses and the strengthening of essential connections for optimal neural function.

o    This reduction in synaptic density reflects the ongoing maturation and fine-tuning of neural circuits in response to environmental stimuli and experiences, shaping the functional organization of the brain during postnatal development.

4.     Pruning of Neuronal Processes:

o    Neuronal processes undergo pruning postnatally, involving the elimination of excess dendrites and axonal branches to enhance the specificity of neural connections and optimize neural signaling.

o    This process of pruning neuronal processes is crucial for shaping the structural and functional connectivity of the brain, allowing for efficient information processing and neural communication in the developing nervous system.

5.     Contribution to Brain Maturation:

o    Regressive events in the postnatal period, including cell death in glial populations, synaptic pruning, and reduction in synaptic density, contribute to the maturation and refinement of neural circuits, supporting the development of complex cognitive and behavioral functions.

o    These regressive events are essential for eliminating redundant or inefficient neural elements, promoting the establishment of precise and effective neural networks that underlie various cognitive processes and adaptive behaviors in children and adolescents.

In summary, regressive events in the postnatal period play a critical role in sculpting the developing brain by eliminating excess neural elements, refining synaptic connections, and optimizing neural circuits for efficient information processing and neural communication. These processes are essential for the maturation and functional specialization of the brain during early postnatal development, shaping the neural architecture and cognitive abilities of individuals as they grow and learn.

 

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