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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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Neuro-Computational Model of Subcortical Growth

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Dr. Rishabh Pathak

A neuro-computational model of subcortical growth integrates principles from neuroscience and computational modeling to study the development of brain regions beneath the cerebral cortex, known as the subcortex. Here are the key aspects of a neuro-computational model of subcortical growth:


1. Biologically Realistic Representation: The model incorporates biologically relevant features of subcortical development, such as the growth and elongation of axons, the formation of neural circuits, and the influence of growth factors on subcortical structures. By simulating these processes computationally, researchers can study how subcortical regions develop and interact with the cortex.


2.     Axonal Growth and Connectivity: The model accounts for the growth of axons and the establishment of connections between subcortical regions and cortical areas. By simulating axonal elongation and branching, researchers can study how subcortical structures contribute to the overall connectivity and function of the brain.


3. Mechanical Interactions: The model considers the mechanical interactions between the subcortex and the overlying cortex, as well as the effects of growth-induced deformations on subcortical structures. By incorporating mechanical properties and growth-induced stresses, the model can investigate how mechanical forces influence subcortical growth patterns.


4.  Stretch-Induced Growth: The model includes mechanisms of stretch-induced growth, where chronic stretching of axons in the subcortex leads to gradual elongation and deformation. By simulating how axons respond to mechanical stimuli, researchers can study the effects of stretch-induced growth on subcortical morphology.


5. Computational Simulations: Neuro-computational models use computational simulations, such as finite element analysis or agent-based models, to study the dynamics of subcortical growth. These simulations allow researchers to investigate how interactions between neurons, glial cells, and mechanical forces shape the development of subcortical structures.


6.  Sensitivity Analysis: The model can perform sensitivity analyses to assess the impact of varying parameters, such as growth rates, mechanical properties, and external stimuli, on subcortical growth. By systematically varying these parameters in simulations, researchers can identify key factors influencing the morphogenesis of subcortical regions.


7.    Validation and Comparison: Neuro-computational models are validated against experimental data, such as neuroimaging studies or histological analyses, to ensure their biological accuracy. By comparing model predictions with empirical observations, researchers can evaluate the model's ability to capture the dynamics of subcortical growth.


8.  Insights into Brain Development: By studying subcortical growth processes computationally, researchers can gain insights into the mechanisms underlying the development of brain structures below the cortex. These models help elucidate how subcortical regions contribute to overall brain function and connectivity, providing a deeper understanding of brain development. 


In summary, a neuro-computational model of subcortical growth offers a valuable framework for investigating the complex processes involved in the development of brain regions beneath the cerebral cortex. By combining neuroscience principles with computational modeling techniques, researchers can explore the dynamics of subcortical growth, connectivity formation, and mechanical interactions within the developing brain.

 

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