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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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Different measures of neuronal morphology change independently of each other and sometimes in opposite directions.

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Dr. Rishabh Pathak

Different measures of neuronal morphology can change independently of each other and occasionally in opposite directions, highlighting the complexity of structural adaptations in the brain. Here are some key points regarding the independent changes in neuronal morphology:


1.     Spine Density vs. Dendritic Length: Spine density, which reflects the number of dendritic spines (small protrusions on dendrites where synapses form), and dendritic length, which indicates the extent of dendritic branching, are two distinct measures of neuronal morphology. Studies have shown that changes in spine density and dendritic length can occur independently in response to various experiences.


2.     Independent Responses to Experiences: Neurons in different cortical layers or regions may exhibit unique responses to environmental stimuli or learning tasks. For example, experiences that promote dendritic growth in one brain region may not necessarily lead to changes in spine density in another region. This variability underscores the specificity of structural adaptations in the brain.


3.     Opposite Directions of Change: In some cases, changes in neuronal morphology may occur in opposite directions in response to different stimuli or experiences. For instance, a particular intervention or environmental factor may lead to an increase in spine density but a decrease in dendritic length in certain neuronal populations. These divergent changes highlight the nuanced and context-dependent nature of structural plasticity.


4. Functional Implications: The independent changes in neuronal morphology suggest that different aspects of neural architecture can be selectively modified based on specific inputs or behavioral demands. This flexibility allows the brain to adapt to diverse environmental conditions and optimize neural circuitry for different functions.


By recognizing that measures of neuronal morphology can change independently and sometimes in opposing directions, researchers can gain a more nuanced understanding of how structural plasticity in the brain is regulated and how it contributes to adaptive behaviors and cognitive functions. Studying the diverse responses of neurons to experiences provides valuable insights into the complex mechanisms underlying brain plasticity.

 

 

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