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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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What role do epigenetics and neuronal morphology play in changes in behaviour in the developing brain?

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Dr. Rishabh Pathak

Epigenetics and neuronal morphology are key factors that contribute to changes in behavior in the developing brain. Here is an explanation of the roles they play:


1.     Epigenetics: Epigenetics refers to changes in gene expression that do not involve alterations in the DNA sequence. In the developing brain, epigenetic mechanisms play a crucial role in regulating the expression of genes that are involved in neuronal development, synaptic plasticity, and behavior. These mechanisms can be influenced by various environmental factors and experiences, leading to long-lasting changes in brain function and behavior.

o    Impact on Behavior: Epigenetic modifications can influence the expression of genes that are important for learning, memory, and emotional regulation. By regulating gene expression, epigenetic mechanisms can shape the development of neural circuits and synaptic connections that underlie behavior. Changes in epigenetic marks can impact how the brain responds to experiences and stimuli, ultimately influencing behavior in the developing brain.

2.     Neuronal Morphology: Neuronal morphology refers to the structure and shape of neurons, including the formation of dendrites, axons, and synapses. Changes in neuronal morphology are essential for the establishment of neural circuits, synaptic connections, and communication between neurons. During development, neuronal morphology undergoes dynamic changes in response to various experiences and stimuli.

o    Impact on Behavior: The morphology of neurons plays a critical role in determining how information is processed and transmitted in the brain. Changes in neuronal morphology, such as dendritic branching, spine density, and synapse formation, can impact the strength and efficiency of neural connections. These structural changes influence the neural networks involved in behavior, cognition, and sensory processing. Alterations in neuronal morphology in response to experiences contribute to the plasticity of the developing brain and shape behavioral outcomes.

In summary, epigenetics and neuronal morphology are interconnected processes that contribute to changes in behavior in the developing brain. Epigenetic mechanisms regulate gene expression patterns that influence neural development and synaptic plasticity, while neuronal morphology shapes the structural basis of neural circuits and communication. Together, these factors play a critical role in the adaptive changes that occur in the developing brain in response to experiences, ultimately influencing behavior and cognitive functions.

 

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