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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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Experience-dependent changes in the brain

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Dr. Rishabh Pathak

Experience-dependent changes in the brain can interact in complex ways, influencing neural plasticity, structural adaptations, and functional outcomes. Here are some key points regarding the interactions of experience-dependent changes:


1. Cumulative Effects: Experiences accumulate over time, leading to cumulative effects on brain plasticity. Sequential or concurrent experiences can interact to shape neural circuits, synaptic connections, and cognitive functions in a synergistic or additive manner.


2.     Cross-Modal Interactions: Different types of experiences, such as sensory inputs from multiple modalities or cognitive tasks engaging diverse brain regions, can interact to produce integrated changes in neural networks. Cross-modal interactions highlight the interconnected nature of brain plasticity and sensory processing.


3.     Experience-Drug Interactions: Experiences and exposure to psychoactive drugs can interact to modulate neuronal morphology and synaptic plasticity. For example, prior exposure to drugs may influence the effects of subsequent experiences on brain structure, highlighting the complex interplay between pharmacological and environmental factors.


4.  Developmental Interactions: Experiences during critical periods of development can interact with genetic, environmental, and epigenetic factors to shape neural circuits and behavioral outcomes. Early-life experiences, in particular, can have profound and lasting effects on brain development and function.


5.  Behavioral Consequences: Interactions between experiences can impact behavior by shaping cognitive processes, emotional responses, and adaptive behaviors. The integration of diverse experiences influences neural networks and functional connectivity, ultimately influencing behavioral outcomes.


6.   Plasticity Modulation: The interactions of experience-dependent changes can modulate the extent and direction of neural plasticity. Positive or negative experiences, enriched environments, learning tasks, and social interactions can interact to regulate synaptic strength, dendritic morphology, and neural connectivity.


Understanding how experience-dependent changes interact in the brain provides insights into the complex mechanisms underlying neural plasticity, learning, and adaptation. By considering the dynamic interplay between various experiences and their effects on brain structure and function, researchers can unravel the intricate relationships that shape neural development, cognitive abilities, and behavioral responses.

 

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