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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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General Principles of Plasticity and Behavior in the Development of Brain

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Dr. Rishabh Pathak

"Brain Plasticity and Behaviour in the Developing Brain" discusses general principles of plasticity and behavior in brain development. Here are some key points regarding this topic:


1.     Complex Interplay of Genetic and Experiential Factors: Brain development is not solely determined by genetic factors but also involves a complex interaction with environmental experiences. This interplay shapes the emerging brain and influences its development and function.


2.     Brain Development Progresses Through Stages: Brain development involves a series of stages, including neurogenesis, cell migration, maturation, synaptogenesis, synaptic pruning, and myelination. Each stage plays a crucial role in shaping the structure and function of the brain.


3.     Dendritic and Axonal Growth: The formation of dendrites and axons is essential for establishing neural connections and synaptic networks in the brain. Dendritic growth is slower than axonal growth, but both processes are crucial for proper brain development.


4.     Synapse Formation and Pruning: The brain forms a vast number of synapses, guided by environmental cues and signals. Synaptic pruning eliminates unnecessary connections, refining neural circuits and optimizing brain function. The manipulation of environmental cues can lead to significant changes in cerebral circuitry.


5.     Plasticity Throughout Life: Plastic changes in the brain support improved motor and cognitive functions. However, not all plasticity is beneficial, and maladaptive changes can occur in response to factors like psychoactive drugs, stress, and pathological conditions.


6. Impact of Environmental Events: Environmental factors such as sensory stimuli, psychoactive drugs, and parental-child relationships can influence brain development and function. Positive experiences can promote healthy brain development, while adverse events can lead to detrimental effects on the brain.


Understanding the general principles of plasticity and behavior in brain development provides insights into the dynamic processes that shape the developing brain. The intricate interplay between genetic predispositions and environmental influences highlights the complexity of brain plasticity and its impact on behavior throughout the lifespan.

 

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