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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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Plastic Changes are time dependent

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Dr. Rishabh Pathak

Plastic changes in the brain are indeed time-dependent, with the timing of experiences playing a crucial role in shaping neural plasticity and adaptive responses. Here are some key aspects of the time-dependent nature of plastic changes in the brain:


1.     Temporal Dynamics: The brain exhibits varying degrees of plasticity at different stages of development and throughout the lifespan. Critical periods, during which the brain is particularly sensitive to environmental influences, highlight the importance of timing in shaping neural circuits and functional connectivity.


2.     Sensitive Periods: Certain developmental stages are characterized by heightened plasticity, allowing the brain to undergo rapid structural and functional changes in response to sensory inputs, learning experiences, and environmental stimuli. Sensitive periods represent windows of opportunity for optimal learning and neural development.


3.     Experience-Dependent Effects: The effects of experiences on brain plasticity can vary depending on when they occur. For example, exposure to enriching environments or learning tasks at specific developmental stages may lead to distinct patterns of synaptic reorganization and neural connectivity compared to similar experiences at other times.


4.     Long-Term Consequences: Plastic changes that occur during critical periods or in response to significant experiences can have long-lasting effects on brain structure and function. Early-life experiences, in particular, can shape neural circuits and behavioral outcomes well into adulthood, highlighting the enduring impact of timing on brain plasticity.


5.     Adaptive Responses: The brain's ability to adapt to changing environmental demands is influenced by the timing of experiences. By responding to stimuli and challenges in a timely manner, the brain can optimize its neural architecture, synaptic connections, and functional organization to support adaptive behaviors and cognitive processes.


By recognizing the time-dependent nature of plastic changes in the brain, researchers can gain insights into the mechanisms underlying neural adaptation, learning, and memory formation. Understanding how the timing of experiences influences brain plasticity is essential for elucidating the dynamic interplay between environmental inputs and neural responses across different stages of development and throughout life.

 

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