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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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Patterns of Change in Experience and the Brain

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Dr. Rishabh Pathak

The relationship between experience and the brain is characterized by dynamic patterns of change that reflect the impact of environmental stimuli, learning, and behavioral interactions on neural structure and function. Here are key patterns of change in the relationship between experience and the brain:


1.     Sensitive Periods:

o    Early Development: Experience plays a crucial role during sensitive periods in early development when the brain is highly responsive to environmental input. These critical periods are characterized by rapid and efficient learning, such as language acquisition, sensory processing, and social interactions.

o    Neural Plasticity: During sensitive periods, the brain exhibits heightened neural plasticity, allowing for the formation of synaptic connections and neural circuits in response to specific experiences. This plasticity enables the brain to adapt to environmental stimuli and optimize cognitive development.

2.     Experience-Expectant vs. Experience-Dependent Processes:

o    Environmental Information: Experience- expectant processes involve storing environmental information that is expected to be present in the typical environment, such as motion or visual contrasts. These processes rely on the overgeneration of synaptic connections early in life, with synaptic pruning refining connections based on experience.

o    Individual Learning: Experience-dependent processes store information specific to the individual, such as the location of resources or personal experiences. These processes involve the formation of new synaptic connections in response to unique learning occasions, allowing for individualized adaptations based on personal experiences.

3.     Neural Reorganization:

o    Synaptic Pruning: Experience shapes the developing brain through synaptic pruning, where unused or less relevant synaptic connections are eliminated while strengthening and maintaining connections that are frequently activated. This process refines neural circuits and optimizes brain function based on experience.

o    Adaptive Changes: Neural reorganization in response to experience allows the brain to adapt to changing environmental demands and learning opportunities. The formation of new synaptic connections and the refinement of existing circuits support adaptive behaviors and cognitive flexibility.

4.     Lifelong Learning:

o    Continual Impact: Throughout life, experiences continue to influence brain structure and function, contributing to ongoing learning and cognitive development. Learning new skills, acquiring knowledge, and engaging in novel experiences can lead to structural changes in the brain at any age.

o    Cognitive Health: Active engagement with the world mentally and physically promotes cognitive health and neurological well-being in later stages of life. Lifelong learning and cognitive stimulation support brain plasticity, resilience, and cognitive vitality across the lifespan.

Understanding the patterns of change in the relationship between experience and the brain highlights the dynamic nature of neural development, the role of environmental influences in shaping brain structure, and the lifelong impact of experiences on cognitive function and behavioral adaptation. These patterns underscore the importance of enriched environments, learning opportunities, and social interactions in promoting healthy brain development and cognitive well-being.

 

 

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