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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 relation between structural changes and behaviour

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Dr. Rishabh Pathak

The relationship between structural changes in the brain and behavior is a complex and dynamic interplay that underscores the neural basis of cognitive functions and behaviors. Here are some key patterns of change in the relationship between structural changes in the brain and behavior:


1.     Neuroplasticity:

o    Experience-Dependent Changes: Structural changes in the brain, such as synaptic pruning, dendritic growth, and myelination, are influenced by environmental stimuli and experiences. This neuroplasticity allows the brain to adapt and reorganize in response to learning, practice, and environmental demands.

o    Behavioral Adaptation: Changes in brain structure support behavioral adaptation by optimizing neural circuits for specific tasks or skills. For example, learning a new language may lead to structural changes in language-related brain regions, enhancing language proficiency and fluency.

2.     Functional Specialization:

o    Localization of Function: Structural changes in specific brain regions are associated with the development of functional specialization. Different brain areas are responsible for distinct cognitive functions, such as the prefrontal cortex for executive functions and the temporal lobe for memory processing.

o    Behavioral Correlates: Changes in brain structure in these specialized regions are linked to corresponding changes in behavior. For instance, alterations in the volume or connectivity of the hippocampus may impact memory formation and retrieval abilities.

3.     Developmental Trajectories:

o    Age-Related Changes: Structural changes in the brain follow developmental trajectories across the lifespan. During childhood and adolescence, ongoing maturation of neural circuits supports the acquisition of cognitive skills and the refinement of behaviors.

o    Behavioral Maturation: Changes in brain structure contribute to the maturation of behaviors, such as improved impulse control, decision-making, and social cognition. The development of executive functions is closely linked to the structural changes in the prefrontal cortex.

4.     Individual Differences:

o    Variability in Brain-Behavior Relationships: Individual differences in brain structure can influence behavioral outcomes. Variations in gray matter volume, white matter integrity, or connectivity patterns may underlie differences in cognitive abilities, emotional regulation, and personality traits.

o    Behavioral Plasticity: Behavioral flexibility and adaptability are supported by the brain's capacity to undergo structural changes in response to new challenges or experiences. This plasticity enables individuals to learn, unlearn, and relearn behaviors based on changing environmental demands.

Understanding the patterns of change in the relationship between structural changes in the brain and behavior provides insights into the neural mechanisms underlying cognitive functions, emotional processing, and adaptive behaviors. The dynamic interplay between brain structure and behavior highlights the intricate connections between neural architecture and functional outcomes in diverse cognitive and behavioral domains.

 

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