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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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Lateral Prefrontal Cortex Circuit development

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Dr. Rishabh Pathak

The development of the lateral prefrontal cortex (PFC) circuitry is a complex and dynamic process that undergoes significant changes across childhood, adolescence, and into adulthood. Here are key aspects of lateral PFC circuit development:


1.     Structural Maturation:

o    Synaptic Pruning: During early development, there is an overproduction of synapses in the PFC, followed by a process of synaptic pruning that refines neural connections. This pruning helps to eliminate unnecessary or weak connections while strengthening important pathways, enhancing the efficiency of information processing.

o   Myelination: Myelination, the process of insulating axons with myelin sheaths, continues throughout childhood and adolescence, improving the speed and efficiency of neural communication within the PFC circuitry.

o   Cortical Thickness: Changes in cortical thickness in the PFC reflect ongoing maturation and synaptic reorganization, with different regions showing varying rates of development during different developmental stages.

2.     Functional Connectivity:

o   Intra- and Inter-regional Connections: The lateral PFC is involved in integrating information from various brain regions, including sensory areas, limbic structures, and other prefrontal regions. The development of functional connectivity within the PFC circuitry allows for coordinated processing of cognitive and emotional information.

o   Network Development: As children and adolescents engage in cognitive tasks and executive functions, the connectivity between the lateral PFC and other brain regions involved in attention, working memory, and decision-making strengthens, supporting the development of efficient neural networks.

3.     Cognitive Control Development:

o    Executive Function Maturation: The lateral PFC is critical for executive functions such as working memory, cognitive flexibility, and inhibitory control. The development of these functions is associated with changes in PFC circuitry, including increased activation patterns, improved connectivity, and enhanced coordination with other brain regions.

o    Task-Specific Activation: Studies have shown that as individuals mature, there is a shift towards more efficient and specialized activation patterns in the lateral PFC during cognitive tasks, reflecting the refinement of neural circuits and the optimization of cognitive processes.

4.     Plasticity and Experience:

o Environmental Influence: Environmental factors, such as cognitive stimulation, social interactions, and educational experiences, play a crucial role in shaping the development of lateral PFC circuitry. Enriched environments can promote synaptic connectivity, neural plasticity, and cognitive skill acquisition.

o    Developmental Trajectories: Individual differences in lateral PFC circuit development can be influenced by genetic factors, early experiences, and ongoing learning opportunities. These factors contribute to the diverse trajectories of cognitive development observed across individuals.

Understanding the structural and functional changes in lateral PFC circuitry during development provides insights into the neural mechanisms underlying cognitive control, decision-making, and adaptive behavior across different stages of life. The maturation of PFC circuits supports the refinement of executive functions and the integration of cognitive and emotional processes, contributing to the complex interplay of brain networks involved in goal-directed behavior and self-regulation.

 

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