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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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Development of Prefrontal Cortex: Regions of PFC

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Dr. Rishabh Pathak


The prefrontal cortex (PFC) is a critical brain region associated with higher-order cognitive functions, including executive function, decision-making, social behavior, and emotional regulation. The PFC undergoes significant development across the lifespan, with distinct regions contributing to various aspects of cognitive control and behavior. Here are the key regions of the prefrontal cortex and their functions:

1.     Orbitofrontal Cortex (BA 11):

o    Location: Located in the ventromedial part of the PFC.

o  Function: The orbitofrontal cortex is involved in decision-making, reward processing, emotional regulation, and social behavior. It plays a role in evaluating the emotional and motivational significance of stimuli and guiding adaptive behavior based on reward outcomes.

2.     Ventrolateral PFC (BA 44, 45, 47):

o    Location: Situated in the lower lateral aspects of the PFC.

o Function: The ventrolateral PFC is associated with cognitive control, working memory, language processing, and response inhibition. It plays a role in maintaining task-relevant information, manipulating information, and regulating attention during complex cognitive tasks.

3.     Dorsolateral PFC (BA 9, 46):

o    Location: Located in the upper lateral aspects of the PFC.

o   Function: The dorsolateral PFC is involved in executive functions such as planning, problem-solving, cognitive flexibility, and goal-directed behavior. It plays a crucial role in working memory, mental manipulation of information, and strategic decision-making.

4.     Rostrolateral PFC (BA 10):

o    Location: Situated in the rostral part of the lateral PFC.

o Function: The rostrolateral PFC is associated with cognitive control, attentional processes, and multitasking. It plays a role in monitoring and coordinating complex cognitive operations, integrating information from multiple sources, and maintaining task sets for goal-directed behavior.

These regions of the prefrontal cortex work in concert to support various aspects of executive function and cognitive control. The hierarchical organization of the PFC allows for the integration of information, the regulation of behavior, and the coordination of complex cognitive processes. Understanding the functions of different regions within the prefrontal cortex provides insights into the neural basis of higher cognitive functions and the role of the PFC in adaptive behavior and decision-making processes.

 

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