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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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Explain the functions of the anterior cingulate cortex and lateral prefrontal cortex in relation to brain development?

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Dr. Rishabh Pathak

The anterior cingulate cortex (ACC) and lateral prefrontal cortex (LPFC) are two key regions of the brain that play critical roles in various cognitive functions and are integral to brain development. Here is an overview of their functions in relation to brain development:


1.     Anterior Cingulate Cortex (ACC):

o    Emotional Regulation: The ACC is involved in emotional regulation and processing. It plays a role in monitoring emotional responses, detecting errors, and regulating emotional reactions to stimuli.

o    Cognitive Control: The ACC is crucial for cognitive control processes such as attention, decision-making, conflict monitoring, and response inhibition. It helps in coordinating cognitive functions and adjusting behavior based on task demands.

o    Social Cognition: The ACC is implicated in social cognition, empathy, and theory of mind. It contributes to understanding others' emotions, intentions, and mental states.

o    Brain Development: The ACC undergoes developmental changes across the lifespan, with significant maturation during adolescence and into adulthood. Its structural and functional development is linked to improvements in cognitive control and emotional regulation.

2.     Lateral Prefrontal Cortex (LPFC):

o    Executive Functions: The LPFC is associated with higher-order cognitive functions known as executive functions. These include working memory, cognitive flexibility, planning, decision-making, and goal-directed behavior.

o    Inhibition and Control: The LPFC plays a crucial role in inhibitory control, allowing individuals to suppress irrelevant information, resist impulses, and focus on task-relevant stimuli. It is essential for self-regulation and goal-directed behavior.

o    Working Memory: The LPFC is involved in working memory processes, which enable the temporary storage and manipulation of information for cognitive tasks. It supports the maintenance and updating of information in the mind.

o    Brain Development: The LPFC undergoes protracted development, with structural and functional changes occurring throughout childhood, adolescence, and into adulthood. Maturation of the LPFC is associated with improvements in executive functions and cognitive control.

Both the ACC and LPFC are critical for cognitive, emotional, and social functioning, and their development is closely linked to the maturation of higher-order cognitive processes. Understanding the roles of these brain regions in brain development provides insights into how cognitive abilities evolve across different stages of life.

 

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