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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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LPFC Functions

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Dr. Rishabh Pathak

The lateral prefrontal cortex (LPFC) plays a crucial role in various cognitive functions, particularly those related to executive control, working memory, decision-making, and goal-directed behavior. Here are key functions associated with the lateral prefrontal cortex:

1.     Executive Functions:

o    The LPFC is central to executive functions, which encompass higher-order cognitive processes involved in goal setting, planning, problem-solving, cognitive flexibility, and inhibitory control.

o   It is responsible for coordinating and regulating other brain regions to support complex cognitive tasks, such as task switching, attentional control, and response inhibition, essential for adaptive behavior in changing environments.

2.     Working Memory:

o   The LPFC is critical for working memory processes, which involve the temporary storage and manipulation of information to guide behavior and decision-making.

o  It supports the maintenance of task-relevant information, updating of information in real-time, and the integration of multiple sources of information to facilitate cognitive tasks requiring active processing.

3.     Cognitive Flexibility:

o    Cognitive flexibility, the ability to adapt cognitive strategies in response to changing demands or environmental cues, relies on the LPFC for shifting between tasks, rules, or mental sets.

o  The LPFC is involved in updating cognitive representations, inhibiting prepotent responses, and facilitating the transition between different cognitive processes to optimize performance in dynamic situations.

4.     Decision-Making:

o    The LPFC contributes to decision-making processes by integrating sensory information, evaluating potential outcomes, and selecting appropriate actions based on internal goals and external cues.

o  It plays a role in assessing risks and rewards, considering long-term consequences, and resolving conflicts between competing options to make optimal decisions in uncertain or complex situations.

5.     Goal-Directed Behavior:

o    Goal-directed behavior, the ability to pursue and achieve desired outcomes through planning and self-regulation, relies on the LPFC for setting goals, monitoring progress, and adjusting strategies as needed.

o   The LPFC supports the implementation of action plans, the inhibition of irrelevant information or impulses, and the maintenance of goal-relevant information to guide behavior towards successful goal attainment.

6.     Emotion Regulation:

o    While traditionally associated with cognitive functions, the LPFC also plays a role in emotion regulation by modulating emotional responses, integrating emotional information with cognitive processes, and exerting top-down control over affective states.

o   Dysfunction in the LPFC can lead to difficulties in emotion regulation, impulsivity, and emotional lability, highlighting its involvement in balancing cognitive control with emotional processing.

Understanding the diverse functions of the lateral prefrontal cortex provides insights into its contributions to cognitive control, decision-making, working memory, and goal-directed behavior. The LPFC's role in executive functions, cognitive flexibility, decision-making processes, and emotion regulation underscores its significance in supporting adaptive behavior and complex cognitive operations in various contexts.

 

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