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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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Anterior Cingulate Cortex Functions

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Dr. Rishabh Pathak

The anterior cingulate cortex (ACC) plays a crucial role in various cognitive and emotional functions, contributing to executive control, error monitoring, conflict resolution, and decision-making processes. Here are key functions associated with the anterior cingulate cortex:


1.     Error Monitoring:

o  The ACC is involved in detecting errors and signaling the need for adjustments in behavior. It generates the error-related negativity (ERN) component in event-related potentials (ERPs) when an individual realizes that an error has been committed.

o    Studies have shown that the ACC is sensitive to performance errors and is activated when discrepancies between expected and actual outcomes occur, leading to adaptive behavioral changes.

2.     Conflict Monitoring:

o    The ACC plays a role in monitoring conflicts between competing response options or cognitive demands. It helps in detecting and resolving conflicts to facilitate accurate and efficient decision-making.

o  Activation of the ACC is observed during tasks that require response inhibition, cognitive control, and overcoming interference from irrelevant information, indicating its involvement in conflict resolution processes.

3.     Performance Monitoring:

o    The ACC acts as a performance monitor, assessing task performance and signaling the need for adjustments in cognitive control. It evaluates the effectiveness of ongoing behavior and guides adaptive responses based on task requirements.

o    Changes in ACC activation patterns are associated with variations in task difficulty, error rates, and cognitive demands, reflecting its role in monitoring performance and regulating goal-directed behavior.

4.     Emotional Regulation:

o    The ACC is implicated in emotional processing and regulation, particularly in response to emotionally salient stimuli. It integrates emotional information with cognitive control processes to modulate affective responses and decision-making.

o    Dysfunction in the ACC has been linked to difficulties in emotion regulation, impulsivity, and risk-taking behavior, highlighting its role in balancing emotional reactivity with cognitive control.

5.     Developmental Changes:

o    Studies have shown that the ACC undergoes developmental changes across childhood and adolescence, with improvements in error monitoring, conflict resolution, and performance adjustments over time.

o    The maturation of the ACC is associated with enhanced executive function, cognitive control, and adaptive decision-making abilities, reflecting the dynamic development of this region during different stages of life.

Understanding the multifaceted functions of the anterior cingulate cortex provides insights into its contributions to cognitive control, emotional regulation, and adaptive behavior in various contexts. The ACC's role in error detection, conflict monitoring, performance evaluation, and emotion-cognition interactions underscores its significance in supporting goal-directed behavior and decision-making processes.

 

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