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...
A comprehensive model of prefrontal cortex (PFC)
functions integrates various cognitive processes and neural mechanisms
associated with executive function, cognitive control, decision-making, and
emotional regulation. Here is an overview of a model that captures the
complexity of PFC functions:
1. Thalamus and Amygdala:
o Quick Emotional Responses: The model posits that the thalamus and amygdala
generate rapid emotional response tendencies in reaction to stimuli.
2. Orbitofrontal Cortex:
o Evaluation and Reward Processing: The orbitofrontal cortex receives input from the
thalamus and amygdala and is involved in evaluating the emotional and
motivational significance of stimuli. It generates simple approach-avoidance
rules based on emotional valence and is crucial for learning to reverse these
rules in response to changing contexts.
3. Anterior Cingulate Cortex:
o Performance Monitoring: The anterior cingulate cortex acts as a
performance monitor, signaling the need for higher-level processing in the
lateral PFC when the initial response is inadequate. It is involved in error
detection, conflict monitoring, and adjusting cognitive control based on task
demands.
4. Lateral Prefrontal Cortex:
o Reprocessing and Rule Representation:
§ Ventrolateral PFC and Dorsolateral PFC: These regions are involved in reprocessing
information and representing rules at different levels of complexity. They
support the maintenance of task sets, working memory, and cognitive
flexibility.
§ Rostrolateral PFC: This region is responsible for explicit consideration of task sets and
coordinating complex cognitive operations. It integrates information from
multiple sources and supports strategic decision-making.
5. Information Processing:
o The model emphasizes the hierarchical organization
of the PFC, with different regions contributing to distinct aspects of
cognitive control, decision-making, and goal-directed behavior.
o The PFC integrates emotional, motivational, and
cognitive information to guide adaptive responses and regulate behavior in
dynamic environments.
6. Iterative Reprocessing:
o The model suggests that information processing in
the PFC involves iterative reprocessing of stimuli at multiple levels of
complexity, from basic emotional responses to higher-order cognitive rules and
strategies.
o This iterative reprocessing allows for the flexible
adaptation of behavior based on changing internal and external demands,
supporting adaptive decision-making and goal pursuit.
By incorporating the roles of different PFC regions
in emotional evaluation, cognitive control, and rule representation, this model
provides a framework for understanding the neural mechanisms underlying
executive function and adaptive behavior mediated by the prefrontal cortex.
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