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...
At the functional organization level, plasticity in
the brain involves studying changes in the functional organization of neural
circuits and brain regions in response to various stimuli, experiences, or
tasks. Here is an overview of functional plasticity at the organizational
level:
1. Definition:
o Functional plasticity refers to the brain's ability
to reorganize neural networks, alter connectivity patterns, and adapt the
activation of specific brain regions in response to environmental demands,
learning experiences, or sensory inputs.
o It encompasses changes in brain activity, network
dynamics, and information processing that support adaptive behaviors and
cognitive functions.
2. Neural Reorganization:
o Functional plasticity involves the reorganization of
neural circuits, including changes in synaptic strength, connectivity, and
activity patterns, to optimize brain function in different contexts.
o Neural reorganization can occur in response to
learning, sensory stimulation, motor tasks, cognitive challenges, or
environmental changes.
3. Adaptive Responses:
o The brain exhibits functional plasticity to adapt to
new learning tasks, recover from injuries, compensate for deficits, and
optimize performance in response to changing environmental demands.
o Adaptive responses at the functional level involve
dynamic adjustments in neural activity, network connectivity, and information
processing strategies.
4. Neuroimaging Techniques:
o Functional neuroimaging techniques, such as fMRI,
PET, EEG, and MEG, are used to study changes in brain activity and functional
connectivity associated with functional plasticity.
o These imaging methods provide insights into how
neural circuits are recruited, synchronized, and modulated during different
cognitive tasks, sensory processing, or behavioral states.
5. Plasticity Mechanisms:
o Synaptic plasticity mechanisms, such as long-term
potentiation (LTP) and long-term depression (LTD), play a crucial role in
shaping functional plasticity by modifying synaptic efficacy and neural circuit
dynamics.
o Changes in neurotransmitter release, receptor
expression, and synaptic connectivity contribute to the adaptive reorganization
of functional brain networks.
6. Cognitive Flexibility:
o Functional plasticity supports cognitive
flexibility, the ability to switch between different tasks, strategies, or
mental sets, by facilitating the dynamic reconfiguration of neural circuits and
cognitive processes.
o Cognitive flexibility is essential for
problem-solving, decision-making, creativity, and adaptive behavior in complex
and changing environments.
By investigating functional plasticity at the
organizational level, researchers can uncover the neural mechanisms underlying
adaptive behaviors, cognitive functions, and brain resilience, providing
insights into how the brain dynamically reorganizes to meet the challenges of
everyday life and recover from perturbations.
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