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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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Experience Dependent changes tend to be focal.

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Dr. Rishabh Pathak

Experience-dependent changes in the brain tend to be focal, meaning they are often localized to specific brain regions or circuits in response to particular stimuli or environmental inputs. Here are some key points regarding the focal nature of experience-dependent changes:


1.   Specificity of Neural Plasticity: Experience-dependent changes in the brain are often specific to the neural circuits or regions that are actively engaged or stimulated by a particular experience. For example, learning a new motor skill may lead to structural changes in the motor cortex, while acquiring language skills may result in alterations in language-related brain areas.


2. Localization of Synaptic Modifications: Synaptic plasticity, which underlies learning and memory processes, is often concentrated in specific synapses within neural networks. These changes can occur in response to focused sensory inputs, cognitive tasks, or behavioral training, leading to selective modifications in synaptic strength and connectivity.


3. Regional Specialization: Different brain regions exhibit varying degrees of plasticity in response to experiences. While some regions may show robust changes in synaptic connectivity and neuronal morphology following specific stimuli, other areas may remain relatively stable or exhibit minimal alterations. This regional specialization reflects the functional diversity of the brain.


4. Task-Specific Adaptations: Experience-dependent changes are tailored to the demands of specific tasks or environmental challenges. Neural circuits involved in processing visual information, for instance, may undergo adaptive changes in response to visual stimuli, while circuits responsible for auditory processing may show distinct modifications in response to auditory inputs.


5.  Behavioral Relevance: The focal nature of experience-dependent changes ensures that neural adaptations are closely aligned with behavioral outcomes. By targeting specific brain regions or circuits, the brain can optimize its functional organization to support adaptive behaviors, learning, and memory.


Understanding the focal nature of experience-dependent changes in the brain provides insights into how neural plasticity is finely tuned to environmental demands and behavioral requirements. By focusing on specific brain regions and circuits, the brain can efficiently reorganize its structure and function in response to diverse experiences, ultimately shaping behavior and cognition in a context-dependent manner.

 

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