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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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General Types of Brain Plasticity

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Dr. Rishabh Pathak

Brain plasticity refers to the brain's ability to reorganize itself by forming new neural connections in response to learning, experience, or injury. There are several general types of brain plasticity that occur at different levels of analysis, ranging from behavior to molecules. Here is an overview of the general types of brain plasticity:


1.     Behavioral Plasticity:

o   Definition: Behavioral plasticity refers to changes in an individual's behavior in response to environmental stimuli, learning experiences, or alterations in neural circuits.

o    Examples: Behavioral plasticity can manifest as changes in motor skills, cognitive abilities, emotional responses, and adaptive behaviors in various contexts.

o Neuroplasticity: Behavioral changes are often accompanied by corresponding changes in neural circuits and synaptic connections, reflecting the brain's adaptive capacity.

2.     Functional Plasticity:

o  Definition: Functional plasticity involves the reorganization of brain functions and neural networks to compensate for damage, enhance performance, or adapt to new tasks or environments.

o    Neural Reorganization: Functional plasticity may involve the recruitment of alternative brain regions, changes in neural activation patterns, or the development of new cognitive strategies to support functional recovery or adaptation.

3.     Structural Plasticity:

o    Definition: Structural plasticity refers to changes in the physical structure of the brain, including alterations in dendritic morphology, synaptic connectivity, and neurogenesis.

o    Synaptic Remodeling: Structural plasticity encompasses processes such as dendritic growth, synaptogenesis, synaptic pruning, and myelination, which shape neural circuits and optimize brain function.

o    Experience-Dependent Changes: Structural plasticity is influenced by sensory experiences, learning activities, environmental enrichment, and other factors that drive the remodeling of neural connections.

4.     Molecular Plasticity:

o    Definition: Molecular plasticity involves changes in gene expression, protein synthesis, neurotransmitter release, and synaptic signaling pathways that underlie synaptic plasticity and neural adaptation.

o    Long-Term Changes: Molecular plasticity mechanisms, such as long-term potentiation (LTP) and long-term depression (LTD), mediate enduring changes in synaptic strength and neuronal connectivity in response to learning and experience.

5.     Developmental Plasticity:

o    Definition: Developmental plasticity refers to the brain's capacity for adaptive changes during different stages of development, including neurogenesis, cell migration, synaptogenesis, and myelination.

o    Critical Periods: Developmental plasticity is particularly prominent during critical periods of brain development when neural circuits are highly malleable and sensitive to environmental influences.

o    Impact of Experience: Early experiences and environmental factors can have lasting effects on brain development and functional outcomes through developmental plasticity mechanisms.

Understanding the various types of brain plasticity provides insights into how the brain adapts, learns, and responds to changes in the environment, highlighting the dynamic nature of neural circuits and the brain's capacity for reorganization throughout life.

 

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