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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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Excitation Inhibition Balance

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Dr. Rishabh Pathak

Excitation-inhibition balance refers to the equilibrium between excitatory and inhibitory neural activity in the brain. Maintaining a proper balance between excitation and inhibition is crucial for normal brain function, information processing, and neural network stability. Here are key points about excitation-inhibition balance:


1.   Excitatory Neurotransmission: Excitatory neurotransmitters, such as glutamate, promote the depolarization of neurons and the generation of action potentials. Excitatory signals facilitate neural communication and are essential for processes like learning, memory, and sensory perception.


2.  Inhibitory Neurotransmission: Inhibitory neurotransmitters, such as gamma-aminobutyric acid (GABA), counteract excitatory signals by hyperpolarizing neurons and reducing their likelihood of firing action potentials. Inhibition helps regulate neural activity, prevent excessive excitation, and maintain network stability.


3.     Role in Neural Circuits: The balance between excitation and inhibition is critical for the proper functioning of neural circuits. Imbalances, such as excessive excitation or reduced inhibition, can lead to hyperexcitability, seizures, cognitive deficits, and neurological disorders.


4.  Plasticity and Learning: Excitation-inhibition balance plays a key role in synaptic plasticity, the ability of synapses to strengthen or weaken in response to activity. Proper balance allows for adaptive changes in neural connectivity that underlie learning and memory. Disruptions in this balance can impair synaptic plasticity and cognitive function.


5.     Development and Critical Periods: Excitation-inhibition balance is particularly important during critical periods of brain development when neural circuits are forming and refining. Imbalances during these sensitive periods can have long-lasting effects on brain function and behavior.


6.  Clinical Implications: Dysregulation of excitation-inhibition balance has been implicated in various neurological and psychiatric disorders, including epilepsy, autism spectrum disorders, schizophrenia, and mood disorders. Therapeutic interventions targeting this balance, such as modulating neurotransmitter systems or enhancing inhibitory signaling, may offer potential treatments for these conditions.


In summary, excitation-inhibition balance is a fundamental aspect of neural function that ensures proper communication within the brain, supports synaptic plasticity and learning, and contributes to overall brain health. Maintaining this balance is essential for normal brain function and cognitive processes.

 

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