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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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PV Circuits

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Dr. Rishabh Pathak

PV circuits refer to neural circuits in the brain that are characterized by the presence of parvalbumin (PV)-expressing interneurons. Parvalbumin is a calcium-binding protein found in a specific subtype of inhibitory interneurons that play a crucial role in regulating neural activity, maintaining excitation-inhibition balance, and modulating network dynamics. Here are key points about PV circuits:


1.     Inhibitory Interneurons: PV-expressing interneurons are a subtype of inhibitory neurons in the brain that release the neurotransmitter gamma-aminobutyric acid (GABA). These interneurons play a key role in controlling the activity of excitatory neurons by providing inhibitory input and regulating the timing and synchronization of neural firing.


2. Fast-Spiking Properties: PV interneurons are known for their fast-spiking properties, meaning they can generate action potentials at high frequencies with rapid precision. This characteristic allows PV interneurons to efficiently inhibit the activity of excitatory neurons and contribute to the generation of gamma oscillations, which are important for information processing and cognitive functions.


3.     Synchronization and Oscillations: PV circuits are involved in the generation and synchronization of neural oscillations, particularly in the gamma frequency range (30-80 Hz). Gamma oscillations are associated with various cognitive processes, including attention, sensory perception, memory encoding, and motor coordination. PV interneurons help coordinate the timing of neural activity within and across brain regions.


4.     Role in Plasticity: PV circuits play a critical role in synaptic plasticity, the ability of synapses to strengthen or weaken in response to activity. By providing precise and temporally coordinated inhibition, PV interneurons help shape the plasticity of neural circuits, regulate the balance between excitation and inhibition, and support learning and memory processes.


5.     Implications for Neurological Disorders: Dysregulation of PV circuits has been implicated in various neurological and psychiatric disorders, including epilepsy, schizophrenia, autism spectrum disorders, and mood disorders. Alterations in PV interneuron function can disrupt neural network dynamics, lead to imbalances in excitation-inhibition, and contribute to cognitive and behavioral symptoms.


In summary, PV circuits, characterized by the presence of PV-expressing interneurons, play a crucial role in regulating neural activity, maintaining excitation-inhibition balance, modulating network dynamics, and supporting cognitive functions. Understanding the function of PV circuits is essential for unraveling the complexities of brain function and developing targeted interventions for neurological disorders.

 

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