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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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Pro-Survival And Pro-Death Molecular Events Downstream Of NMDA Receptor Activity

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Dr. Rishabh Pathak

Pro-survival and pro-death molecular events downstream of NMDA receptor activity play a crucial role in determining the fate of neurons in the central nervous system. Here are key insights into the molecular events associated with both pro-survival and pro-death signaling pathways following NMDA receptor activation:


1.      Pro-Survival Pathways:

o    Akt (Protein Kinase B) Pathway: Activation of NMDA receptors can lead to the activation of the Akt pathway, which promotes cell survival by inhibiting apoptosis and regulating various cellular processes.

o Brain-Derived Neurotrophic Factor (BDNF) Signaling: NMDA receptor activation can induce the release of BDNF, a neurotrophic factor that promotes neuronal survival, growth, and differentiation.

oCREB (cAMP Response Element-Binding Protein) Activation: NMDA receptor-mediated activation of CREB can regulate the expression of genes involved in cell survival and synaptic plasticity.

2.     Pro-Death Pathways:

o    Calcium Overload: Excessive activation of NMDA receptors can lead to an influx of calcium ions, triggering excitotoxicity and cell death pathways.

o    Mitochondrial Dysfunction: Calcium overload and excitotoxicity can disrupt mitochondrial function, leading to the release of pro-apoptotic factors and activation of cell death pathways.

o    Activation of Caspases: NMDA receptor-mediated excitotoxicity can activate caspases, a family of proteases that play a central role in apoptotic cell death.

3.     Role of Glutamate Excitotoxicity:

oProlonged activation of NMDA receptors by glutamate can lead to excitotoxicity, a process where excessive glutamate signaling results in neuronal damage and cell death.

oExcitotoxicity is associated with the dysregulation of calcium homeostasis, mitochondrial dysfunction, oxidative stress, and activation of pro-apoptotic pathways.

4.    Neuroprotective Strategies:

o  Targeting pro-survival pathways and modulating NMDA receptor activity through pharmacological agents or neuroprotective factors can help mitigate excitotoxicity and promote neuronal survival.

o    Strategies aimed at reducing calcium influx, enhancing antioxidant defenses, and promoting cell survival signaling pathways are under investigation for their potential neuroprotective effects.

Understanding the balance between pro-survival and pro-death molecular events downstream of NMDA receptor activity is essential for developing therapeutic interventions to protect neurons from excitotoxic damage and promote neuronal survival in various neurological conditions.

 

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