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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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Synaptic Dysfunction in Mental Disorders and Addiction

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Dr. Rishabh Pathak

Synaptic dysfunction plays a critical role in the pathophysiology of mental disorders and addiction. Here are key insights into how synaptic dysfunction contributes to these conditions:


1.      Mental Disorders:

oSynaptic Plasticity Alterations: Disruption of synaptic plasticity, including long-term potentiation (LTP) and long-term depression (LTD), can impact learning, memory, and cognitive functions in mental disorders.

oGlutamatergic System Dysfunction: Dysregulation of glutamatergic neurotransmission, particularly involving NMDA receptors, AMPA receptors, and metabotropic glutamate receptors, is implicated in conditions like schizophrenia, depression, and bipolar disorder.

oSynaptic Pruning: Abnormal synaptic pruning, the process of eliminating unnecessary synapses during brain development, has been linked to conditions such as autism spectrum disorders and schizophrenia.

oNeurotransmitter Imbalance: Alterations in neurotransmitter systems, including dopamine, serotonin, and GABA, can disrupt synaptic communication and contribute to the pathogenesis of various mental disorders.

2.     Addiction:

o Synaptic Plasticity Changes: Drug addiction is associated with alterations in synaptic plasticity in brain regions involved in reward processing, leading to persistent changes in synaptic strength and connectivity.

oDopaminergic Signaling: Drugs of abuse often target the mesolimbic dopamine system, altering synaptic transmission and reinforcing addictive behaviors.

oNeuroadaptations: Chronic drug exposure induces neuroadaptations at the synaptic level, including changes in glutamatergic and GABAergic signaling, which contribute to the development of addiction.

o  Synaptic Homeostasis: The concept of synaptic homeostasis, where neurons adjust synaptic strength to maintain overall stability, is disrupted in addiction, leading to maladaptive synaptic changes.

3.     Therapeutic Implications:

oTargeting synaptic dysfunction through pharmacological interventions, neuromodulation techniques, and behavioral therapies holds promise for treating mental disorders and addiction.

oStrategies aimed at restoring synaptic plasticity, rebalancing neurotransmitter systems, and modulating synaptic strength are being explored for their therapeutic potential.

oAdvancements in understanding the molecular mechanisms underlying synaptic dysfunction in these conditions are driving the development of novel treatment approaches that target specific synaptic pathways.

By elucidating the role of synaptic dysfunction in mental disorders and addiction, researchers aim to uncover novel therapeutic targets and interventions that can restore normal synaptic function and improve outcomes for individuals affected by these conditions.

 

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