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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 Deficits In Psychiatric Disorders

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Dr. Rishabh Pathak

Synaptic deficits are a common feature observed in various psychiatric disorders, contributing to the pathophysiology and symptoms associated with these conditions. Here are key insights into synaptic deficits in psychiatric disorders:


1.      Schizophrenia:

o Hypoconnectivity: Schizophrenia is characterized by synaptic hypoconnectivity, involving deficits in synaptic density, dendritic spine morphology, and synaptic protein expression in brain regions like the prefrontal cortex and hippocampus.

oGlutamatergic Dysfunction: Alterations in glutamatergic neurotransmission, including NMDA receptor hypofunction and disrupted synaptic plasticity, are implicated in schizophrenia pathogenesis.

o Synaptic Pruning Abnormalities: Dysregulation of synaptic pruning processes during neurodevelopment contributes to aberrant synaptic connectivity and cognitive impairments in schizophrenia.

2.     Depression:

o    Synaptic Atrophy: Depression is associated with synaptic atrophy, reduced synaptic density, and impaired synaptic plasticity in regions like the prefrontal cortex and hippocampus, affecting mood regulation and cognitive functions.

o    Neurotransmitter Imbalance: Dysregulation of monoaminergic neurotransmitters, such as serotonin and dopamine, can lead to synaptic deficits and altered synaptic transmission in depression.

oStress-Induced Changes: Chronic stress and elevated glucocorticoid levels associated with depression can impact synaptic structure and function, contributing to neuronal atrophy and synaptic loss.

3.     Bipolar Disorder:

o  Synaptic Dysfunction: Bipolar disorder is characterized by synaptic dysfunction, including alterations in synaptic plasticity mechanisms, neurotransmitter release, and dendritic spine morphology in brain regions like the amygdala and prefrontal cortex.

o    Excitatory/Inhibitory Imbalance: Imbalance between excitatory and inhibitory synaptic transmission, involving disruptions in glutamatergic and GABAergic signaling, is implicated in the pathophysiology of bipolar disorder.

o Circadian Rhythm Disruption: Dysregulation of circadian rhythms and clock genes can impact synaptic function and neuronal connectivity in individuals with bipolar disorder.

4.    Therapeutic Implications:

o  Targeting synaptic deficits through pharmacological interventions, cognitive-behavioral therapies, and neuromodulation techniques is a key focus in the treatment of psychiatric disorders.

o Strategies aimed at restoring synaptic plasticity, rebalancing neurotransmitter systems, and promoting neuroplasticity are being explored for their therapeutic potential in managing symptoms associated with synaptic deficits in psychiatric conditions.

By elucidating the synaptic deficits present in psychiatric disorders, researchers aim to develop novel treatment approaches that target specific synaptic pathways to restore normal synaptic function, improve neural connectivity, and alleviate symptoms in affected individuals.

 

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