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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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Epigenetics and Histone Deacetylases in Neurodegenerative Disease, Aging, and CNS Repair

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Dr. Rishabh Pathak

Epigenetic modifications, including histone acetylation, play a critical role in gene expression regulation, cellular differentiation, and various physiological processes in the central nervous system (CNS). Histone deacetylases (HDACs) are enzymes that modulate histone acetylation levels, thereby influencing chromatin structure and gene transcription. Here is an overview of the involvement of epigenetics and HDACs in neurodegenerative diseases, aging, and CNS repair:


1.      Epigenetic Regulation in Neurodegenerative Diseases:

o    Alzheimer's Disease (AD):

§Epigenetic alterations, including changes in histone acetylation patterns, have been implicated in AD pathogenesis.

§Dysregulation of HDAC activity can lead to aberrant gene expression associated with AD pathology, such as amyloid beta accumulation and tau hyperphosphorylation.

o    Parkinson's Disease (PD):

§Epigenetic modifications, including histone acetylation changes, have been linked to PD pathophysiology.

§HDAC inhibitors have shown neuroprotective effects in preclinical models of PD by modulating gene expression and promoting neuronal survival.

o    Huntington's Disease (HD):

§  Altered histone acetylation levels and HDAC dysregulation have been observed in HD, contributing to transcriptional dysregulation and neuronal dysfunction.

§ Targeting HDACs with specific inhibitors has shown therapeutic potential in ameliorating HD-related phenotypes in experimental models.

2.     Epigenetic Changes in Aging:

o    Aging-Related Epigenetic Modifications:

§Aging is associated with global changes in epigenetic marks, including histone modifications, that impact gene expression patterns and cellular functions.

§Dysregulation of HDACs and histone acetylation dynamics during aging can contribute to age-related cognitive decline and neurodegenerative processes.

o    Role of HDACs in Aging:

§HDACs play a role in regulating longevity pathways, cellular senescence, and age-related gene expression changes in the CNS.

§Modulating HDAC activity through pharmacological interventions or genetic manipulation has been explored as a potential strategy to counteract age-related epigenetic alterations.

3.     Epigenetic Regulation in CNS Repair:

o    Neuroregeneration and Plasticity:

§Epigenetic mechanisms, including histone acetylation, are involved in regulating neurogenesis, synaptic plasticity, and axonal regeneration in the CNS.

§ HDAC inhibitors have been investigated for their potential to enhance CNS repair processes by promoting neuronal growth, synaptic connectivity, and functional recovery following injury or neurodegenerative insults.

Understanding the role of epigenetics and HDACs in neurodegenerative diseases, aging, and CNS repair provides insights into the molecular mechanisms underlying these processes and identifies potential therapeutic targets for intervention. Further research on the specific epigenetic modifications, HDAC isoforms, and regulatory pathways involved in these contexts may lead to the development of novel epigenetic-based therapies for neurological disorders and age-related CNS conditions.

 

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