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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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Towards A Molecular Understanding Of The Molecular Identity Of Oligodendrocytes

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Dr. Rishabh Pathak

Oligodendrocytes are a type of glial cell in the central nervous system that play a crucial role in producing myelin, the insulating sheath that surrounds neuronal axons. Understanding the molecular identity of oligodendrocytes is essential for unraveling their function in myelination and their involvement in neurological disorders. Here are key insights towards a molecular understanding of the identity of oligodendrocytes:


1.      Transcription Factors:

o    Transcription factors such as Olig1, Olig2, Sox10, and Nkx2.2 are critical for the specification and differentiation of oligodendrocyte lineage cells from neural progenitors.

o Olig2, in particular, is considered a master regulator of oligodendrocyte development and is essential for oligodendrocyte specification and maturation.

2.     Myelin-Related Genes:

o Oligodendrocytes express a range of genes that are essential for myelin formation and maintenance, including proteolipid protein (PLP), myelin basic protein (MBP), and myelin-associated glycoprotein (MAG).

o  These myelin-related genes are regulated by specific transcription factors and signaling pathways that control oligodendrocyte differentiation and myelination.

3.     Signaling Pathways:

o Several signaling pathways, such as the Notch, Wnt, and Sonic Hedgehog pathways, play crucial roles in regulating oligodendrocyte development and myelination.

o Growth factors like platelet-derived growth factor (PDGF) and insulin-like growth factor-1 (IGF-1) are important for oligodendrocyte proliferation and survival.

4.    Epigenetic Regulation:

oEpigenetic mechanisms, including DNA methylation, histone modifications, and non-coding RNAs, play a significant role in controlling gene expression during oligodendrocyte development and myelination.

o Epigenetic changes contribute to the transition of oligodendrocyte progenitor cells to mature myelinating oligodendrocytes.

5.     Single-Cell Transcriptomics:

o    Recent advances in single-cell transcriptomic analysis have provided insights into the heterogeneity of oligodendrocyte populations and their gene expression profiles in the brain.

o    Single-cell studies have revealed subpopulations of oligodendrocytes with distinct molecular signatures and functional roles in myelination and remyelination.

By integrating knowledge of transcription factors, myelin-related genes, signaling pathways, epigenetic regulation, and single-cell transcriptomics, researchers are advancing towards a comprehensive molecular understanding of the identity and function of oligodendrocytes in the central nervous system. This knowledge is crucial for developing targeted therapies for demyelinating disorders and promoting remyelination in neurological diseases.

 

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