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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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RB/E2F pathway regulates neurogenesis by modulating the composition of Neural Precursor population

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Dr. Rishabh Pathak

The Retinoblastoma (Rb)/E2F pathway plays a crucial role in regulating neurogenesis by modulating the composition of the neural precursor population. Here are key points regarding how the Rb/E2F pathway influences neurogenesis:


1.      Neural Precursor Cell Fate:

o    Regulation of Cell Cycle Exit: The Rb/E2F pathway controls the transition of neural precursor cells from proliferation to differentiation by promoting cell cycle exit. Activation of the Rb protein leads to the repression of E2F transcription factors, which are essential for driving cell cycle progression. By inhibiting E2F activity, Rb facilitates the exit of neural precursor cells from the cell cycle, allowing them to undergo differentiation.

o    Maintenance of Terminal Differentiation: Proper functioning of the Rb/E2F pathway is essential for maintaining terminal differentiation of neural precursor cells. Disruption of Rb-mediated regulation can result in defects in neuronal maturation and migration, leading to abnormalities in the composition of the neural precursor population.

2.     DLX Transcription Factors:

o    Regulation of DLX Genes: The Rb/E2F pathway modulates the expression of DLX homeodomain genes, particularly Dlx2, which are critical for ventral telencephalic development and the generation of specific interneuron subtypes. Rb interacts with regulatory regions of the Dlx1/Dlx2 locus, including enhancers and promoters, to control DLX gene expression. E2F functional sites act as repressor elements in these regions, influencing the transcriptional activity of DLX genes.

o  Role in Neuronal Differentiation: By directly regulating DLX gene expression, the Rb/E2F pathway contributes to the differentiation and specification of neural precursor cells into distinct neuronal subtypes. Dysregulation of DLX genes due to Rb pathway dysfunction can impact the diversity and maturation of the neural precursor population.

3.     Cell Cycle Dynamics:

o Coordination of Proliferation and Differentiation: The Rb/E2F pathway coordinates the balance between proliferation and differentiation in neural precursor cells. By controlling the expression of key transcription factors and cell cycle regulators, Rb ensures that neural precursors appropriately exit the cell cycle and commit to neuronal differentiation pathways.

o Temporal Progression of Neurodevelopment: Through its interactions with downstream targets such as Znf238, the Rb/E2F pathway orchestrates the temporal progression of neurodevelopment. Negative feedback loops mediated by Rb/E2F-regulated factors help consolidate cell cycle exit and regulate the migration and differentiation of newborn cortical neurons.

In summary, the Rb/E2F pathway plays a pivotal role in regulating neurogenesis by modulating the composition of the neural precursor population. By controlling cell cycle exit, maintaining terminal differentiation, regulating DLX transcription factors, and coordinating proliferation and differentiation processes, the Rb/E2F pathway influences the generation and maturation of neurons during brain development. Understanding the mechanisms by which the Rb/E2F pathway shapes the neural precursor population provides insights into neurodevelopmental processes and potential therapeutic targets for neurodevelopmental disorders.

 

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