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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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How Does RP Blindness Affect Functional Connectivity to V1 at Rest?

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Dr. Rishabh Pathak


 RP (Retinitis Pigmentosa) blindness can affect functional connectivity to V1 (primary visual cortex) at rest. Studies have shown that individuals with RP experience alterations in the functional connectivity patterns of the visual cortex, particularly V1, due to the progressive degeneration of retinal cells and the loss of visual input. Here is a summary of how RP blindness affects functional connectivity to V1 at rest based on the provided information:

 

1. Impact on Functional Connectivity: RP blindness is associated with changes in the functional connectivity of V1 at rest. Functional connectivity refers to the synchronized activity between different brain regions, reflecting the strength of neural communication and network organization. In individuals with RP, the connectivity patterns involving V1 may be altered compared to sighted individuals, indicating disruptions in the neural circuits associated with visual processing.

2. Altered Connectivity Patterns: Resting-state functional connectivity studies have revealed that individuals with RP exhibit differences in the connectivity of V1 with other brain regions during rest periods. These alterations may involve weakened or disrupted connections between V1 and regions involved in visual processing, somatosensory functions, and higher-level cognitive processing.

3. Reduced Connectivity Strength: RP blindness may lead to a reduction in the strength of functional connectivity between V1 and other cortical areas. Weaker connectivity between V1 and regions responsible for visual, somatosensory, and motor functions may reflect the impact of visual deprivation on the neural networks supporting visual processing and integration with other sensory modalities.

4. Specific Connectivity Changes: The altered functional connectivity to V1 in individuals with RP may involve regions associated with higher-level visual processing, somatosensory integration, motor functions, and parietal association cortex. These changes in connectivity patterns suggest a reorganization of neural circuits in response to the loss of visual input and the adaptive processing of non-visual sensory information.

5. Implications for Visual Processing: The disruptions in functional connectivity to V1 in RP blindness have implications for visual processing and the integration of sensory information in the absence of vision. Understanding how RP affects functional connectivity to V1 at rest can provide insights into the neural mechanisms underlying visual deprivation and the adaptive changes that occur in the brain to compensate for the loss of vision.

 

Overall, RP blindness can impact the functional connectivity of V1 at rest, reflecting the neural adaptations and reorganization that occur in response to visual deprivation. Studying these connectivity changes is essential for elucidating the effects of RP on the brain's network dynamics and for informing the development of interventions aimed at restoring visual function in individuals with retinal degenerative disorders.

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