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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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The resting-state functional organization of the brain in blindness and sight recovery.

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Dr. Rishabh Pathak

 

Neuroplasticity, also known as brain plasticity, refers to the brain's ability to reorganize itself by forming new neural connections in response to learning, experience, or injury. Vision loss can have a profound impact on neuroplasticity in the brain, leading to adaptive changes in neural circuits and functional organization. Here are some ways in which neuroplasticity is affected by vision loss in the brain:

 

1. Cross-Modal Plasticity: In the absence of visual input, the brain may undergo cross-modal plasticity, where areas of the brain that were originally dedicated to processing visual information may become recruited for processing information from other sensory modalities, such as touch or hearing. This adaptive reorganization allows the brain to compensate for the loss of vision by enhancing processing in remaining sensory modalities.

2. Functional Reorganization: Vision loss can trigger functional reorganization in the brain, leading to changes in how different brain regions communicate and interact. For example, studies have shown that the visual cortex in blind individuals may become involved in processing non-visual tasks, such as language or spatial navigation. This reorganization reflects the brain's ability to adapt to the altered sensory environment.

3. Enhanced Sensory Processing: In some cases, vision loss can result in enhanced sensory processing in non-visual modalities. For example, blind individuals may exhibit heightened auditory or tactile abilities as a result of neuroplastic changes in the brain. This enhanced sensory processing reflects the brain's ability to allocate resources to remaining sensory modalities to compensate for the loss of vision.

4. Cortical Reorganization: Neuroplasticity in response to vision loss can involve changes in the structure and function of cortical areas involved in visual processing. Studies have shown that the organization of the visual cortex can be altered in blind individuals, with regions typically dedicated to visual processing being repurposed for processing non-visual information. This cortical reorganization reflects the brain's adaptive response to sensory deprivation.

5. Critical Period Effects: The timing of vision loss can influence the extent of neuroplastic changes in the brain. For example, individuals who experience blindness during the critical period of visual development may exhibit more pronounced neuroplasticity compared to those who lose vision later in life. This highlights the importance of early sensory experiences in shaping the functional organization of the brain.

 

Overall, vision loss can trigger a cascade of neuroplastic changes in the brain, leading to adaptive reorganization of neural circuits and functional networks. Understanding how neuroplasticity is affected by vision loss is crucial for developing interventions and rehabilitation strategies that harness the brain's adaptive capabilities to improve outcomes for individuals with visual impairments.

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