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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 the Neural Circuits are useful to check the Prognosis of Neural Plasticity?

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Dr. Rishabh Pathak

 


Neural circuits are intricate networks of interconnected neurons that play a crucial role in determining the prognosis of neural plasticity, which refers to the brain's ability to reorganize itself by forming new neural connections in response to learning, experience, or injury. Understanding how neural circuits function and interact is essential for evaluating the brain's capacity for plasticity and recovery in various scenarios. Here's how neural circuits contribute to assessing neural plasticity:


1. Functional Connectivity: Neural circuits provide a structural framework for understanding how different brain regions communicate and work together. By studying the organization and information flow within neural circuits, researchers can assess the brain's potential for adapting and forming new connections in response to stimuli or experiences.

2.  Plasticity Mechanisms: Neural circuits are central to the mechanisms underlying neural plasticity, such as synaptic strengthening or pruning. By examining the activity and connections within specific circuits, researchers can gauge the brain's ability to adapt, rewire, and modify its neural pathways in response to changes in the environment or internal stimuli.

3. Recovery from Injury: Following brain injury or neurological disorders, the brain's ability to reorganize neural circuits is crucial for recovery. Evaluating the integrity and flexibility of neural circuits can help predict the extent to which the brain can recover function and adapt to new conditions, highlighting the importance of neural plasticity in rehabilitation and recovery processes.

4. Neuroimaging Techniques: Advanced neuroimaging technologies like functional magnetic resonance imaging (fMRI) and diffusion tensor imaging (DTI) allow researchers to visualize and map neural circuits in living organisms. By monitoring changes in circuit connectivity over time, clinicians can assess the brain's potential for plasticity and recovery, providing valuable insights for treatment planning and monitoring progress.

5.   Intervention Strategies: Knowledge of the status of neural circuits can guide the development of targeted intervention strategies aimed at enhancing neural plasticity. By influencing activity within specific circuits through therapies or stimulation techniques, clinicians can promote adaptive changes in the brain, potentially improving outcomes for individuals with brain injuries or neurological conditions.


By leveraging our understanding of neural circuits and their role in neural plasticity, researchers and clinicians can better predict outcomes, design effective treatments, and optimize rehabilitation strategies for individuals facing brain injuries or neurological challenges. This comprehensive approach underscores the importance of neural circuits in assessing and promoting brain plasticity and recovery.

 

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