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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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Unilateral and Bilateral Injury

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Dr. Rishabh Pathak

Unilateral and bilateral brain injuries have distinct effects on brain function, recovery, and neural reorganization. Here is an overview of unilateral and bilateral brain injuries:


1.     Unilateral Injury:

§  Definition: Unilateral brain injury affects one hemisphere or a specific region of the brain, leading to functional deficits in the contralateral side of the body or corresponding cognitive impairments.

§  Effects: Unilateral injuries often result in asymmetrical impairments, with preserved function in the non-injured hemisphere compensating for deficits in the injured hemisphere.

§  Recovery: Individuals with unilateral injuries may exhibit better recovery outcomes compared to those with bilateral injuries, as the intact hemisphere can support some degree of functional compensation and neural reorganization.

§  Neural Plasticity: Unilateral injuries can trigger neuroplastic changes in the intact hemisphere, including rewiring of neural circuits, increased synaptic connectivity, and functional adaptations to compensate for the lost functions.

2.     Bilateral Injury:

§  Definition: Bilateral brain injury affects both hemispheres or multiple brain regions, leading to more widespread and symmetrical deficits in motor, sensory, or cognitive functions.

§  Effects: Bilateral injuries often result in more severe and global impairments compared to unilateral injuries, as both hemispheres are compromised, limiting the brain's ability to compensate for lost functions.

§  Recovery: Individuals with bilateral injuries may face greater challenges in recovery and functional adaptation due to the bilateral nature of the damage, which can impact multiple cognitive domains and motor functions simultaneously.

§  Neural Plasticity: Bilateral injuries can still trigger some degree of neural plasticity and adaptive changes in the brain, but the extent of recovery and functional compensation may be more limited compared to unilateral injuries.

3.     Hemispheric Specialization:

§  Unilateral brain injuries can disrupt hemispheric specialization and functional lateralization, leading to alterations in cognitive processing, language functions, and motor control depending on the location and extent of the injury.

§  Bilateral brain injuries may result in more generalized cognitive impairments, affecting a wider range of functions such as attention, memory, executive functions, and emotional regulation due to the involvement of both hemispheres.

4.     Rehabilitation Considerations:

§  Rehabilitation strategies for unilateral and bilateral brain injuries may differ based on the extent of damage, functional deficits, and individual needs. Tailored interventions focusing on functional retraining, compensatory strategies, and cognitive rehabilitation are essential for optimizing outcomes in both types of injuries.

§  Multidisciplinary rehabilitation teams, including neurologists, neuropsychologists, therapists, and educators, play a crucial role in providing comprehensive care and support for individuals with unilateral and bilateral brain injuries, addressing physical, cognitive, and emotional challenges.

Understanding the differences between unilateral and bilateral brain injuries is essential for developing targeted interventions, rehabilitation plans, and support systems that address the unique needs and challenges associated with each type of injury, promoting optimal recovery, functional adaptation, and quality of life for individuals affected by brain injuries.

 

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