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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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Balint's Syndrome

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Dr. Rishabh Pathak

Balint's syndrome is a rare neurological disorder characterized by a triad of visuospatial and visuomotor deficits. 

1.     Definition:

    • Balint's syndrome is a rare neurological condition that results from bilateral damage to the parieto-occipital region of the brain, particularly the posterior parietal and occipital lobes.
    • It is characterized by a triad of symptoms: simultanagnosia, optic ataxia, and ocular apraxia, which collectively impact visual perception and spatial awareness.

2.     Symptoms:

    • Simultanagnosia: Individuals with Balint's syndrome have difficulty perceiving more than one object at a time, leading to a restricted visual field and an inability to integrate multiple visual stimuli into a coherent whole.
    • Optic Ataxia: This symptom involves impaired coordination of visual input with motor actions, resulting in difficulties reaching or grasping objects accurately based on visual cues.
    • Ocular Apraxia: Ocular or gaze apraxia refers to the inability to voluntarily direct the eyes towards specific targets, leading to difficulties in shifting gaze or following objects smoothly.

3.     Causes:

    • Balint's syndrome is typically caused by bilateral lesions or damage to the parieto-occipital regions of the brain, often resulting from conditions such as stroke, traumatic brain injury, or neurodegenerative diseases.
    • The disruption of neural pathways involved in visual processing, spatial awareness, and eye movement control contributes to the characteristic symptoms of the syndrome.

4.     Diagnosis and Management:

    • Diagnosis of Balint's syndrome involves comprehensive neurological assessments, including visual field testing, eye movement evaluations, and neuropsychological testing to identify the specific deficits.
    • Management of Balint's syndrome focuses on rehabilitation strategies to improve visual perception, spatial orientation, and motor coordination through visual training, occupational therapy, and compensatory strategies to enhance daily functioning.

In summary, Balint's syndrome is a rare neurological disorder characterized by a triad of visuospatial and visuomotor deficits resulting from bilateral damage to the parieto-occipital regions of the brain. Understanding the symptoms, causes, and management of Balint's syndrome is essential for providing appropriate care and support to individuals affected by this complex condition.

 

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