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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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Needle Spikes in Different Neurological Conditions

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Dr. Rishabh Pathak

Needle spikes, also known as occipital spikes of blindness, are primarily associated with visual impairment, but they can also be observed in various neurological conditions. 

1. Congenital Blindness

    • Primary Association: Needle spikes are most commonly seen in individuals with congenital blindness or severe visual impairment from early infancy. They are often benign and do not necessarily indicate the presence of epilepsy.
    • Retinopathy: The presence of needle spikes is particularly associated with retinopathy, such as retrolental fibroplasia, which is linked to cerebral pathology.

2. Epilepsy

    • Co-occurrence with Epileptic Disorders: While needle spikes are generally benign, they can occur in patients with epilepsy. In these cases, the presence of needle spikes may be associated with other interictal epileptiform discharges, indicating a potential risk for seizures.
    • Differentiation from Other Patterns: It is crucial to differentiate needle spikes from other types of interictal epileptiform discharges (IEDs), as the latter may suggest a higher likelihood of seizure activity.

3. Cerebral Pathologies

    • Cortical Dysplasia: Needle spikes may be observed in patients with cortical dysplasia, a condition that can lead to focal epilepsies. The presence of needle spikes in these patients may indicate underlying structural brain abnormalities.
    • Other Neurological Disorders: Needle spikes can also be seen in various neurological conditions that involve cerebral pathology, such as traumatic brain injury or developmental disorders, where visual impairment is present.

4. Developmental Disorders

    • Intellectual Disabilities: In children with intellectual disabilities or developmental delays, needle spikes may be present alongside other EEG abnormalities. The clinical significance in these cases can vary, and the presence of needle spikes may not always correlate with seizure activity.
    • Visual Afferent Abnormalities: Needle spikes may occur in the context of visual afferent abnormalities, where the visual system is affected but not necessarily leading to seizures.

5. Age-Related Considerations

    • Changes Over Time: The characteristics of needle spikes can change with age. They are typically more prominent in early childhood and may decrease in frequency and amplitude during adolescence. This age-related change can be significant in understanding their clinical relevance in different neurological conditions.

Summary

In summary, needle spikes are primarily associated with congenital blindness but can also be observed in various neurological conditions, including epilepsy, cortical dysplasia, and developmental disorders. Their presence may indicate underlying cerebral pathology, and while they are often benign, careful interpretation in the context of the patient's clinical history is essential for accurate diagnosis and management.

 

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