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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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Focal seizure with broad neocortical onset

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Dr. Rishabh Pathak


 

Focal seizures with broad neocortical onset involve seizure activity that begins in a broad area of the neocortex, which is the outer layer of the brain responsible for higher-order functions such as sensory perception, cognition, and motor control.

1.      Ictal Patterns:

o    The EEG during focal seizures with broad neocortical onset typically shows rhythmic slowing that evolves over time. This may include higher amplitude activity and phase-reversing spikes, indicating a more widespread involvement of the cortical areas.

2.     Clinical Manifestations:

o    Patients may exhibit a variety of clinical symptoms depending on the specific areas of the neocortex involved. These can include motor manifestations (such as jerking movements), sensory symptoms, or alterations in consciousness. The clinical presentation can be diverse due to the extensive involvement of the neocortex.

3.     EEG Characteristics:

o    The ictal pattern often starts with right-sided, frontally predominant rhythmic slowing, which can evolve to include more organized rhythmic activity. The presence of phase-reversing spikes at specific electrodes (e.g., P4) is a notable feature that can help in identifying the seizure onset zone.

4.    Associated Conditions:

o    Focal seizures with broad neocortical onset can be associated with various structural abnormalities, including cortical dysplasia, tumors, or other lesions affecting the neocortex. These seizures may also occur in the context of more diffuse brain pathology.

5.     Diagnosis and Management:

o    Diagnosis typically involves a comprehensive evaluation that includes clinical history, EEG monitoring, and neuroimaging (such as MRI) to identify any underlying structural changes. Management may include antiepileptic medications, and in cases of refractory seizures, surgical options may be considered.

6.    Prognosis:

o    The prognosis for patients with focal seizures of broad neocortical onset can vary widely based on the underlying cause and the effectiveness of treatment. Some patients may respond well to medical therapy, while others may require surgical intervention for better seizure control.

In summary, focal seizures with broad neocortical onset are characterized by specific ictal patterns and a wide range of clinical manifestations due to their extensive cortical involvement. Understanding these seizures is crucial for accurate diagnosis and effective management, particularly in the context of neocortical epilepsy.

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