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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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Co-occurring Patterns of Periodic Epileptiform Discharges

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Dr. Rishabh Pathak

Periodic Epileptiform Discharges (PEDs) can occur alongside various other EEG patterns, reflecting different underlying neurological conditions and brain states. 

Co-occurring Patterns of Periodic Epileptiform Discharges (PEDs):

1.      Bilateral Periodic Epileptiform Discharges (BiPEDs):

§  BiPEDs are a specific type of PEDs that occur symmetrically and synchronously across both hemispheres. They are often maximal in the midfrontal region and can be associated with conditions such as subacute sclerosing panencephalitis (SSPE).

2.     Triphasic Waves:

§  While PEDs are characterized by their triphasic waveform, they can also co-occur with other triphasic patterns. However, the distinguishing feature is that PEDs are periodic, whereas triphasic waves may not have a consistent interval. Triphasic waves are often associated with metabolic disturbances and can appear in conditions like hepatic encephalopathy.

3.     Frontal Intermittent Rhythmic Delta Activity (FIRDA):

§  FIRDA is another EEG pattern that can co-occur with PEDs. FIRDA is characterized by rhythmic delta activity in the frontal regions and is often associated with diffuse cerebral dysfunction. The presence of both FIRDA and PEDs may indicate a more severe underlying condition.

4.    Background Activity Changes:

§  The background activity accompanying PEDs is typically disorganized and may show generalized theta or delta frequency range activity. In cases of anoxia, the background may be suppressed or demonstrate electrocerebral inactivity. This disorganized background can coexist with PEDs, reflecting the diffuse cerebral dysfunction .

5.     Myoclonic Activity:

§  In cases where PEDs are associated with SSPE, they are often accompanied by myoclonic jerks. The myoclonic activity may produce movement artifacts that can complicate the interpretation of the EEG but are clinically significant in the context of PEDs.

6.    Other Epileptiform Discharges:

§  PEDs can also coexist with other types of epileptiform discharges, such as Interictal Epileptiform Discharges (IEDs). The presence of both patterns may indicate a more complex seizure disorder or underlying brain pathology.

Summary:

Periodic Epileptiform Discharges (PEDs) can co-occur with various EEG patterns, including Bilateral Periodic Epileptiform Discharges (BiPEDs), triphasic waves, FIRDA, changes in background activity, myoclonic activity, and other epileptiform discharges. The presence of these co-occurring patterns can provide valuable insights into the underlying neurological conditions and help guide clinical management.

 

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